Orthonormal Expansion l1-Minimization Algorithms for Compressed Sensing

Details Orthonormal Expansion l1-Minimization Algorithms for Compressed Sensing Orthonormal Expansion l1-Minimization Algorithms for Compressed Sensing

2011-08-25

arxiv.org/abs/1108.5037v2

IEEE Transactions on Signal Processing, vol. 59, no. 12, pp. 6285-6290, 2011

Computer Science

Information Theory

7 pages, 2 figures, 1 table

Scientific paper

Compressed sensing aims at reconstructing sparse signals from significantly reduced number of samples, and a popular reconstruction approach is $\ell_1$-norm minimization. In this correspondence, a method called orthonormal expansion is presented to reformulate the basis pursuit problem for noiseless compressed sensing. Two algorithms are proposed based on convex optimization: one exactly solves the problem and the other is a relaxed version of the first one. The latter can be considered as a modified iterative soft thresholding algorithm and is easy to implement. Numerical simulation shows that, in dealing with noise-free measurements of sparse signals, the relaxed version is accurate, fast and competitive to the recent state-of-the-art algorithms. Its practical application is demonstrated in a more general case where signals of interest are approximately sparse and measurements are contaminated with noise.

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