Robust Blind Deconvolution via Mirror Descent

Abstract: We revisit the Blind Deconvolution problem with a focus on understanding its robustness and convergence properties. Provable robustness to noise and other perturbations is receiving recent interest in vision, from obtaining immunity to adversarial attacks to assessing and describing failure modes of algorithms in mission critical applications. Further, many blind deconvolution methods based on deep architectures internally make use of or optimize the basic formulation, so a clearer understanding of how this sub-module behaves, when it can be solved, and what noise injection it can tolerate is a first order requirement. We derive new insights into the theoretical underpinnings of blind deconvolution. The algorithm that emerges has nice convergence guarantees and is provably robust in a sense we formalize in the paper. Interestingly, these technical results play out very well in practice, where on standard datasets our algorithm yields results competitive with or superior to the state of the art. Keywords: blind deconvolution, robust continuous optimization