Spatially adaptive iterative algorithm for the restoration of astronomical images

This article develops an iterative spatially adaptive regularized image restoration algorithm. The proposed algorithm is based on the minimization of a weighted smoothing functional. The weighting matrices are defined as functions of the partially restored image at each iteration step. As a result, no prior knowledge about the image and the noise is required, but the weighting matrices as well as the regularization parameter are updated based on the restored image at every step. Conditions for the convexity of the weighted smoothing functional and for the convergence of the iterative algorithm are established for a unique global solution which does not depend on initial conditions. Experimental results are shown with astronomical images which demonstrate the effectiveness of the proposed algorithm.