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Two-level l1 minimization for compressed sensing
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DOI：10.1016/j.sigpro.2014.09.028.png)
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Compressed sensing using l(1) minimization has been widely and successfully applied. To further enhance the sparsity, a non-convex and piecewise linear penalty is proposed. This penalty gives two different weights according to the order of the absolute value and hence is called the two-level l(1)-norm. The two-level l(1)-norm can be minimized by an iteratively reweighted l(1) method. Compared with some existing non-convex methods, the two-level l(1) minimization has similar sparsity and enjoys good convergence behavior. More importantly, the related soft thresholding algorithm has been established. The shrinkage operator for the two-level l(1)-norm is not non-expansive and its convergence is proved by showing the monotone of the objective value in the iterations. In numerical experiments, the proposed algorithms achieve good sparse signal estimation performance, which makes the two-level l(1) minimization a promising technique for compressed sensing. (C) 2014 Elsevier B.V. All rights reserved.
Keyword:
Compressed sensing
Non-convex penalty
l1 minimization
Thresholding algorithm
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