Các bài toán ngược với nghiệm thưa không âm: Các giải thuật và ứng dụng cho bài toán khôi phục pha

Inverse Problems with Nonnegative and Sparse Solutions: Algorithms and Application to the Phase Retrieval Problem
Nơi đăng: , Số: , Trang: , Năm: 2018, Loại bài viết: Bài báo, Quốc gia: United Kingdom.


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.