Levenberg–Marquardt hard thresholding pursuit for sparse bilinear inverse problems
Abstract
Abstract In this paper, we propose two Levenberg–Marquardt methods merged with hard thresholding pursuits for solving sparse bilinear inverse problems. Our second method is an improvement of the first one by incorporating a novel support set refinement step. Under suitable assumptions, we show that the proposed methods are globally and locally quadratically convergent to an optimal solution of the underlying problem. The efficiency of the algorithms is demonstrated through numerical experiments on randomly generated problems which indicate the superior performance of the proposed methods compared to several existing methods.
Fields of Study & Subjects
Sparse and Compressive Sensing Techniques
Numerical methods in inverse problems
Image and Signal Denoising Methods
Publication details
- Journal / source
- Inverse Problems
- Volume
- 42
- Issue
- 1
- Pages
- 015011–015011
- Publication date
- 13 January 2026