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Restoration of images degraded by spatially varying blurs is an issue ofincreasing importance in the context of photography, satellite or microscopyimaging. One of the main difficulty to solve this problem comes from the hugedimensions of the blur matrix. It prevents the use of naive approaches forperforming matrix-vector multiplications. In this paper, we propose toapproximate the blur operator by a matrix sparse in the wavelet domain. Wejustify this approach from a mathematical point of view and investigate theapproximation quality numerically. We finish by showing that the sparsitypattern of the matrix can be pre-defined, which is central in tasks such asblind deconvolution.

Image restoration using sparse approximations of spatially varying blur operators in the wavelet domain