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Title: Inverse problems with nonnegative and sparse solutions : algorithms and application to the phase retrieval problem
Authors: Muoi, Pham Quy
Hào, Dinh Nho
Sahoo, Sujit Kumar
Tang, Dongliang
Cong, Nguyen Huu
Dang, Cuong
Keywords: Gradient-type Algorithm
Inverse Problems
DRNTU::Engineering::Electrical and electronic engineering
Issue Date: 2018
Source: Muoi, P. Q., Hào, D. N., Sahoo, S. K., Tang, D., Cong, N. H., & Dang, C. (2018). Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem. Inverse Problems, 34(5), 055007-. doi:10.1088/1361-6420/aab6c9
Series/Report no.: Inverse Problems
Abstract: In this paper, we study a gradient-type method and a semismooth Newton method for minimization problems in regularizing inverse problems with nonnegative and sparse solutions. We propose a special penalty functional forcing the minimizers of regularized minimization problems to be nonnegative and sparse, and then we apply the proposed algorithms in a practical the problem. The strong convergence of the gradient-type method and the local superlinear convergence of the semismooth Newton method are proven. Then, we use these algorithms for the phase retrieval problem and illustrate their efficiency in numerical examples, particularly in the practical problem of optical imaging through scattering media where all the noises from experiment are presented.
ISSN: 0266-5611
DOI: 10.1088/1361-6420/aab6c9
Rights: © 2018 IOP Publishing Ltd. All rights reserved. This is an author-created, un-copyedited version of an article accepted for publication in Inverse Problems. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:EEE Journal Articles

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