Eigenvalue-free iterative shrinkage-thresholding algorithm for solving the linear inverse problems

The iterative shrinkage threshold algorithm (ISTA) is widely used in solving linear inverse problems due to its simplicity. However, it depends on the calculation of eigenvalues during the iterative process, which will cost a lot of computing time. In this paper, we propose an eigenvalue-free iterative shrinkage threshold algorithm (EFISTA) based on the majorization-minimization to avoid the calculation of eigenvalues which performs better in large-scale problems. Similar to ISTA, this algorithm can also be extended to a fast EFISTA. Moreover, we provide the proofs of convergence and convergence rate. The experimental results show that the algorithm is effective and feasible.