Sparse signal recovery via minimax- concave penalty and l 1-norm loss function

In sparse signal recovery, to overcome the l 1- norm sparse regularisation's disadvantages tendency of uniformly penalise the signal amplitude and underestimate the high- amplitude components, a new algorithm based on a non- convex minimax- concave penalty is proposed, which can approximate the l 0- norm more accurately. Moreover, the authors employ the l 1- norm loss function instead of the l 2- norm for the residual error, as the l 1- loss is less sensitive to the outliers in the measurements. To rise to the challenges introduced by the non- convex non- smooth problem, they first employ a smoothed strategy to approximate the l 1- norm loss function, and then use the difference- of- convex algorithm framework to solve the nonconvex problem. They also show that any cluster point of the sequence generated by the proposed algorithm converges to a stationary point. The simulation result demonstrates the authors' conclusions and indicates that the algorithm proposed in this study can obviously improve the reconstruction quality.