Computationally efficient radio astronomical image formation using constrained least squares and and the MVDR beamformer

Abstract

Linear image deconvolution for radio-astronomy is an ill-posed problem. For this reason, a-priori knowledge is crucial for improving the performance of the deconvolution. In this paper we show that combining non-negativity constraints with an upper bound on the magnitude of each pixel in the image can significantly improve the image formation algorithm. We also show that the minimum variance distortionless response (MVDR) dirty image provides the tightest upper bound out of all beamformers. We then show how the LS-MVI image formation algorithm can be reformulated as a preconditioned weighted least squares algorithm. The resulting algorithm can be efficiently solved using the active-set method. The performance of the algorithm is demonstrated in simulation and compared with constrained least squares based on the classical dirty image.