A L_q Proximal Gradient Algorithm for Radio-interferometric Imaging

Abstract The reconstruction from the measured visibilities to the signal in radio interferometry is an ill-posed inverse problem. The compressed sensing technology represented by the sparsity averaging reweighted analysis (SARA) has been successfully applied to radio-interferometric imaging. However, the traditional SARA algorithm solves the L 1 norm minimization problem instead of the L 0 norm one, which has a bias problem. In this paper, a L q proximal gradient algorithm with 0 < q < 1 is proposed to ameliorate the bias problem and obtain an accurate solution in radio interferometry. The proposed method efficiently solves the L q norm minimization problem by using the proximal gradient algorithm, and adopts restart and lazy-start strategies to reduce oscillations and accelerate the convergence rate. Numerical experiment results and quantitative analyses verify the effectiveness of the proposed method.