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, $ l_2 $ 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.


Dilip Krishnan
Joan Bruna
Rob Fergus