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Volume 7
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Article

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

by
Suthep Suantai
1,
Suparat Kesornprom
2,* and
Prasit Cholamjiak
2,*
1
Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2
School of Science, University of Phayao, Phayao 56000, Thailand
*
Authors to whom correspondence should be addressed.
Mathematics 2019, 7(9), 789; https://doi.org/10.3390/math7090789
Submission received: 24 June 2019 / Revised: 31 July 2019 / Accepted: 23 August 2019 / Published: 27 August 2019
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
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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 split feasibility problem; CQ algorithm; gradient method; line-search

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MDPI and ACS Style

Suantai, S.; Kesornprom, S.; Cholamjiak, P. A New Hybrid CQ Algorithm for the Split Feasibility Problem in Hilbert Spaces and Its Applications to Compressed Sensing. Mathematics 2019, 7, 789. https://doi.org/10.3390/math7090789

AMA Style

Suantai S, Kesornprom S, Cholamjiak P. A New Hybrid CQ Algorithm for the Split Feasibility Problem in Hilbert Spaces and Its Applications to Compressed Sensing. Mathematics. 2019; 7(9):789. https://doi.org/10.3390/math7090789

Chicago/Turabian Style

Suantai, Suthep, Suparat Kesornprom, and Prasit Cholamjiak. 2019. "A New Hybrid CQ Algorithm for the Split Feasibility Problem in Hilbert Spaces and Its Applications to Compressed Sensing" Mathematics 7, no. 9: 789. https://doi.org/10.3390/math7090789

APA Style

Suantai, S., Kesornprom, S., & Cholamjiak, P. (2019). A New Hybrid CQ Algorithm for the Split Feasibility Problem in Hilbert Spaces and Its Applications to Compressed Sensing. Mathematics, 7(9), 789. https://doi.org/10.3390/math7090789

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