A new hybrid CQ algorithm for the split feasibility problem in Hilbert spaces and its applications to compressed sensing
© 2019 by the authors. 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 converge...
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th-cmuir.6653943832-679012020-04-02T15:10:38Z A new hybrid CQ algorithm for the split feasibility problem in Hilbert spaces and its applications to compressed sensing Suthep Suantai Suparat Kesornprom Prasit Cholamjiak Mathematics © 2019 by the authors. 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. 2020-04-02T15:10:38Z 2020-04-02T15:10:38Z 2019-09-01 Journal 22277390 2-s2.0-85072312287 10.3390/math7090789 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85072312287&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/67901 |
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Mathematics Suthep Suantai Suparat Kesornprom Prasit Cholamjiak A new hybrid CQ algorithm for the split feasibility problem in Hilbert spaces and its applications to compressed sensing |
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© 2019 by the authors. 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. |
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Suthep Suantai Suparat Kesornprom Prasit Cholamjiak |
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Suthep Suantai Suparat Kesornprom Prasit Cholamjiak |
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Suthep Suantai |
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A new hybrid CQ algorithm for the split feasibility problem in Hilbert spaces and its applications to compressed sensing |
title_short |
A new hybrid CQ algorithm for the split feasibility problem in Hilbert spaces and its applications to compressed sensing |
title_full |
A new hybrid CQ algorithm for the split feasibility problem in Hilbert spaces and its applications to compressed sensing |
title_fullStr |
A new hybrid CQ algorithm for the split feasibility problem in Hilbert spaces and its applications to compressed sensing |
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A new hybrid CQ algorithm for the split feasibility problem in Hilbert spaces and its applications to compressed sensing |
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new hybrid cq algorithm for the split feasibility problem in hilbert spaces and its applications to compressed sensing |
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2020 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85072312287&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/67901 |
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