Fast iterative reweighted least squares algorithm for sparse signals recovery

Iterative Re-weighted Least Squares (IRLS) is an effective recovery algorithm for compressed sensing (CS). However, it suffers from a large computational load for the recovery of high dimensional sparse signals due to the repeated multiplication and inversion of large matrices. This paper proposes a fast IRLS algorithm. In this algorithm, the signal weights in each iteration are computed based on the result from the current iteration, simplifying the calculation of weights and avoiding repeated multiplication and inversion of large matrices in each iteration. The fast IRLS algorithm is more efficient than the original IRLS, especially for the high dimensional sparse signals recovery. Finally, some experiments are provided to illustrate the effectiveness of the proposed algorithm.