Sparse Recovery Algorithm for Compressed Sensing Using Smoothed <i>l</i>₀ Norm and Randomized Coordinate Descent

Abstract

Compressed sensing theory is widely used in the field of fault signal diagnosis and image processing. Sparse recovery is one of the core concepts of this theory. In this paper, we proposed a sparse recovery algorithm using a smoothed l0 norm and a randomized coordinate descent (RCD), then applied it to sparse signal recovery and image denoising. We adopted a new strategy to express the (P0) problem approximately and put forward a sparse recovery algorithm using RCD. In the computer simulation experiments, we compared the performance of this algorithm to other typical methods. The results show that our algorithm possesses higher precision in sparse signal recovery. Moreover, it achieves higher signal to noise ratio (SNR) and faster convergence speed in image denoising.

Keywords

• compressed sensing
• sparse recovery
• approximate (<i>P</i>₀) problem
• randomized coordinate descent