Sparse Signal Inversion with Impulsive Noise by Dual Spectral Projected Gradient Method
Joint Authors
Ding, Liang
Dou, Yixin
Zhao, Hui
Source
Mathematical Problems in Engineering
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-09-14
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
We consider sparse signal inversion with impulsive noise.
There are three major ingredients.
The first is regularizing properties; we discuss convergence rate of regularized solutions.
The second is devoted to the numerical solutions.
It is challenging due to the fact that both fidelity and regularization term lack differentiability.
Moreover, for ill-conditioned problems, sparsity regularization is often unstable.
We propose a novel dual spectral projected gradient (DSPG) method which combines the dual problem of multiparameter regularization with spectral projection gradient method to solve the nonsmooth l1+l1 optimization functional.
We show that one can overcome the nondifferentiability and instability by adding a smooth l2 regularization term to the original optimization functional.
The advantage of the proposed functional is that its convex duality reduced to a constraint smooth functional.
Moreover, it is stable even for ill-conditioned problems.
Spectral projected gradient algorithm is used to compute the minimizers and we prove the convergence.
The third is numerical simulation.
Some experiments are performed, using compressed sensing and image inpainting, to demonstrate the efficiency of the proposed approach.
American Psychological Association (APA)
Ding, Liang& Zhao, Hui& Dou, Yixin. 2017. Sparse Signal Inversion with Impulsive Noise by Dual Spectral Projected Gradient Method. Mathematical Problems in Engineering،Vol. 2017, no. 2017, pp.1-17.
https://search.emarefa.net/detail/BIM-1189925
Modern Language Association (MLA)
Ding, Liang…[et al.]. Sparse Signal Inversion with Impulsive Noise by Dual Spectral Projected Gradient Method. Mathematical Problems in Engineering No. 2017 (2017), pp.1-17.
https://search.emarefa.net/detail/BIM-1189925
American Medical Association (AMA)
Ding, Liang& Zhao, Hui& Dou, Yixin. Sparse Signal Inversion with Impulsive Noise by Dual Spectral Projected Gradient Method. Mathematical Problems in Engineering. 2017. Vol. 2017, no. 2017, pp.1-17.
https://search.emarefa.net/detail/BIM-1189925
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1189925