Non-convex sparse regularization for radio interferometric imaging via smoothly clipped absolute deviation

Context: Reconstructing a high-resolution image of observed radio sources from the incomplete visibilities poses a challenging ill-posed inverse problem. Although compressive sensing has demonstrated remarkable performance in radio interferometric imaging, traditional compressed sensing methods approximately replace the L0-norm minimization problem by the L1-norm minimization problem, which brings about a bias issue.Aims: To ameliorate the bias problem and efficiently obtain an accurate solution in radio interferometry, we propose a novel non convex sparse regularization method based on smoothly clipped absolute deviation (SCAD) in this paper.Methods: The proposed method utilizes the continuous SCAD penalty function to approximate the L0-norm and efficiently solves the non-convex optimization problem by using an improved proximal gradient algorithm. The improved proximal gradient algorithm introduces a restart strategy and an adaptive non-monotonic step size strategy to improve the convergence speed of the algorithm. Besides, the regularization parameter is adaptively updated by using the prior information of the image.Results: Numerical simulation experiments are carried out on the Very Large Array (VLA) and Square Kilometre Array (SKA). We compare the proposed method with state-of-the-art imaging methods. The results show that it performs better in terms of reconstruction quality and computational efficiency.