Non-convex sparse regularisation 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 minimisation problem with the L1-norm minimisation 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 regularisation method based on smoothly clipped absolute deviation (SCAD) in this paper. Methods. The proposed method utilises the continuous SCAD penalty function to approximate the L0 norm and efficiently solves the non-convex optimisation 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. Moreover, the regularisation parameter was adaptively updated 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 thatitperforms better in terms of reconstruction quality and computational efficiency.