An imaging algorithm based on generalized minimax-concave penalty in radio interferometry

Reconstructing the sky brightness distribution from the incomplete visibilities involves an ill-posed inverse problem. Although compressive sensing methods based on convex optimization have demonstrated outstanding performance in radio interferometry, convex optimization yields a computable but biased approximate solution for compressive sensing. To reduce the bias and efficiently obtain an accurate solution, we proposed an imaging algorithm based on generalized minimax-concave penalty (GMCP), which maintains the convexity of the sparsity-regularized least squares objective function. Furthermore, we employ the forward-backward splitting algorithm to solve the optimization problem and adaptively update the regularization parameter by using a maximum likelihood estimator. We have verified the effectiveness of the proposed method based on the Very Large Array (VLA) and DAocheng Radio Telescope (DART).