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A Mathematical Introduction to Compressive Sensing
TLDR
A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing and provides a detailed account of the core theory upon which the field is build. Expand
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Compressive Sensing
TLDR
Compressive sensing is a new type of sampling theory, which predicts that sparse signals and images can be reconstructed from what was previously believed to be incomplete information. Expand
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Average Case Analysis of Multichannel Sparse Recovery Using Convex Relaxation
TLDR
This paper considers recovery of jointly sparse multichannel signals from incomplete measurements. Expand
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Sparse Legendre expansions via l1-minimization
TLDR
We show that a Legendre s-sparse polynomial of maximal degree N can be recovered from [email protected]?slog^4(N) random samples that are chosen independently according to the Chebyshev probability measure. As an efficient recovery method, @?"1-minimization can be used. Expand
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Compressed Sensing and Redundant Dictionaries
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We show that a matrix, which is a composition of a random matrix of certain type and a deterministic dictionary, has small restricted isometry constants and can be recovered via basis pursuit from a small number of random measurements. Expand
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Low-rank Matrix Recovery via Iteratively Reweighted Least Squares Minimization
TLDR
We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements with an error of the order of the best $k$-rank approximation. Expand
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Continuous Frames, Function Spaces, and the Discretization Problem
A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certainExpand
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Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints
TLDR
We show how to compute solutions of linear inverse problems with joint sparsity regularization constraints by fast thresholded Landweber algorithms. Expand
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Interpolation via weighted $l_1$ minimization
Functions of interest are often smooth and sparse in some sense, and both priors should be taken into account when interpolating sampled data. Classical linear interpolation methods are effectiveExpand
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Compressive Estimation of Doubly Selective Channels in Multicarrier Systems: Leakage Effects and Sparsity-Enhancing Processing
TLDR
We consider the application of compressed sensing (CS) to the estimation of doubly selective channels within pulse-shaping multicarrier systems (which include orthogonal frequency-division multiplexing (OFDM) systems as a special case). Expand
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