Sparse signal recovery via minimax‐concave penalty and ℓ1 ‐norm loss function - Sun, Yuli; Chen, Hao; Tao, Jinxu (IET signal processing, 2018)
In sparse signal recovery, to overcome the ℓ1 ‐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 ℓ0 ‐norm more accurately. Moreover, the authors employ the ℓ1 ‐norm loss function instead of the ℓ2 ‐norm for the residual error, as the ℓ1 ‐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 ℓ1 ‐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.