Sparse signal recovery via minimax‐concave penalty and ‐norm loss function

Abstract

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 thel 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 non-convex 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.