Error estimation for non-convex relaxation cosparse optimization problems

doi:10.1007/s11075-025-02216-4

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Error estimation for non-convex relaxation cosparse optimization problems

2025-09-01

PRE

Zisheng Liu *

杨旭 (Xu Yang)

Jianchao Bai

DOI：10.1007/s11075-025-02216-4

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Abstract

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This paper addresses the error estimation problem for cosparse signal recovery via non-convex relaxation under noisy conditions. Compared to prior work, we significantly broaden the theoretical guarantees for such recovery by deriving a more inclusive range of admissible parameters in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Omega }$$\end{document}-RIP framework. Our analysis demonstrates that non-convex methods achieve tighter error bounds than convex approaches. Moreover, the derived error bounds are independent of algorithm design, so the results of this paper are universal and can be widely used in various of the cosparse signal recovery. Through preliminary numerical examples, we show that under \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Omega }$$\end{document}-RIP conditions, our non-convex methods achieve tighter bounds compared with convex relaxation methods.

Keywords:

Error estimation

Sparse model

Cosparse optimization problem

Non-convex relaxation method