Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem. (4th April 2018)

• Record Type: Journal Article
• Authors: Muoi, Pham Quy; Hào, Dinh Nho; Sahoo, Sujit Kumar; Tang, Dongliang; Cong, Nguyen Huu; Dang, Cuong
• Is Part Of: Inverse problems. Volume 34:Number 5(2018:May)
• Publication Date: 2018-04-04
• Subjects: gradient-type algorithm -- inverse problems -- nonnegative and sparse solutions -- nonnegative sparse regularization -- phase retrieve problem; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aab6c9
• Languages: English
• ISSNs: 0266-5611

Abstract

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.