A new approach to blind deconvolution of astronomical images

We readdress the strategy of finding approximate regularized solutions to the blind deconvolution problem, when both the object and the point-spread function (PSF) have finite support. Our approach consists in addressing fixed points of an iteration in which both the object x and the PSF y are approximated in an alternating manner, discarding the previous approximation for x when updating x (similarly for y), and considering the resultant fixed points as candidates for a sensible solution. Alternating approximations are performed by truncated iterative least-squares descents. The number of descents in the object-and in the PSF-space play a role of two regularization parameters. Selection of appropriate fixed points (which may not be unique) is performed by relaxing the regularization gradually, using the previous fixed point as an initial guess for finding the next one, which brings an approximation of better spatial resolution. We report the results of artificial experiments with noisefree data, targeted at examining the potential capability of the technique to deconvolve images of high complexity. We also show the results obtained with two sets of satellite images acquired using ground-based telescopes with and without adaptive optics compensation. The new approach brings much better results when compared with an alternating minimization technique based on positivity-constrained conjugate gradients, where the iterations stagnate when addressing data of high complexity. In the alternating-approximation step, we examine the performance of three different non-blind iterative deconvolution algorithms. The best results are provided by the non-negativity-constrained successive over-relaxation technique (+ SOR) supplemented with an adaptive scheduling of the relaxation parameter. Results of comparable quality are obtained with steepest descents modified by imposing the non-negativity constraint, at the expense of higher numerical costs. The Richardson-Lucy (or expectation-maximization) algorithm fails to locate stable fixed points in our experiments, due apparently to inappropriate regularization properties.