A New Hybrid CQ Algorithm for the Split Feasibility Problem in Hilbert Spaces and Its Applications to Compressed Sensing

Suthep Suantai, Suparat Kesornprom and Prasit Cholamjiak
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Suthep Suantai: Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Suparat Kesornprom: School of Science, University of Phayao, Phayao 56000, Thailand
Prasit Cholamjiak: School of Science, University of Phayao, Phayao 56000, Thailand

Mathematics, 2019, vol. 7, issue 9, 1-15

Abstract: In this paper, we focus on studying the split feasibility problem (SFP), which has many applications in signal processing and image reconstruction. A popular technique is to employ the iterative method which is so called the relaxed CQ algorithm. However, the speed of convergence usually depends on the way of selecting the step size of such algorithms. We aim to suggest a new hybrid CQ algorithm for the SFP by using the self adaptive and the line-search techniques. There is no computation on the inverse and the spectral radius of a matrix. We then prove the weak convergence theorem under mild conditions. Numerical experiments are included to illustrate its performance in compressed sensing. Some comparisons are also given to show the efficiency with other CQ methods in the literature.

Keywords: split feasibility problem; CQ algorithm; gradient method; line-search (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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