Space Variant Blind Image Restoration

We are interested in blind restoration of optical space variant blurred Poissonian images. For example, blur variation is due to refractive index mismatch in three-dimensional fluorescence microscopy or due to atmospheric turbulence in astrophysical images. In this work, the space variant point spread function (PSF) is approximated by a convex combination of a set of space invariant blurring functions. The latter is jointly estimated with the image by optimizing a given criterion including l₁ and l₂ norms for regularizing the image and the PSFs. We prove, in the continuous setting, the existence of a solution to this optimization problem. We then propose an alternating optimization algorithm based on a scaled gradient projection method. We show the efficiency of the proposed method on simulated and real optical images.