JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (1): 65-73.doi: 10.6040/j.issn.1671-9352.0.2016.059

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The application of a supermemory gradient method for large-scale signal reconstruction problem

LI Shuang-an, CHEN Feng-hua, ZHAO Yan-wei   

  1. Department of Public Basic Courses Teaching, Zhengzhou Technology and Business University, Zhengzhou 451400, Henan, China
  • Received:2016-02-03 Online:2017-01-20 Published:2017-01-16

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Abstract: We study a nonmonotone supermemory gradient algorithm for solving large-scale sparse signal recovery problems. The l1 penalty function of the constrained l1-regularized least-squares recovery problem is replaced by the smoothly clipped absolute deviation(SCAD)sparsity-promoting penalty function. In addition, a convex and differentiable local quadratic approximation for the SCAD function is employed to render the computation of the gradient and Hessian tractable. The proposed method sufficiently uses the previous multi-step iterative information at each iteration, avoids the storage and computation of matrices associated with the Hessian of objective functions, thus it is suitable to solve large-scale sparse signal recovery problems. Under some assumptions, the convergence properties of the proposed algorithm are analyzed. Numerical results are also reported to show the efficiency of this proposed method.

Key words: compressed sensing, SCAD penalty function, supermemory gradient method, sparse signal

CLC Number: 

  • O221.1
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