Alternating minimization for Poisson blind deconvolution in astronomy

Although the continuous progresses in the design of devices which reduce the distorting effects of an optical system, a correct model of the point spread function (PSF) is often unavailable and in general it has to be estimated manually from a measured image. As an alternative to this approach, one can address the so-called blind deconvolution problem, in which the reconstruction of both the target distribution and the model is performed simultaneously by considering the minimization of a fit-to-data function in which both the object and the PSF are unknown. Due to the strong ill-posedness of the resulting inverse problem, suitable a priori information are needed to recover a meaningful solution, which can be included in the minimization problem under the form of constraints on the unknowns. In this work we consider a recent optimization algorithm for the solution of the blind deconvolution problem from data affected by Poisson noise, and we propose a strategy to automatically select its parameters based on a measure of the optimality condition violation. Some numerical simulations on astronomical images show that the proposed approach allows to provide reconstructions very close to those obtained by manually optimizing the algorithm parameters.