Seminars.Seminars History
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%maroon%'''Felix (Katholische Ingolstadt)'''%%: %green%''Approximation theoretic properties of deep ReLU neural networks''%%.
%abbox% %maroon%Abstract%%:
Studying the approximation theoretic properties of neural networks with smooth activation function is a classical topic.The networks that are used in practice, however, most often use the nonsmooth rectified linear unit (ReLU) activation function. Despite the recent incredible performance of such networks in many classification tasks, a solid theoretical explanation of this success story is still missing.\\
In this talk, we will present recent results concerning the approximation theoretic properties of deep ReLU neural networks which help to explain some of the characteristics of such networks; in particular we will see that deeper networks can approximate certain classification functions much more efficiently than shallow networks, which is not the case for most smooth activation functions.
We emphasize though that these approximation theoretic properties do not explain why simple algorithms like stochastic gradient descent work so well in practice, or why deep neural networks tend to generalize so well; we purely focus on the expressive power of such networks.\\
As a model class for classifier functions we consider the class of (possibly discontinuous) piecewise smooth functions for which the different "smooth regions" are separated by smooth hypersurfaces.
Given such a function, and a desired approximation accuracy, we construct a neural network which achieves the desired approximation accuracy, where the error is measured in L^p. We give precise bounds on the required size (in terms of the number of weights) and depth of the network, depending on the approximation accuracy, on the smoothness parameters of the given function, and on the dimension of its domain of definition. Finally, we show that this size of the networks is optimal, and that networks of smaller depth would need significantly more weights than the deep networks that we construct, in order to achieve the desired approximation accuracy.
\\
(''lunch seminar, 10.10.2018 at 12:05, DTU, Building 324/Room 141'')%%
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%maroon%'''Eugenio Hernandez'''%%: %green%''Systems generated by unitary representations of discrete groups''%%.
%abbox% %maroon%Abstract%%:Unitary representations of discrete groups acting on a Hilbert space {$\mathbb H$} (such as translations, modulations and dilations) play an important role in Multiresolution Analysis and approximation theory. For a group {$\Gamma$} and a unitary representation {$\Pi : \Gamma \to \cal U (\mathbb H)$} we study reproducing properties of the orbit of {$\psi \in \mathbb H$} under {$\Pi$}, that is {$O_{\Pi, \Gamma}(\psi)=\{\Pi(\gamma)\psi: \gamma \in \Gamma\}$}. Previous results known for the case of {$\Gamma$} been abelian are extended to the non abelian case. The results are obtained using left regular representations and the von Neumann algebra of the group {$\Gamma.$}
%abbox% %maroon%Abstract%%:
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[[#pasttalks]]
!! Past talks
%maroon%'''Qaiser Jahan'''%%: %green%''Characterization of lowpass filters on local fields of positive characteristic''%%.
%abbox% %maroon%Abstract%%: In this talk, we will start from basic definition of local fields after that we give necessary and sufficient conditions on a function to be a lowpass filter on a local field {$K$} of positive characteristic associated to the scaling function for multiresolution analysis of {$L^2(K)$}. We also give the sketch of the proof of main result.
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%maroon%'''Eugenio Hernandez'''%%: %green%''Systems generated by unitary representations of discrete groups''%%.
%abbox% %maroon%Abstract%%: Unitary representations of discrete groups acting on a Hilbert space {$\mathbb H$} (such as translations, modulations and dilations) play an important role in Multiresolution Analysis and approximation theory. For a group {$\Gamma$} and a unitary representation {$\Pi : \Gamma \to \cal U (\mathbb H)$} we study reproducing properties of the orbit of {$\psi \in \mathbb H$} under {$\Pi$}, that is {$O_{\Pi, \Gamma}(\psi)=\{\Pi(\gamma)\psi: \gamma \in \Gamma\}$}. Previous results known for the case of {$\Gamma$} been abelian are extended to the non abelian case. The results are obtained using left regular representations and the von Neumann algebra of the group {$\Gamma.$}
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(''HATA seminar, 1.11.2016 at 13:00, DTU, Building 324/Room 141'')%%
[[#pasttalks]]
!! Past talks
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!! Past talks
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(''HATA seminar, 27.10.2016 at 13:00, DTU, Building 324/Room 1xx'')%%
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%abbox% %maroon%Abstract%%: In this talk, we will start from basic definition of local fields after that we give necessary and sufficient conditions on a function to be a lowpass filter on a local field $K$ of positive characteristic associated to the scaling function for multiresolution analysis of $L^2(K)$. We also give the sketch of the proof of main result.
to:
%abbox% %maroon%Abstract%%: In this talk, we will start from basic definition of local fields after that we give necessary and sufficient conditions on a function to be a lowpass filter on a local field {$K$} of positive characteristic associated to the scaling function for multiresolution analysis of {$L^2(K)$}. We also give the sketch of the proof of main result.
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%abbox% %maroon%Abstract%%: Unitary representations of discrete groups acting on a Hilbert space {$\mathbb H$} (such as translations, modulations and dilations) play an important role in Multiresolution Analysis and approximation theory. For a group {$\Gamma$} and a unitary representation $\Pi : \Gamma \to \cal U (\mathbb H)$ we study reproducing properties of the orbit of $\psi \in \mathbb H$ under $\Pi$, that is $O_{\Pi, \Gamma}(\psi)=\{\Pi(\gamma)\psi: \gamma \in \Gamma\}$. Previous results known for the case of $\Gamma$ been abelian are extended to the non abelian case. The results are obtained using left regular representations and the von Neumann algebra of the group $\Gamma.$
to:
%abbox% %maroon%Abstract%%: Unitary representations of discrete groups acting on a Hilbert space {$\mathbb H$} (such as translations, modulations and dilations) play an important role in Multiresolution Analysis and approximation theory. For a group {$\Gamma$} and a unitary representation {$\Pi : \Gamma \to \cal U (\mathbb H)$} we study reproducing properties of the orbit of {$\psi \in \mathbb H$} under {$\Pi$}, that is {$O_{\Pi, \Gamma}(\psi)=\{\Pi(\gamma)\psi: \gamma \in \Gamma\}$}. Previous results known for the case of {$\Gamma$} been abelian are extended to the non abelian case. The results are obtained using left regular representations and the von Neumann algebra of the group {$\Gamma.$}
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%abbox% %maroon%Abstract%%: Unitary representations of discrete groups acting on a Hilbert space $\mathbb H$ (such as translations, modulations and dilations) play an important role in Multiresolution Analysis and approximation theory. For a group $\Gamma$ and a unitary representation $\Pi : \Gamma \to \cal U (\mathbb H)$ we study reproducing properties of the orbit of $\psi \in \mathbb H$ under $\Pi$, that is $O_{\Pi, \Gamma}(\psi)=\{\Pi(\gamma)\psi: \gamma \in \Gamma\}$. Previous results known for the case of $\Gamma$ been abelian are extended to the non abelian case. The results are obtained using left regular representations and the von Neumann algebra of the group $\Gamma.$
to:
%abbox% %maroon%Abstract%%: Unitary representations of discrete groups acting on a Hilbert space {$\mathbb H$} (such as translations, modulations and dilations) play an important role in Multiresolution Analysis and approximation theory. For a group {$\Gamma$} and a unitary representation $\Pi : \Gamma \to \cal U (\mathbb H)$ we study reproducing properties of the orbit of $\psi \in \mathbb H$ under $\Pi$, that is $O_{\Pi, \Gamma}(\psi)=\{\Pi(\gamma)\psi: \gamma \in \Gamma\}$. Previous results known for the case of $\Gamma$ been abelian are extended to the non abelian case. The results are obtained using left regular representations and the von Neumann algebra of the group $\Gamma.$
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%maroon%'''Qaiser Jahan'''%%: %green%''Characterization of lowpass filters on local fields of positive characteristic''%%.
%abbox% %maroon%Abstract%%: In this talk, we will start from basic definition of local fields after that we give necessary and sufficient conditions on a function to be a lowpass filter on a local field $K$ of positive characteristic associated to the scaling function for multiresolution analysis of $L^2(K)$. We also give the sketch of the proof of main result.
to:
%maroon%'''Eugenio Hernandez'''%%: %green%''Systems generated by unitary representations of discrete groups''%%.
%abbox% %maroon%Abstract%%: Unitary representations of discrete groups acting on a Hilbert space $\mathbb H$ (such as translations, modulations and dilations) play an important role in Multiresolution Analysis and approximation theory. For a group $\Gamma$ and a unitary representation $\Pi : \Gamma \to \cal U (\mathbb H)$ we study reproducing properties of the orbit of $\psi \in \mathbb H$ under $\Pi$, that is $O_{\Pi, \Gamma}(\psi)=\{\Pi(\gamma)\psi: \gamma \in \Gamma\}$. Previous results known for the case of $\Gamma$ been abelian are extended to the non abelian case. The results are obtained using left regular representations and the von Neumann algebra of the group $\Gamma.$
%abbox% %maroon%Abstract%%: Unitary representations of discrete groups acting on a Hilbert space $\mathbb H$ (such as translations, modulations and dilations) play an important role in Multiresolution Analysis and approximation theory. For a group $\Gamma$ and a unitary representation $\Pi : \Gamma \to \cal U (\mathbb H)$ we study reproducing properties of the orbit of $\psi \in \mathbb H$ under $\Pi$, that is $O_{\Pi, \Gamma}(\psi)=\{\Pi(\gamma)\psi: \gamma \in \Gamma\}$. Previous results known for the case of $\Gamma$ been abelian are extended to the non abelian case. The results are obtained using left regular representations and the von Neumann algebra of the group $\Gamma.$
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%maroon%'''Qaiser Jahan'''%%: %green%''Characterization of lowpass filters on local fields of positive characteristic''%%.
%abbox% %maroon%Abstract%%: In this talk, we will start from basic definition of local fields after that we give necessary and sufficient conditions on a function to be a lowpass filter on a local field $K$ of positive characteristic associated to the scaling function for multiresolution analysis of $L^2(K)$. We also give the sketch of the proof of main result.
\\
(''HATA seminar, 1.11.2016 at 13:00, DTU, Building 324/Room 1xx'')%%
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%abbox% %maroon%Abstract%%: This thesis consists of four papers. The first one introduces generalized translation invariant systems and considers their frame properties, the second and third paper give new results on the theory of Gabor frames, and the fourth is a review paper with proofs and new results on the Feichtinger algebra.
to:
%abbox% %maroon%Abstract%%: This thesis consists of four papers. The first one introduces generalized translation invariant systems and considers their frame properties, the second and third paper give new results on the theory of Gabor frames, and the fourth is a review paper with proofs and new results on the Feichtinger algebra.\\
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shearlettype and for (generalized) shiftinvariant systems and their continuous formulations.
This thesis advances the theory of both separable and nonseparable, discrete, semicontinuous and continuous Gabor systems. In particular, the well established structure theory for separable lattice Gabor frames is extended and generalized significantly to Gabor systems with timefrequency shifts along closed subgroups in the timefrequency plane. This includes density results, the Walnut representation, the WexlerRaz biorthogonality relations, the Bessel duality and the duality principle between Gabor frames and Gabor Riesz bases.
The theory of GTI systems and Gabor frames in this thesis is developed and presented in the setting of locally compact abelian groups, however, even in the euclidean setting the results given here improve the existing theory.
This thesis advances the theory of both separable and nonseparable, discrete, semicontinuous and continuous Gabor systems. In particular, the well established structure theory for separable lattice Gabor frames is extended and generalized significantly to Gabor systems with timefrequency shifts along closed subgroups in the timefrequency plane. This includes density results, the Walnut representation, the WexlerRaz biorthogonality relations, the Bessel duality and the duality principle between Gabor frames and Gabor Riesz bases.
The theory of GTI systems and Gabor frames in this thesis is developed and presented in the setting of locally compact abelian groups, however, even in the euclidean setting the results given here improve the existing theory.
to:
shearlettype and for (generalized) shiftinvariant systems and their continuous formulations.\\
This thesis advances the theory of both separable and nonseparable, discrete, semicontinuous and continuous Gabor systems. In particular, the well established structure theory for separable lattice Gabor frames is extended and generalized significantly to Gabor systems with timefrequency shifts along closed subgroups in the timefrequency plane. This includes density results, the Walnut representation, the WexlerRaz biorthogonality relations, the Bessel duality and the duality principle between Gabor frames and Gabor Riesz bases.\\
The theory of GTI systems and Gabor frames in this thesis is developed and presented in the setting of locally compact abelian groups, however, even in the euclidean setting the results given here improve the existing theory.\\
This thesis advances the theory of both separable and nonseparable, discrete, semicontinuous and continuous Gabor systems. In particular, the well established structure theory for separable lattice Gabor frames is extended and generalized significantly to Gabor systems with timefrequency shifts along closed subgroups in the timefrequency plane. This includes density results, the Walnut representation, the WexlerRaz biorthogonality relations, the Bessel duality and the duality principle between Gabor frames and Gabor Riesz bases.\\
The theory of GTI systems and Gabor frames in this thesis is developed and presented in the setting of locally compact abelian groups, however, even in the euclidean setting the results given here improve the existing theory.\\
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%abbox% %maroon%Abstract%%: This thesis consists of four papers. The first one introduces generalized translation invariant systems and considers their frame properties, the second and third paper give new results on the theory of Gabor frames, and the fourth is a review paper with proofs and new results on the Feichtinger algebra.
The generalized translation invariant (GTI) systems provide, for the first time, a framework which can describe frame properties of both discrete and continuous systems. The results yield the wellknown characterizations of dual frame pairs and Parseval frames of Gabor, wavelet, curvelet and
shearlettype and for (generalized) shiftinvariant systems and their continuous formulations.
This thesis advances the theory of both separable and nonseparable, discrete, semicontinuous and continuous Gabor systems. In particular, the well established structure theory for separable lattice Gabor frames is extended and generalized significantly to Gabor systems with timefrequency shifts along closed subgroups in the timefrequency plane. This includes density results, the Walnut representation, the WexlerRaz biorthogonality relations, the Bessel duality and the duality principle between Gabor frames and Gabor Riesz bases.
The theory of GTI systems and Gabor frames in this thesis is developed and presented in the setting of locally compact abelian groups, however, even in the euclidean setting the results given here improve the existing theory.
Finally, the thesis contains a review paper with proofs of all the major results on the Banach space of functions known as the Feichtinger algebra. This includes many of its different characterizations and treatment of its many equivalent norms, its minimality among all timefrequency shift invariant Banach spaces and aspects of its dual space, operators on the space and the kernel theorem for the Feichtinger algebra. The work also includes new findings such as a characterization among all Banach spaces, a forgotten theorem by Reiter on Banach space isomorphisms of the Feichtinger algebra, and new useful inequalities.
The generalized translation invariant (GTI) systems provide, for the first time, a framework which can describe frame properties of both discrete and continuous systems. The results yield the wellknown characterizations of dual frame pairs and Parseval frames of Gabor, wavelet, curvelet and
shearlettype and for (generalized) shiftinvariant systems and their continuous formulations.
This thesis advances the theory of both separable and nonseparable, discrete, semicontinuous and continuous Gabor systems. In particular, the well established structure theory for separable lattice Gabor frames is extended and generalized significantly to Gabor systems with timefrequency shifts along closed subgroups in the timefrequency plane. This includes density results, the Walnut representation, the WexlerRaz biorthogonality relations, the Bessel duality and the duality principle between Gabor frames and Gabor Riesz bases.
The theory of GTI systems and Gabor frames in this thesis is developed and presented in the setting of locally compact abelian groups, however, even in the euclidean setting the results given here improve the existing theory.
Finally, the thesis contains a review paper with proofs of all the major results on the Banach space of functions known as the Feichtinger algebra. This includes many of its different characterizations and treatment of its many equivalent norms, its minimality among all timefrequency shift invariant Banach spaces and aspects of its dual space, operators on the space and the kernel theorem for the Feichtinger algebra. The work also includes new findings such as a characterization among all Banach spaces, a forgotten theorem by Reiter on Banach space isomorphisms of the Feichtinger algebra, and new useful inequalities.
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%maroon%'''Mads S. Jakobsen'''%%: %green%''Gabor frames on locally compact abelian groups and related topics''%%.
\\
(''PhD defense, 28.10.2016 at 14:00, DTU, Building 303A/Aud 41'')%%
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[[#pasttalks]]
!! Past talks
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[[#pasttalks]]
!! Past talks
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%maroon%'''Qaiser Jahan'''%%: %green%''Characterization of lowpass filters on local fields of positive characteristic''%%.
%abbox% %maroon%Abstract%%: In this talk, we will start from basic definition of local fields after that we give necessary and sufficient conditions on a function to be a lowpass filter on a local field $K$ of positive characteristic associated to the scaling function for multiresolution analysis of $L^2(K)$. We also give the sketch of the proof of main result.
\\
(''HATA seminar, 1.11.2016 at 13:00, DTU, Building 324/Room 1xx'')%%
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(''HATA seminar, 13.10.2016 at 13:15, DTU, Building 324B/Room 141'')%%
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%abbox% %maron%Abstract%%: Analysis approaches for compressed sensing problems with sparse (coherent) frame representations will be discussed. A notion of the sparsityinducing dual frame of a nonexact frame and its properties is introduced. The sparse dual frame is a new notion of optimal dual frames。It is motivated in the study of compressed sensing problems where signals are sparse with respect to redundant dictionaries (frames). A sparsedualframe based 1_1analysis approach for compressed sensing (CS) will also be presented. An alternating iterative algorithm is proposed. An error bound ensuring the correct signal recovery is obtained. Empirical studies over generally difficult CS problems demonstrate that the new sparsedualbased approach provides satisfactory solutions, whereas other existing means do not.
to:
%abbox% %maroon%Abstract%%: Analysis approaches for compressed sensing problems with sparse (coherent) frame representations will be discussed. A notion of the sparsityinducing dual frame of a nonexact frame and its properties is introduced. The sparse dual frame is a new notion of optimal dual frames。It is motivated in the study of compressed sensing problems where signals are sparse with respect to redundant dictionaries (frames). A sparsedualframe based 1_1analysis approach for compressed sensing (CS) will also be presented. An alternating iterative algorithm is proposed. An error bound ensuring the correct signal recovery is obtained. Empirical studies over generally difficult CS problems demonstrate that the new sparsedualbased approach provides satisfactory solutions, whereas other existing means do not.
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%abbox% %maron%Abstract%%:
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%abbox% %maroon%Abstract%%:
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%abbox% %maron%Abstract%%: We investigate sparseness of various Gabor expansions both stationary and nonstationary applied to piano music. Also, we show that socalled decomposition spaces can be used as smoothness spaces for certain nonstationary Gabor frames. Both practical examples and theoretical results will be discussed.
to:
%abbox% %maroon%Abstract%%: We investigate sparseness of various Gabor expansions both stationary and nonstationary applied to piano music. Also, we show that socalled decomposition spaces can be used as smoothness spaces for certain nonstationary Gabor frames. Both practical examples and theoretical results will be discussed.
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%abbox% %maron%Abstract%%: The duality theory for frames is well developed by now. However, often it is not possible to
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%abbox% %maroon%Abstract%%: The duality theory for frames is well developed by now. However, often it is not possible to
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%abbox% %maron%Abstract%%: Abdollahpour and Faroughi introduced and invistigated
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%abbox% %maroon%Abstract%%: Abdollahpour and Faroughi introduced and invistigated
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%maroon%'''Hans G. Feichtinger'''%%: %green%''An Alternative Approach to Convolution and the Fourier Transform''%%.
%abbox% %maroon%Abstract%%: When one looks at the Fourier transform in the mathematical literature the description starts usually with Fourier Series for periodic functions or right away with the Fourier transform as an integral transform. In either case the transform requires to use integrals, and of course the Lebesgue integral appears to provide the natural domain, namely the space L^1 of integrable functions. Similar arguments apply to the convolution integral. Combining the two concepts one can then derive the allimportant convolution theorem, Fourier inversion and Plancherel's theorem,
showing that the ``complicated convolution'' is turned into easy pointwise multiplication. But why should we be interested in convolution? Is it a natural product for integrable functions? And which functions do ``have a Fourier transform''?
Aside from heuristic manipulations, leading to the forward and inverse Fourier transform the above results are certainly important to (electrical) engineers, when they deal with translation invariant systems, which are usually described by black boxes. They correspond to convolution operators with the socalled impulse response, which is the output of the system to a ``Dirac deltafunction'', and can be described alternatively by their transfer function.
We will describe a mathematically correct approach to convolution and Fourier transform which is based on simple functional analytic principles and encompasses the two aspects of basic Fourier analysis in a way (hopefully well) understandable for both sides (mathematicians and engineers). Furthermore, many aspects of this approach can by supported by a set of simple MATLAB experiments, which connects the material with basic concepts from linear algebra and polynomials with complex coefficients.
\\
(''HATA seminar, 13.10.2016 at 13:15, DTU, Building 324B/Room 141'')%%
%abbox% %maroon%Abstract%%: When one looks at the Fourier transform in the mathematical literature the description starts usually with Fourier Series for periodic functions or right away with the Fourier transform as an integral transform. In either case the transform requires to use integrals, and of course the Lebesgue integral appears to provide the natural domain, namely the space L^1 of integrable functions. Similar arguments apply to the convolution integral. Combining the two concepts one can then derive the allimportant convolution theorem, Fourier inversion and Plancherel's theorem,
showing that the ``complicated convolution'' is turned into easy pointwise multiplication. But why should we be interested in convolution? Is it a natural product for integrable functions? And which functions do ``have a Fourier transform''?
Aside from heuristic manipulations, leading to the forward and inverse Fourier transform the above results are certainly important to (electrical) engineers, when they deal with translation invariant systems, which are usually described by black boxes. They correspond to convolution operators with the socalled impulse response, which is the output of the system to a ``Dirac deltafunction'', and can be described alternatively by their transfer function.
We will describe a mathematically correct approach to convolution and Fourier transform which is based on simple functional analytic principles and encompasses the two aspects of basic Fourier analysis in a way (hopefully well) understandable for both sides (mathematicians and engineers). Furthermore, many aspects of this approach can by supported by a set of simple MATLAB experiments, which connects the material with basic concepts from linear algebra and polynomials with complex coefficients.
\\
(''HATA seminar, 13.10.2016 at 13:15, DTU, Building 324B/Room 141'')%%
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[[#pasttalks]]
!! Past talks
%maroon%'''Shidong Li'''%%: %green%''On Analysis Approaches to Compressed Sensing with Coherent Frames''%%.
%abbox% %maron%Abstract%%: Analysis approaches for compressed sensing problems with sparse (coherent) frame representations will be discussed. A notion of the sparsityinducing dual frame of a nonexact frame and its properties is introduced. The sparse dual frame is a new notion of optimal dual frames。It is motivated in the study of compressed sensing problems where signals are sparse with respect to redundant dictionaries (frames). A sparsedualframe based 1_1analysis approach for compressed sensing (CS) will also be presented. An alternating iterative algorithm is proposed. An error bound ensuring the correct signal recovery is obtained. Empirical studies over generally difficult CS problems demonstrate that the new sparsedualbased approach provides satisfactory solutions, whereas other existing means do not.
\\
(''HATA seminar, 27.9.2016 at 14:00, DTU, Building 303B/Room 136'')%%
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%maroon%'''Shidong Li'''%%: %green%''On Analysis Approaches to Compressed Sensing with Coherent Frames''%%.
%abbox% %maron%Abstract%%: Analysis approaches for compressed sensing problems with sparse (coherent) frame representations will be discussed. A notion of the sparsityinducing dual frame of a nonexact frame and its properties is introduced. The sparse dual frame is a new notion of optimal dual frames。It is motivated in the study of compressed sensing problems where signals are sparse with respect to redundant dictionaries (frames). A sparsedualframe based 1_1analysis approach for compressed sensing (CS) will also be presented. An alternating iterative algorithm is proposed. An error bound ensuring the correct signal recovery is obtained. Empirical studies over generally difficult CS problems demonstrate that the new sparsedualbased approach provides satisfactory solutions, whereas other existing means do not.
\\
(''HATA seminar, 27.9.2016 at 14:00, DTU, Building 303B/Room 136'')%%
[[#pasttalks]]
!! Past talks
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%abbox% %maron%Abstract%%:
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%maroon%'''Emily King'''%%: %green%''Difference Sets and Grassmannian Packings''%%.
%abbox% %maron%Abstract%%:
It is often of interest to find subspaces which are optimally spread apart. For example, if one wants a set of vectors (representing one dimensional subspaces) which have similar properties to orthonormal bases, the vectors should as nonparallel as possible. There are a number of constructions possible using tools from combinatorial design theory: difference sets and their generalizations. In this talk, the connection between algebraic combinatorics and geometric packings will be presented, including brand new constructions of packings.
%abbox% %maron%Abstract%%:
It is often of interest to find subspaces which are optimally spread apart. For example, if one wants a set of vectors (representing one dimensional subspaces) which have similar properties to orthonormal bases, the vectors should as nonparallel as possible. There are a number of constructions possible using tools from combinatorial design theory: difference sets and their generalizations. In this talk, the connection between algebraic combinatorics and geometric packings will be presented, including brand new constructions of packings.
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%maroon%'''Shidong Li'''%%: %green%''On Analysis Approaches to Compressed Sensing with Coherent Frames''%%.
%abbox% %maron%Abstract%%: Analysis approaches for compressed sensing problems with sparse (coherent) frame representations will be discussed. A notion of the sparsityinducing dual frame of a nonexact frame and its properties is introduced. The sparse dual frame is a new notion of optimal dual frames。It is motivated in the study of compressed sensing problems where signals are sparse with respect to redundant dictionaries (frames). A sparsedualframe based 1_1analysis approach for compressed sensing (CS) will also be presented. An alternating iterative algorithm is proposed. An error bound ensuring the correct signal recovery is obtained. Empirical studies over generally difficult CS problems demonstrate that the new sparsedualbased approach provides satisfactory solutions, whereas other existing means do not.
\\
(''HATA seminar, 27.9.2016 at 14:00, DTU, Building 303B/Room 136'')%%
%maroon%'''Shidong Li'''%%: %green%''On Analysis Approaches to Compressed Sensing with Coherent Frames''%%.
%abbox% %maron%Abstract%%: Analysis approaches for compressed sensing problems with sparse (coherent) frame representations will be discussed. A notion of the sparsityinducing dual frame of a nonexact frame and its properties is introduced. The sparse dual frame is a new notion of optimal dual frames。It is motivated in the study of compressed sensing problems where signals are sparse with respect to redundant dictionaries (frames). A sparsedualframe based 1_1analysis approach for compressed sensing (CS) will also be presented. An alternating iterative algorithm is proposed. An error bound ensuring the correct signal recovery is obtained. Empirical studies over generally difficult CS problems demonstrate that the new sparsedualbased approach provides satisfactory solutions, whereas other existing means do not.
\\
(''HATA seminar, 27.9.2016 at 14:00, DTU, Building 303B/Room 136'')%%
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%maroon%'''Emil Ottosen'''%%: %green%''Sparse Gabor expansions of music signals''%%.
%abbox% %maron%Abstract%%:We investigate sparseness of various Gabor expansions both stationary and nonstationary applied to piano music. Also, we show that socalled decomposition spaces can be used as smoothness spaces for certain nonstationary Gabor frames. Both practical examples and theoretical results will be discussed.
%abbox% %maron%Abstract%%:
to:
%maroon%'''Shidong Li'''%%: %green%''On Analysis Approaches to Compressed Sensing with Coherent Frames''%%.
%abbox% %maron%Abstract%%: Analysis approaches for compressed sensing problems with sparse (coherent) frame representations will be discussed. A notion of the sparsityinducing dual frame of a nonexact frame and its properties is introduced. The sparse dual frame is a new notion of optimal dual frames。It is motivated in the study of compressed sensing problems where signals are sparse with respect to redundant dictionaries (frames). A sparsedualframe based 1_1analysis approach for compressed sensing (CS) will also be presented. An alternating iterative algorithm is proposed. An error bound ensuring the correct signal recovery is obtained. Empirical studies over generally difficult CS problems demonstrate that the new sparsedualbased approach provides satisfactory solutions, whereas other existing means do not.
%abbox% %maron%Abstract%%: Analysis approaches for compressed sensing problems with sparse (coherent) frame representations will be discussed. A notion of the sparsityinducing dual frame of a nonexact frame and its properties is introduced. The sparse dual frame is a new notion of optimal dual frames。It is motivated in the study of compressed sensing problems where signals are sparse with respect to redundant dictionaries (frames). A sparsedualframe based 1_1analysis approach for compressed sensing (CS) will also be presented. An alternating iterative algorithm is proposed. An error bound ensuring the correct signal recovery is obtained. Empirical studies over generally difficult CS problems demonstrate that the new sparsedualbased approach provides satisfactory solutions, whereas other existing means do not.
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%maroon%'''Emil Ottosen'''%%: %green%''Sparse Gabor expansions of music signals''%%.
%abbox% %maron%Abstract%%: We investigate sparseness of various Gabor expansions both stationary and nonstationary applied to piano music. Also, we show that socalled decomposition spaces can be used as smoothness spaces for certain nonstationary Gabor frames. Both practical examples and theoretical results will be discussed.
\\
(''HATA seminar, 18.8.2016 at 13:00, DTU, Building 303B/Room 134'')%%
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(''HATA seminar, 18.8.2016 at ??:??, DTU, Building 303B/Room ??'')%%
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to:
%maroon%'''Emil Ottosen'''%%: %green%''Sparse Gabor expansions of music signals''%%.
%abbox% %maron%Abstract%%: We investigate sparseness of various Gabor expansions both stationary and nonstationary applied to piano music. Also, we show that socalled decomposition spaces can be used as smoothness spaces for certain nonstationary Gabor frames. Both practical examples and theoretical results will be discussed.
\\
(''HATA seminar, 18 or 19.8.2016 at ??:??, DTU, Building 303B/Room ??'')%%
%abbox% %maron%Abstract%%: We investigate sparseness of various Gabor expansions both stationary and nonstationary applied to piano music. Also, we show that socalled decomposition spaces can be used as smoothness spaces for certain nonstationary Gabor frames. Both practical examples and theoretical results will be discussed.
\\
(''HATA seminar, 18 or 19.8.2016 at ??:??, DTU, Building 303B/Room ??'')%%
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[[#pasttalks]]
!! Past talks
[[#pasttalks]]
!! Past talks
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[[#pasttalks]]
!! Past talks
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(''HATA seminar, 10.5.2016 at 14:00, DTU, Building 303B/Room 134'')%%
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(''HATA seminar, 10.5.2016 at 14:00, DTU, Building 306/Aud. 36'')%%
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%maroon%'''Ole Christensen'''%%: %green%''TBA''%%.
%abbox% %maron%Abstract%%:
%abbox% %maron%Abstract%%:
to:
%maroon%'''Ole Christensen'''%%: %green%''On approximately dual frames''%%.
%abbox% %maron%Abstract%%: The duality theory for frames is well developed by now. However, often it is not possible to
apply dual frames directly, due to practical constraints. The talk will discuss the more flexible concept
of approximately dual frames and its relation to perturbation theory.
%abbox% %maron%Abstract%%: The duality theory for frames is well developed by now. However, often it is not possible to
apply dual frames directly, due to practical constraints. The talk will discuss the more flexible concept
of approximately dual frames and its relation to perturbation theory.
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%abbox% %maron%Abstract%%: 
\\
(''HATA seminar, 10.5.2016 at 14:00, DTU, Building 303B/Room 134'')%%
\\
(''HATA seminar, 10.5.2016 at 14:00, DTU, Building 303B/Room 134'')%%
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%maroon%'''Ole Christensen'''%%: %green%''TBA''%%.
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[[#pasttalks]]
!! Past talks
[[#pasttalks]]
!! Past talks
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!! Past talks
to:
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(''HATA seminar, 19.4.2016 at 14:00, DTU, Building 303B/134'')%%
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(''HATA seminar, 19.4.2016 at 14:00, DTU, Building 303B/Room 134'')%%
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(''HATA seminar, 19.4.2016 at 14:00, DTU, Building 303B/TBA'')%%
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(''HATA seminar, 19.4.2016 at 14:00, DTU, Building 303B/134'')%%
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%maroon%'''Yavar Khedmati Yengejeh'''%%: %green%''Continuous Generalized Frames in Hilbert Spaces''%%.
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continuous gframe and Riesztype continuous gframe. We
provide some necessary and sufficient conditions under which, a
provide some necessary and sufficient conditions under which
to:
continuous gframes and Riesztype continuous gframes. We
provide some necessary and sufficient conditions under which a
provide some necessary and sufficient conditions under which a
Changed line 12 from:
continuous gframe). Also, we introduced concepts of disjoint,
to:
continuous gframe). Also, we introduce concepts of disjoint,
Added lines 717:
%abbox% %maron%Abstract%%: Abdollahpour and Faroughi introduced and invistigated
continuous gframe and Riesztype continuous gframe. We
provide some necessary and sufficient conditions under which, a
family of bounded operators is a continuous gframe (Riesztype
continuous gframe). Also, we introduced concepts of disjoint,
strongly disjoint, weakly disjoint continuous gframes in Hilbert
spaces and we get equivalent conditions to these notions.
\\
(''HATA seminar, 19.4.2016 at 14:00, DTU, Building 303B/TBA'')%%
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[[#pasttalks]]
!! Past talks
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!! Past talks
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%maroon%'''James Murphy'''%% (Duke University): %green%''TBA''%%.
%abbox% %maroon%Abstract%%:TBA
%abbox% %maroon%Abstract%%:
to:
%maroon%'''James Murphy'''%% (Duke University): %green%''Single image superresolution through directional representations''%%.
%abbox% %maroon%Abstract%%: The problem of image superresolution has been significant in the image processing community for many years, and has seen a recent mathematical resurgence. We discuss a superresolution algorithm based on sparse mixing estimators (SME) with shearlet frames. This work introduces the anisotropic frame regime to the stateoftheart SME algorithm of Mallat and Yu. Synthetic and remotely sensed images will be analyzed, showing the gains from incorporating anisotropy. Joint work with W. Czaja and D. Weinberg.
%abbox% %maroon%Abstract%%: The problem of image superresolution has been significant in the image processing community for many years, and has seen a recent mathematical resurgence. We discuss a superresolution algorithm based on sparse mixing estimators (SME) with shearlet frames. This work introduces the anisotropic frame regime to the stateoftheart SME algorithm of Mallat and Yu. Synthetic and remotely sensed images will be analyzed, showing the gains from incorporating anisotropy. Joint work with W. Czaja and D. Weinberg.
Changed lines 710 from:
to:
%maroon%'''James Murphy'''%% (Duke University): %green%''TBA''%%.
%abbox% %maroon%Abstract%%: TBA
\\
(''HATA seminar, 9.2.2016 at 14:00, DTU, Building 303B/Room 130'')%%
%abbox% %maroon%Abstract%%: TBA
\\
(''HATA seminar, 9.2.2016 at 14:00, DTU, Building 303B/Room 130'')%%
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[[#pasttalks]]
!! Past talks
[[#pasttalks]]
!! Past talks
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[[#pasttalks]]
!! Past talks
Deleted lines 720:
%abbox% %maroon%Abstract%%: We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams a a limiting process to the straightline interval [A,A]yield new insights into the {$L^{p}(\mathbb{R})$} theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
\\
(''HATA seminar, 4.11.2015 at 13:00, DTU, Building 303B/Room 134'')%%
%maroon%'''Peter Massopust'''%% (TU Munich): %green%''Fractional Cone and Hex Splines''%%.
%abbox% %maroon%Abstract%%: We introduce an extension of cone splines and box splines to fractional and complex orders. These new families of multivariate splines are defined in the Fourier domain along certain sdimensional meshes and include as special cases the threedirectional box splines and hex splines previously considered by Condat, Van De Ville et al. These cone and hex splines of fractional and complex order generalize the univariate fractional and complex Bsplines in a natural way. Explicit time domain representations are derived for these splines on 3directional meshes. We present some properties of these two multivariate spline families such as recurrence, decay and refinement. Finally it is shown that a bivariate hex spline and its integer lattice translates form a Riesz basis of its linear span. This is joint work with Pat Van Fleet, University of St. Thomas, St. Paul, MN, USA.
\\
(''HATA seminar, 4.11.2015 at 14:00, DTU, Building 303B/Room 134'')%%
Added line 30:
Added lines 3445:
%maroon%'''Brigitte ForsterHeinlein'''%% (University Passau): %green%''The commutative diagram of signal processing''%%.
%abbox% %maroon%Abstract%%: We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams a a limiting process to the straightline interval [A,A]yield new insights into the {$L^{p}(\mathbb{R})$} theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
\\
(''HATA seminar, 4.11.2015 at 14:00, DTU, Building 303B/Room 134'')%%
%maroon%'''Peter Massopust'''%% (TU Munich): %green%''Fractional Cone and Hex Splines''%%.
%abbox% %maroon%Abstract%%: We introduce an extension of cone splines and box splines to fractional and complex orders. These new families of multivariate splines are defined in the Fourier domain along certain sdimensional meshes and include as special cases the threedirectional box splines and hex splines previously considered by Condat, Van De Ville et al. These cone and hex splines of fractional and complex order generalize the univariate fractional and complex Bsplines in a natural way. Explicit time domain representations are derived for these splines on 3directional meshes. We present some properties of these two multivariate spline families such as recurrence, decay and refinement. Finally it is shown that a bivariate hex spline and its integer lattice translates form a Riesz basis of its linear span. This is joint work with Pat Van Fleet, University of St. Thomas, St. Paul, MN, USA.
\\
(''HATA seminar, 4.11.2015 at 13:00, DTU, Building 303B/Room 134'')%%
%abbox% %maroon%Abstract%%: We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams a a limiting process to the straightline interval [A,A]yield new insights into the {$L^{p}(\mathbb{R})$} theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
\\
(''HATA seminar, 4.11.2015 at 14:00, DTU, Building 303B/Room 134'')%%
%maroon%'''Peter Massopust'''%% (TU Munich): %green%''Fractional Cone and Hex Splines''%%.
%abbox% %maroon%Abstract%%: We introduce an extension of cone splines and box splines to fractional and complex orders. These new families of multivariate splines are defined in the Fourier domain along certain sdimensional meshes and include as special cases the threedirectional box splines and hex splines previously considered by Condat, Van De Ville et al. These cone and hex splines of fractional and complex order generalize the univariate fractional and complex Bsplines in a natural way. Explicit time domain representations are derived for these splines on 3directional meshes. We present some properties of these two multivariate spline families such as recurrence, decay and refinement. Finally it is shown that a bivariate hex spline and its integer lattice translates form a Riesz basis of its linear span. This is joint work with Pat Van Fleet, University of St. Thomas, St. Paul, MN, USA.
\\
(''HATA seminar, 4.11.2015 at 13:00, DTU, Building 303B/Room 134'')%%
Changed line 15 from:
%maroon%'''Peter Massopust'''%% (TU Munich): %green%''The commutative diagram of signal processing''%%.
to:
%maroon%'''Peter Massopust'''%% (TU Munich): %green%''Fractional Cone and Hex Splines''%%.
Changed line 15 from:
%maroon%'''Peter Massopust'''%% (University Passau): %green%''The commutative diagram of signal processing''%%.
to:
%maroon%'''Peter Massopust'''%% (TU Munich): %green%''The commutative diagram of signal processing''%%.
Changed lines 1214 from:
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(''HATA seminar, 4.11.2015 at 13:00, DTU, Building 303B/Room 134'')%%
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(''HATA seminar, 18.11.2015 at 13:00, DTU, Building 303B/Room 134'')%%
Changed line 17 from:
%abbox% %maroon%Abstract%%: We introduce an extension of cone splines and box splines to fractional and complex orders. These new families of multivariate splines are defined in the Fourier domain along certain sdimensional meshes and include as special cases the threedirectional box splines and hex splines previously considered by Condat, Van De Ville et al. These cone and hex splines of fractional and complex order generalize the univariate fractional and complex Bsplines in a natural way. Explicit time domain representations are derived for these splines on 3directional meshes. We present some properties of these two multivariate spline families such as recurrence, decay and refinement. Finally it is shown that a bivariate hex spline and its integer lattice translates form a Riesz basis of its linear span.
to:
%abbox% %maroon%Abstract%%: We introduce an extension of cone splines and box splines to fractional and complex orders. These new families of multivariate splines are defined in the Fourier domain along certain sdimensional meshes and include as special cases the threedirectional box splines and hex splines previously considered by Condat, Van De Ville et al. These cone and hex splines of fractional and complex order generalize the univariate fractional and complex Bsplines in a natural way. Explicit time domain representations are derived for these splines on 3directional meshes. We present some properties of these two multivariate spline families such as recurrence, decay and refinement. Finally it is shown that a bivariate hex spline and its integer lattice translates form a Riesz basis of its linear span. This is joint work with Pat Van Fleet, University of St. Thomas, St. Paul, MN, USA.
Changed line 17 from:
%abbox% %maroon%Abstract%%: We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams a a limiting process to the straightline interval [A,A]yield new insights into the {$L^{p}(\mathbb{R})$} theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
to:
%abbox% %maroon%Abstract%%: We introduce an extension of cone splines and box splines to fractional and complex orders. These new families of multivariate splines are defined in the Fourier domain along certain sdimensional meshes and include as special cases the threedirectional box splines and hex splines previously considered by Condat, Van De Ville et al. These cone and hex splines of fractional and complex order generalize the univariate fractional and complex Bsplines in a natural way. Explicit time domain representations are derived for these splines on 3directional meshes. We present some properties of these two multivariate spline families such as recurrence, decay and refinement. Finally it is shown that a bivariate hex spline and its integer lattice translates form a Riesz basis of its linear span.
Added lines 1521:
%maroon%'''Peter Massopust'''%% (University Passau): %green%''The commutative diagram of signal processing''%%.
%abbox% %maroon%Abstract%%: We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams a a limiting process to the straightline interval [A,A]yield new insights into the {$L^{p}(\mathbb{R})$} theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
\\
(''HATA seminar, 4.11.2015 at 14:00, DTU, Building 303B/Matematicum'')%%
%abbox% %maroon%Abstract%%: We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams a a limiting process to the straightline interval [A,A]yield new insights into the {$L^{p}(\mathbb{R})$} theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
\\
(''HATA seminar, 4.11.2015 at 14:00, DTU, Building 303B/Matematicum'')%%
Deleted line 100:
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%abbox% %maroon%Abstract%%: We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams a a limiting process to the straightline interval {$[A,A]$}yield new insights into the {$L^{p}(\mathbb{R})$} theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
to:
%abbox% %maroon%Abstract%%: We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams a a limiting process to the straightline interval [A,A]yield new insights into the {$L^{p}(\mathbb{R})$} theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
Changed line 10 from:
%abbox% %maroon%Abstract%%: We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams a a limiting process to the straightline interval $[A,A]$yield new insights into the {$L^{p}(\mathbb{R})$} theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
to:
%abbox% %maroon%Abstract%%: We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams a a limiting process to the straightline interval {$[A,A]$}yield new insights into the {$L^{p}(\mathbb{R})$} theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
Changed line 10 from:
%abbox% %maroon%Abstract%%: We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams a a limiting process to the straightline interval $[A,A]$yield new insights into the $L^{p}(\mathbb{R})$ theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
to:
%abbox% %maroon%Abstract%%: We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams a a limiting process to the straightline interval $[A,A]$yield new insights into the {$L^{p}(\mathbb{R})$} theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
Added lines 713:
%maroon%'''Brigitte ForsterHeinlein'''%% (University Passau): %green%''The commutative diagram of signal processing''%%.
%abbox% %maroon%Abstract%%: We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams a a limiting process to the straightline interval $[A,A]$yield new insights into the $L^{p}(\mathbb{R})$ theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
\\
(''HATA seminar, 4.11.2015 at 13:00, DTU, Building 303B/Matematicum'')%%
Changed lines 3545 from:
%abbox% (''HATA seminar, 11.12.2014, DTU, Building 303B/Matematicum'')%%
%maroon%'''Hartmut '''%% (RWTH Aachen): %green%''Wavelet analysis in higher dimensions and the resolution of wavefront sets''%%.
%abbox% (''HATA seminar, 25.11.2014, DTU, Building 303B/134'')%%
to:
Deleted lines 3740:
%maroon%'''Marzieh Hasannasab'''%% (Kharazmi University): %green%''Hilbert module frames I''%%.
Added lines 6781:
%maroon%'''Ole Christensen'''%% (DTU): %green%''There are the good guys and the bad guys  Localization of frames''%%.
%abbox% (''HATA seminar, 11.12.2014, DTU, Building 303B/Matematicum'')%%
%maroon%'''Hartmut '''%% (RWTH Aachen): %green%''Wavelet analysis in higher dimensions and the resolution of wavefront sets''%%.
%abbox% (''HATA seminar, 25.11.2014, DTU, Building 303B/134'')%%
%maroon%'''Marzieh Hasannasab'''%% (Kharazmi University): %green%''Hilbert module frames I''%%.
%abbox% (''HATA seminar, 29.10.2014, DTU, Building 303B/Matematicum'')%%
Changed lines 3740 from:
%abbox% (''HATA seminar, 11.12.2015, DTU, Building 303B/Matematicum'')%%
to:
%abbox% (''HATA seminar, 11.12.2014, DTU, Building 303B/Matematicum'')%%
Changed lines 4345 from:
%abbox% (''HATA seminar, 25.11.2015, DTU, Building 303B/134'')%%
to:
%abbox% (''HATA seminar, 25.11.2014, DTU, Building 303B/134'')%%
Changed line 48 from:
%abbox% (''HATA seminar, 29.10.2015, DTU, Building 303B/Matematicum'')%%
to:
%abbox% (''HATA seminar, 29.10.2014, DTU, Building 303B/Matematicum'')%%
Changed line 61 from:
%abbox% (''HATA seminar, 0204.02.2015 at 9:00, DTU, Building 303B/Matematicum'')%%
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%abbox% (''HATA seminar, 0204.02.2015, DTU, Building 303B/Matematicum'')%%
Changed lines 3536 from:
%maroon%'''Kamilla Haahr Nielsen'''%% (DTU): %green%''The frame set of Gabor systems with Bspline generators''%%.
to:
%maroon%'''Ole Christensen'''%% (DTU): %green%''There are the good guys and the bad guys  Localization of frames''%%.
%abbox% (''HATA seminar, 11.12.2015, DTU, Building 303B/Matematicum'')%%
%maroon%'''Hartmut '''%% (RWTH Aachen): %green%''Wavelet analysis in higher dimensions and the resolution of wavefront sets''%%.
%abbox% (''HATA seminar, 25.11.2015, DTU, Building 303B/134'')%%
%maroon%'''Marzieh Hasannasab'''%% (Kharazmi University): %green%''Hilbert module frames II''%%.
%abbox% (''HATA seminar, 29.10.2015, DTU, Building 303B/Matematicum'')%%
%maroon%'''Marzieh Hasannasab'''%% (Kharazmi University): %green%''Hilbert module frames I''%%.
%abbox% (''HATA seminar, 11.12.2015, DTU, Building 303B/Matematicum'')%%
%maroon%'''Hartmut '''%% (RWTH Aachen): %green%''Wavelet analysis in higher dimensions and the resolution of wavefront sets''%%.
%abbox% (''HATA seminar, 25.11.2015, DTU, Building 303B/134'')%%
%maroon%'''Marzieh Hasannasab'''%% (Kharazmi University): %green%''Hilbert module frames II''%%.
%abbox% (''HATA seminar, 29.10.2015, DTU, Building 303B/Matematicum'')%%
%maroon%'''Marzieh Hasannasab'''%% (Kharazmi University): %green%''Hilbert module frames I''%%.
Added lines 5458:
%maroon%'''Kamilla Haahr Nielsen'''%% (DTU): %green%''The frame set of Gabor systems with Bspline generators''%%.
%abbox% (''HATA seminar, 08.06.2015, DTU, Building 303B/Matematicum'')%%
Changed lines 9297 from:
Hartmut F: Wavelet analysis in higher dimensions and the resolution of wavefront sets, Nov. 25, 2014
Marzieh: Title??, October 29??, 2014
Marzieh: Title?????? , June 8, 2015
Kamilla: The frame set of Gabor systems with Bspline generators, June 8, 2015
to:
Added lines 3438:
%maroon%'''Kamilla Haahr Nielsen'''%% (DTU): %green%''The frame set of Gabor systems with Bspline generators''%%.
%abbox% (''HATA seminar, 08.06.2015, DTU, Building 303B/Matematicum'')%%
Changed lines 4344 from:
to:
%maroon%'''Ole Christensen'''%% (DTU): %green%''What I know and would like to know in 2015''%%.
%abbox% (''HATA seminar, 03.02.2015, DTU, Building 303B/Matematicum'')%%
%maroon%'''Jakob Lemvig'''%% (DTU): %green%''Fiberizations and Zak transform methods''%%.
%abbox% (''HATA seminar, 03.02.2015, DTU, Building 303B/Matematicum'')%%
%maroon%'''Diana Stoeva'''%% (Austrian Academy of Sciences): %green%''On the duality principle in Gabor analysis and Rduals''%%.
%abbox% (''HATA seminar, 02.02.2015, DTU, Building 303B/Matematicum'')%%
%maroon%'''Mads S. Jakobsen'''%% (DTU): %green%''The duality principle for Gabor frames''%%.
%abbox% (''HATA seminar, 02.02.2015, DTU, Building 303B/Matematicum'')%%
%abbox% (''HATA seminar, 03.02.2015, DTU, Building 303B/Matematicum'')%%
%maroon%'''Jakob Lemvig'''%% (DTU): %green%''Fiberizations and Zak transform methods''%%.
%abbox% (''HATA seminar, 03.02.2015, DTU, Building 303B/Matematicum'')%%
%maroon%'''Diana Stoeva'''%% (Austrian Academy of Sciences): %green%''On the duality principle in Gabor analysis and Rduals''%%.
%abbox% (''HATA seminar, 02.02.2015, DTU, Building 303B/Matematicum'')%%
%maroon%'''Mads S. Jakobsen'''%% (DTU): %green%''The duality principle for Gabor frames''%%.
%abbox% (''HATA seminar, 02.02.2015, DTU, Building 303B/Matematicum'')%%
Deleted lines 7781:
OC: What I know and would like to know in 2015, Feb. 3, 2015
JL: Fiberizations and Zak transform methods, Feb. 3, 2015
Diana: On the duality principle in Gabor analysis and Rduals, Feb. 2, 2015
MSJ: The duality principle for Gabor frames, Feb. 2, 2015
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%abbox% (''HATA seminar, 0204.02.2015 at 9:00, DTU, Building 303B/Matematicum'')%%
%maroon%'''Peter Massopust'''%% (TU Munich): %green%''Bsplines and fractional splines''%%.
%maroon%'''Peter Massopust'''%% (TU Munich): %green%''Bsplines and fractional splines''%%.
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%maroon%'''Peter Massopust'''%% (TU Munich): %green%''Bsplines and fractional splines''%%.
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OC: There are the good guys and the bad guys  Localization of frames, Dec. 11, 2014
Hartmut F: Wavelet analysis in higher dimensions and the resolution of wavefront sets, Nov. 25, 2014
Marzieh: Title??, October 29??, 2014
Marzieh: Title?????? , June 8, 2015
Kamilla: The frame set of Gabor systems with Bspline generators, June 8, 2015
OC: What I know and would like to know in 2015, Feb. 3, 2015
JL: Fiberizations and Zak transform methods, Feb. 3, 2015
Diana: On the duality principle in Gabor analysis and Rduals, Feb. 2, 2015
MSJ: The duality principle for Gabor frames, Feb. 2, 2015
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%maroon%'''Tobias Kloos'''%% (TU Dortmund): %green%''Totally Positive Functions and Exponential Bsplines in
Gabor Analysis''%%.
%abbox%%maroon%Abstract%%: TBA.\\
(''HATA seminar, 04.02.2015, DTU, Building 303B/Matematicum'')%%
%abbox%
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to:
%maroon%'''Tobias Kloos'''%% (TU Dortmund): %green%''Totally Positive Functions and Exponential Bsplines in Gabor Analysis''%%.
%abbox%
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%abbox%
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%maroon%'''Tobias Kloos'''%% (TU Dortmund): %green%''Totally Positive Functions and Exponential Bsplines in
Gabor Analysis''%%.
%abbox% %maroon%Abstract%%: TBA.\\
(''HATA seminar, 04.02.2015, DTU, Building 303B/Matematicum'')%%
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A
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%maroon%'''Romanos Malikiosis'''%% (TU Berlin): %green%''Full spark Gabor frames in finite dimensions''%%.
%abbox% %maroon%Abstract%%: A Gabor frame is the set of all translates of a complex function
%abbox% %maroon%Abstract%%: A Gabor frame is the set of all translates of a complex function
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\\
(''HATA seminar, 18.11.2015 at 13:00, DTU, Building 303B/Matematicum'')%%
(''HATA seminar, 18.11.2015 at 13:00, DTU, Building 303B/Matematicum'')%%
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* 18.11 kl. 13:0013:45 Full spark Gabor frames in finite dimensions
to:
* Romanos Malikiosis: %green% ''Full spark Gabor frames in finite dimensions'' %%, November 18. 13:0013:45
A Gabor frame is the set of all translates of a complex function
and is a fundamental tool in utilizing communications channels with wide
applications in analysis and signal processing. When the domain
of the function is a finite cyclic group of order N, then the Gabor frame
forms a design on the complex sphere in N dimensions; when the N2 unit vectors
that constitute this Gabor frame are pairwise equiangular then the Gabor
frame forms a spherical 2design, and in addition, it has minimal coherence, an
ideal property in terms of compressive sensing (whether such an equiangular set
exists is also known as the existence problem, which is open since
1999).
In this talk, we will deal with the question of existence of a Gabor frame such
that every N vectors form a basis (the discrete analogue of the HRT conjecture);
such a frame is called a full spark Gabor frame. This question was posed by
Lawrence, Pfander and Walnut in 2005 and was answered in the affirmative by
the speaker in 2013 unconditionally. This result has applications in operator
identification, operator sampling, and compressive sensing.
A Gabor frame is the set of all translates of a complex function
and is a fundamental tool in utilizing communications channels with wide
applications in analysis and signal processing. When the domain
of the function is a finite cyclic group of order N, then the Gabor frame
forms a design on the complex sphere in N dimensions; when the N2 unit vectors
that constitute this Gabor frame are pairwise equiangular then the Gabor
frame forms a spherical 2design, and in addition, it has minimal coherence, an
ideal property in terms of compressive sensing (whether such an equiangular set
exists is also known as the existence problem, which is open since
1999).
In this talk, we will deal with the question of existence of a Gabor frame such
that every N vectors form a basis (the discrete analogue of the HRT conjecture);
such a frame is called a full spark Gabor frame. This question was posed by
Lawrence, Pfander and Walnut in 2005 and was answered in the affirmative by
the speaker in 2013 unconditionally. This result has applications in operator
identification, operator sampling, and compressive sensing.
Changed lines 811 from:
to:
* 18.11 kl. 13:0013:45 Full spark Gabor frames in finite dimensions
Changed line 13 from:
to:
%maroon%'''Peter Massopust'''%% (TU Munich): %green%''Bsplines and fractional splines''%%.
Added lines 117:
%define=abbox block fontsize=100pct bgcolor=#eeeeee margin="0.5em 0em 0.5em 0.5em" padding=0.5em width=95pct border="0.5px solid gray"%
! HATA seminar
[[#upcoming]]
!! Upcoming talks
There are currently no planned events.
[[#pasttalks]]
!! Past talks
Dr. %maroon%'''Peter Massopust'''%% (TU Munich) will give a talk on %green%''Bsplines and fractional splines''%%.
%abbox% %maroon%Abstract%%: TBA.\\
(''HATA seminar, 29.10.2014 at 11:00, DTU, Building 303B/Matematicum'')%%
! HATA seminar
[[#upcoming]]
!! Upcoming talks
There are currently no planned events.
[[#pasttalks]]
!! Past talks
Dr. %maroon%'''Peter Massopust'''%% (TU Munich) will give a talk on %green%''Bsplines and fractional splines''%%.
%abbox% %maroon%Abstract%%: TBA.\\
(''HATA seminar, 29.10.2014 at 11:00, DTU, Building 303B/Matematicum'')%%