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 still 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.
We present a recent optimization algorithm for the solution of the blind deconvolution problem, which on one hand is particularly suited to manage these kind of constraints, and on the other hand it has a strong mathematical background, since it has been proved its convergence to stationary points of the constrained minimization problem. Moreover, it can be easily modified to include boundary effect corrections, which account for the presence of stars near the borders of the image, and regularization terms, which further reduce the set of solutions.
Numerical tests on the reconstruction of stellar fields from ground-based telescopes show that the proposed method is efficient in reconstructing the correct magnitudes of the stars and the unknown PSF with a high accuracy.