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

¹ School of Computer Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China
² State Key Laboratory of Solar Activity and Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China
³ Radio Science and Technology Center (π Center), Chengdu 610041, China

^★ Corresponding author: yanjingye@nssc.ac.cn

Received: 30 May 2025
Accepted: 27 October 2025

Abstract

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.