Total variation image deblurring with space-varying kernel
In this paper, we consider a deconvolution problem where the point spread function (PSF) of the optical imaging system varies between different spatial locations, thus leading to a spatially varying blur. This problem arises, for example, in synthetic aperture instruments and in wide-field optical systems. Unlike the classical deconvolution context where the PSF is assumed to be spatially invariant, the problem cannot be easily solved in the Fourier domain. We propose here an iterative algorithm based on convex optimization techniques and a wavelet frame regularization. This approach allows restoration of the image, taking into account the properties of the blur operator, the latter being known.