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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
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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 certain… Expand
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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 effective… Expand
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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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