Lanczos-based fast blind deconvolution methods

Abstract

The task of restoring an image that has been contaminated by blur and noise arises in many applications. When the blurring matrix (or equivalently, the point-spread function) is explicitly known, this task commonly is referred to as deconvolution. In many applications only an approximation of the blurring matrix is available. The restoration task then is referred to as blind deconvolution. This paper describes a family of blind deconvolution methods that allow a user to adjust the blurring matrix used in the computation to achieve an improved restoration. The methods are inexpensive to use; the major computational effort required for large-scale problems is the partial reduction of an available large symmetric approximate blurring matrix by a few steps of the symmetric Lanczos process. A real-time application to adaptive optics that requires fast blind deconvolution is described.