Blind Deconvolution with Non-local Sparsity Reweighting

Blind deconvolution has made significant progress in the past decade. Most successful algorithms are classified either as Variational or Maximum a-Posteriori (MAP ). In spite of the superior theoretical justification of variational techniques, carefully constructed MAP algorithms have proven equally effective in practice. In this paper, we show that all successful MAP and variational algorithms share a common framework, relying on the following key principles: sparsity promotion in the gradient domain, l2 regularization for kernel estimation, the use of convex (often quadratic) cost functions and multi-scale estimation. We also show that sparsity promotion of latent image gradients is an efficient regularizer for blur kernel estimation. Our observations lead to a unified understanding of the principles required for successful blind deconvolution. We incorporate these principles into a novel algorithm that has two new priors: one on the latent image and the other on the blur kernel. The resulting algorithm improves significantly upon the state of the art.