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

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

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In sparse signal recovery, to overcome the -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 -norm more accurately. Moreover, the authors employ the -norm loss function instead of the -norm for the residual error, as the -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 -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.

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