Variable metric extrapolation proximal iterative hard thresholding method for $\ell_0$ minimization problem

TL;DR

This paper introduces the VMEPIHT method, a novel algorithm combining proximal iterative hard thresholding and quasi-Newton techniques, for solving the  minimization problem with proven convergence and demonstrated efficiency in compressive sensing and CT image reconstruction.

Contribution

The paper proposes the VMEPIHT method, integrating variable metric and extrapolation techniques with PIHT, and analyzes its convergence properties.

Findings

VMEPIHT achieves linear and superlinear convergence rates.

Numerical experiments show VMEPIHT outperforms existing methods.

VMEPIHT is effective for compressive sensing and CT image reconstruction.

Abstract

In this paper, we consider the $\ell_0$ minimization problem whose objective function is the sum of $\ell_0$-norm and convex differentiable function. A variable metric type method which combines the PIHT method and the skill in quasi-newton method, named variable metric extrapolation proximal iterative hard thresholding (VMEPIHT) method, is proposed. Then we analyze its convergence, linear convergence rate and superlinear convergence rate under appropriate assumptions. Finally, we conduct numerical experiments on compressive sensing problem and CT image reconstruction problem to confirm VMPIHT method's efficiency, compared with other state-of-art methods.