One sketch for all: fast algorithms for compressed sensing

One sketch for all: fast algorithms for compressed sensing One Sketch for All: Fast Algorithms for Compressed Sensing A. C. Gilber t, M. J. Strauss, J. A. Tropp {annacg,martinjs,jtropp}@umich.edu ABSTRACT Compressed Sensing is a new paradigm for acquiring the compressible signals that arise in many applications. These signals can be approximated using an amount of information much smaller than the nominal dimension of the signal. Traditional approaches acquire the entire signal and process it to extract the information. The new approach acquires a small number of nonadaptive linear measurements of the signal and uses sophisticated algorithms to determine its information content. Emerging technologies can compute these general linear measurements of a signal at unit cost per measurement. This paper exhibits a randomized measurement ensemble and a signal reconstruction algorithm that satisfy four requirements: 1. The measurement ensemble succeeds for all signals, with high probability over the random choices in its construction. 2. The number of measurements of the signal is optimal, except for a factor polylogarithmic in the signal length. 3. The running time of the algorithm is polynomial in the amount of information in the signal and polylogarithmic in the signal length. 4. The recovery algorithm o €ers the strongest possible type of error guarantee. Moreover, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

One sketch for all: fast algorithms for compressed sensing

Association for Computing Machinery — Jun 11, 2007

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Datasource
Association for Computing Machinery
Copyright
Copyright © 2007 by ACM Inc.
ISBN
978-1-59593-631-8
D.O.I.
10.1145/1250790.1250824
Publisher site
See Article on Publisher Site

Abstract

One Sketch for All: Fast Algorithms for Compressed Sensing A. C. Gilber t, M. J. Strauss, J. A. Tropp {annacg,martinjs,jtropp}@umich.edu ABSTRACT Compressed Sensing is a new paradigm for acquiring the compressible signals that arise in many applications. These signals can be approximated using an amount of information much smaller than the nominal dimension of the signal. Traditional approaches acquire the entire signal and process it to extract the information. The new approach acquires a small number of nonadaptive linear measurements of the signal and uses sophisticated algorithms to determine its information content. Emerging technologies can compute these general linear measurements of a signal at unit cost per measurement. This paper exhibits a randomized measurement ensemble and a signal reconstruction algorithm that satisfy four requirements: 1. The measurement ensemble succeeds for all signals, with high probability over the random choices in its construction. 2. The number of measurements of the signal is optimal, except for a factor polylogarithmic in the signal length. 3. The running time of the algorithm is polynomial in the amount of information in the signal and polylogarithmic in the signal length. 4. The recovery algorithm o €ers the strongest possible type of error guarantee. Moreover,

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