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  1. Journal of Fourier Analysis and Applications
  2. Journal of Fourier Analysis and Applications : Volume 14
  3. Journal of Fourier Analysis and Applications : Volume 14, Issue 5-6, December 2008
  4. Optimal Non-Linear Models for Sparsity and Sampling
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Journal of Fourier Analysis and Applications : Volume 23
Journal of Fourier Analysis and Applications : Volume 22
Journal of Fourier Analysis and Applications : Volume 21
Journal of Fourier Analysis and Applications : Volume 20
Journal of Fourier Analysis and Applications : Volume 19
Journal of Fourier Analysis and Applications : Volume 18
Journal of Fourier Analysis and Applications : Volume 17
Journal of Fourier Analysis and Applications : Volume 16
Journal of Fourier Analysis and Applications : Volume 15
Journal of Fourier Analysis and Applications : Volume 14
Journal of Fourier Analysis and Applications : Volume 14, Issue 5-6, December 2008
Prologue to Sparsity Issue
Weak Convergence of Greedy Algorithms in Banach Spaces
Iterative Thresholding for Sparse Approximations
Atoms of All Channels, Unite! Average Case Analysis of Multi-Channel Sparse Recovery Using Greedy Algorithms
Analysis of Basis Pursuit via Capacity Sets
Adaptive Martingale Approximations
Three Novel Edge Detection Methods for Incomplete and Noisy Spectral Data
Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints
Optimal Non-Linear Models for Sparsity and Sampling
Linear Convergence of Iterative Soft-Thresholding
On the Linear Independence of Spikes and Sines
On Some Deterministic Dictionaries Supporting Sparsity
Enhancing Sparsity by Reweighted ℓ 1 Minimization
Journal of Fourier Analysis and Applications : Volume 14, Issue 4, August 2008
Journal of Fourier Analysis and Applications : Volume 14, Issue 3, June 2008
Journal of Fourier Analysis and Applications : Volume 14, Issue 2, April 2008
Journal of Fourier Analysis and Applications : Volume 14, Issue 1, February 2008
Journal of Fourier Analysis and Applications : Volume 13
Journal of Fourier Analysis and Applications : Volume 12
Journal of Fourier Analysis and Applications : Volume 11
Journal of Fourier Analysis and Applications : Volume 10
Journal of Fourier Analysis and Applications : Volume 9
Journal of Fourier Analysis and Applications : Volume 8
Journal of Fourier Analysis and Applications : Volume 7
Journal of Fourier Analysis and Applications : Volume 6
Journal of Fourier Analysis and Applications : Volume 5
Journal of Fourier Analysis and Applications : Volume 4
Journal of Fourier Analysis and Applications : Volume 3

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Optimal Non-Linear Models for Sparsity and Sampling

Content Provider Springer Nature Link
Author Molter, Ursula Aldroubi, Akram Cabrelli, Carlos
Copyright Year 2008
Abstract Given a set of vectors (the data) in a Hilbert space ℋ, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This collection of subspaces gives the best sparse representation for the given data, in a sense defined in the paper, and provides an optimal model for sampling in union of subspaces. The results are proved in a general setting and then applied to the case of low dimensional subspaces of ℝ N and to infinite dimensional shift-invariant spaces in L 2(ℝ d ). We also present an iterative search algorithm for finding the solution subspaces. These results are tightly connected to the new emergent theories of compressed sensing and dictionary design, signal models for signals with finite rate of innovation, and the subspace segmentation problem.
Ending Page 812
Page Count 20
Starting Page 793
File Format PDF
ISSN 10695869
e-ISSN 15315851
Journal Journal of Fourier Analysis and Applications
Issue Number 5-6
Volume Number 14
Language English
Publisher SP Birkhäuser Verlag Boston
Publisher Date 2008-10-03
Publisher Place Boston
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Frames Signal, Image and Speech Processing Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) Abstract Harmonic Analysis Sampling theory Fourier Analysis Sparsity Approximations and Expansions General harmonic expansions, frames Applications of Mathematics Sampling Compressed sensing Partial Differential Equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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