Normalized Blind Deconvolution

We introduce a family of novel approaches to single-image blind deconvolution, i.e., the problem of recovering a sharp image and a blur kernel from a single blurry input. This problem is highly ill-posed, because infinite (image, blur) pairs produce the same blurry image. Most research effort has been devoted to the design of priors for natural images and blur kernels, which can drastically prune the set of possible solutions. Unfortunately, these priors are usually not sufficient to favor the sharp solution. In this paper we address this issue by looking at a much less studied aspect: the relative scale ambiguity between the sharp image and the blur. Most prior work eliminates this ambiguity by fixing the \(L^1\) norm of the blur kernel. In principle, however, this choice is arbitrary. We show that a careful design of the blur normalization yields a blind deconvolution formulation with remarkable accuracy and robustness to noise. Specifically, we show that using the Frobenius norm to fix the scale ambiguity enables convex image priors, such as the total variation, to achieve state-of-the-art results on both synthetic and real datasets.