l0-regularisation Signal Reconstruction Based on Fast Alternating Direction Method of Multipliers for Compressed Sensing

Fast Alternating Direction Method of Multipliers (FADMM) is proposed to solve the l0-regularisation issue, which is a problem of signal compression and reconstruction for Compressed Sensing (CS). The first step of FADMM is to express the l0-regularisation issue of the sparse coefficient as a constrained optimization issue by using variable splitting technology. Then, by introducing the function of multipliers, the two variables are alternatively minimized by Gauss-Seidel method. And the two variables are updated once again to speed up the convergence rate, and then, the variable of multipliers is updated. Finally, the original signal is reconstructed by the orthogonal inverse transform. FADMM is better than other state-of-the-art algorithms on reconstructing image. And the experimental simulations demonstrate that the FADMM algorithm has a higher Peak Signal to Noise Ratio (PSNR) and a faster convergence rate.