Practical near-optimal sparse recovery in the L1 norm

We consider the approximate sparse recovery problem, where the goal is to (approximately) recover a high-dimensional vector x isin R n from its lower-dimensional sketch Ax isin R m . Specifically, we focus on the sparse recovery problem in the l 1 norm: for a parameter k, given the sketch Ax, comput...

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Bibliographic Details
Published in2008 46th Annual Allerton Conference on Communication, Control, and Computing pp. 198 - 205
Main Authors Berinde, R., Indyk, P., Ruzic, M.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.09.2008
Subjects
Approximation error
Computer errors
Computer science
EMP radiation effects
Encoding
Matching pursuit algorithms
Pursuit algorithms
Signal processing algorithms
Sparse matrices
Vectors
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ISBN1424429250
9781424429257
DOI10.1109/ALLERTON.2008.4797556

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Summary:We consider the approximate sparse recovery problem, where the goal is to (approximately) recover a high-dimensional vector x isin R n from its lower-dimensional sketch Ax isin R m . Specifically, we focus on the sparse recovery problem in the l 1 norm: for a parameter k, given the sketch Ax, compute an approximation xcirc of x such that the l 1 approximation error parx - xcircpar 1 is close to min x' parx - x'par 1 , where x' ranges over all vectors with at most k terms. The sparse recovery problem has been subject to extensive research over the last few years. Many solutions to this problem have been discovered, achieving different trade-offs between various attributes, such as the sketch length, encoding and recovery times.
ISBN:1424429250
9781424429257
DOI:10.1109/ALLERTON.2008.4797556