Orthonormal Expansion $\ell_{1}$-Minimization Algorithms for Compressed Sensing
IEEE Transactions on Signal Processing(2011)
摘要
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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关键词
convex optimization,algorithm design,noise measurement,phase transition,convex programming,basis pursuit,compressed sensing,minimisation,signal reconstruction,iterative methods,indexing terms,lagrange multiplier,numerical simulation,data compression
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