Blind Deconvolution with Re-weighted Sparsity Promotion

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, and the use of convex (often quadratic) cost functions. Our observations lead to a unified understanding of the principles required for successful blind deconvolution. We incorporate these principles into a novel algorithm that improves significantly upon the state of the art.