Sparse signals recovered by non-convex penalty in quasi-linear systems

The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry some strongly nonlinear structures, and the linear model is n...

Full description

Saved in:
Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2018; no. 1; pp. 59 - 11
Main Authors: Cui, Angang, Li, Haiyang, Wen, Meng, Peng, Jigen
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 2018
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Compressed sensing
Iterative thresholding algorithm
Mathematics
Mathematics and Statistics
Non-convex fraction function
Quasi-linear
93C10
Non-convex fraction function
34A34
78M50
Quasi-linear
Iterative thresholding algorithm
Compressed sensing
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry some strongly nonlinear structures, and the linear model is no longer suitable. Compared with the compressed sensing under the linear circumstance, this nonlinear compressed sensing is much more difficult, in fact also NP-hard, combinatorial problem, because of the discrete and discontinuous nature of the ℓ 0 -norm and the nonlinearity. In order to get a convenience for sparse signal recovery, we set the nonlinear models have a smooth quasi-linear nature in this paper, and study a non-convex fraction function ρ a in this quasi-linear compressed sensing. We propose an iterative fraction thresholding algorithm to solve the regularization problem ( Q P a λ ) for all a > 0 . With the change of parameter a > 0 , our algorithm could get a promising result, which is one of the advantages for our algorithm compared with some state-of-art algorithms. Numerical experiments show that our method performs much better than some state-of-the-art methods.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-018-1652-8