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Compressed Sensing: Theory and Applications
TLDR
We present a survey paper on compressed sensing, which explores the theoretical and practical aspects of compressed sensing and its applications. Expand
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Frames of subspaces
One approach to ease the construction of frames is to first construct local components and then build a global frame from these. In this paper we will show that the study of the relation between aExpand
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Introduction to compressed sensing
TLDR
Compressed sensing (CS) is an exciting, rapidly growing, field that has attracted considerable attention in signal processing, statistics, and computer science, and hundreds of conferences, workshops, and special sessions have been dedicated to this growing research field. Expand
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Shearlets: Multiscale Analysis for Multivariate Data
TLDR
Directional multiscale systems, particularly shearlets,are now having the same dramatic impact on the encoding of multidimensional signals. Expand
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Resolution of the wavefront set using continuous shearlets
It is known that the Continuous Wavelet Transform of a distribution f decays rapidly near the points where f is smooth, while it decays slowly near the irregular points. This property allows theExpand
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Sparse multidimensional representation using shearlets
TLDR
In this paper we describe a new class of multidimensional representation systems, called shearlets, obtained by applying the actions of dilation, shear transformation and translation to a fixed function, and exhibit the geometric and mathematical properties, recently advocated by many authors for sparse image processing applications. Expand
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A Haar wavelet-based perceptual similarity index for image quality assessment
TLDR
We introduce the Haar wavelet-based perceptual similarity index (HaarPSI), a novel and computationally inexpensive similarity measure for full reference image quality assessment. Expand
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Optimal Approximation with Sparsely Connected Deep Neural Networks
TLDR
We derive fundamental lower bounds on the connectivity and the memory requirements of deep neural networks guaranteeing uniform approximation rates for arbitrary function classes in $L^2(\mathbb{R}^d)$. Expand
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Duality Principles in Frame Theory
AbstractDuality principles in Gabor theory such as the Ron–Shen duality principle and the Wexler–Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. In this article weExpand
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Finite Frames: Theory and Applications
TLDR
Finite Frames is a comprehensive, systematic study of finite frame theory and applications for Hilbert space frames. Expand
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