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Two-step version of fixed point continuation
method for sparse reconstruction |
| Hao WANG1,Hongying LIU2,Yong XIA2, |
| 1.Key Laboratory of
Ministry of Education for Information Mathematics and Behavior, School
of Mathematics and Systems Science, Beijing University of Aeronautics
and Astronautics, Beijing 100191, China；Department of Industrial
and Systems Engineering, Lehigh University, Bethlehem, PA 18015, USA; 2.Key Laboratory of
Ministry of Education for Information Mathematics and Behavior, School
of Mathematics and Systems Science, Beijing University of Aeronautics
and Astronautics, Beijing 100191, China; |
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Abstract l1-regularized problems have a wide application in various areas such as signal processing. It minimizes a quadratic function combined with an l1 norm term. Iterative soft-thresholding method (IST) is originally proposed to deal with these problems, and fixed point continuation algorithm (FPC) was proposed recently as an improved version of IST. This paper obtains a two-step version of FPC (TwFPC) by combining the new iterate of FPC with its previous two iterates. We also provide an analysis for the convergence of FPC and TwFPC. Various numerical experiments on image deconvolution and compressed sensing show that TwFPC improves IST significantly and is much faster than other competing codes. What is more important, it is very robust to the involved parameters and the regularization parameter.
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| Keywords
l1-regularized problem
iterative soft-thresholding
fixed point continuation
sparse reconstruction
signal processing
image deconvolution
compressed sensing
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Issue Date: 05 September 2010
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