CHEN Peng-qing, HUANG Wei. Block-Sparse Signal Recovery Based on l1-l2 Norm Minimization[J]. Applied Mathematics and Mechanics, 2017, 38(8): 932-942. doi: 10.21656/1000-0887.370230
Citation: CHEN Peng-qing, HUANG Wei. Block-Sparse Signal Recovery Based on l1-l2 Norm Minimization[J]. Applied Mathematics and Mechanics, 2017, 38(8): 932-942. doi: 10.21656/1000-0887.370230

Block-Sparse Signal Recovery Based on l1-l2 Norm Minimization

doi: 10.21656/1000-0887.370230
Funds:  The Major Research Plan of the National Natural Science Foundation of China(91538112);The National Science Fund for Young Scholars of China(11201450)
  • Received Date: 2016-07-22
  • Rev Recd Date: 2017-05-19
  • Publish Date: 2017-08-15
  • Compressed sensing (CS) is a newly developed theoretical framework for information acquisition and processing. Through the solution of non-linear optimization problems, sparse and compressible signals can be recovered from small-scale linear and non-adaptive measurements. Block-sparse signals as typical sparse ones exhibit additional block structures where the non-zero elements occur in blocks (or clusters). Based on the previous l1-2 norm minimization method given by YIN Peng-hang, LOU Yi-fei, HE Qi, et al. for common sparse signal recovery, the l1-l2 minimization recovery algorithm was extended to the block-sparse model, the properties of thel1-l2 norm were proved and the sufficient condition for block-sparse signal recovery was established. Meanwhile, an iterative method for block-sparsel1-l2 minimization was presented by means of the DCA (difference of convex functions algorithm) and the ADMM (alternating direction method of multipliers). The numerical simulation results demonstrate that the signal recovery success rate of the proposed algorithm is higher than those of the existing algorithms.
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