Hybrid blind deconvolution of images using variable splitting and proximal point methods

The problem of blind deconvolution of digital images has long been recognized as one of the central problems in imaging science. In this paper, the problem is solved using a hybrid deconvolution approach. Here, the “hybridization” suggests a two-stage reconstruction procedure. In the first stage, some partial information about the point spread function of the imaging system (namely, its magnitude spectrum) is recovered. Subsequently, the obtained information is exploited to explicitly constrain the procedure of inverse filtering. The latter is realized in the form of an optimization problem which is solved using alternating direction method of multipliers (ADMM). We show that this method leads to a particularly efficient numerical scheme, which can be implemented as a succession of analytically computable proximity operations. The effectiveness of the proposed deconvolution procedure is exemplified by a number of computer experiments.