A nonconvex penalty function with integral convolution approximation for compressed sensing.

Highlights • We propose a novel penalty function for CS using integral convolution approximation. • Our criterion dose not underestimate the large component in signal recovery. • Our methods perform well under both the Gaussian random sensing matrix satisfying RIP and the highly coherent sensing matrix. • We carry out a series of experiments to verify our analysis. Abstract In this paper, we propose a novel nonconvex penalty function for compressed sensing using integral convolution approximation. It is well known that an unconstrained optimization criterion based on ℓ 1 -norm easily underestimates the large component in signal recovery. Moreover, most methods either perform well only under the Gaussian random measurement matrix satisfying restricted isometry property or the highly coherent measurement matrix, which both can not be established at the same time. We introduce a new solver to address both of these concerns by adopting a frame of the difference between two convex functions with integral convolution approximation. What's more, to better boost the recovery performance, a weighted version of it is also provided. Experimental results suggest the effectiveness and robustness of our methods through several signal reconstruction examples in term of success rate and signal-to-noise ratio. [ABSTRACT FROM AUTHOR]