Levenberg–Marquardt hard thresholding pursuit for sparse bilinear inverse problems

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.