Sparse Wavelet Representations of Spatially Varying Blurring Operators.

Restoring images degraded by spatially varying blur is a problem encountered in many disciplines such as astrophysics, computer vision, and biomedical imaging. One of the main challenges in performing this task is to design efficient numerical algorithms to approximate integral operators. We introduce a new method based on a sparse approximation of the blurring operator in the wavelet domain. This method requires O(N epsilon(-d/M)) operations to provide epsilon-approximations, where N is the number of pixels of a d-dimensional image and M >= 1 is a scalar describing the regularity of the blur kernel. In addition, we propose original methods to define sparsity patterns when only the operator regularity is known. Numerical experiments reveal that our algorithm provides a significant improvement compared to standard methods based on windowed convolutions.