Graph-Based Blind Image Deblurring From a Single Photograph

Blind image deblurring, i.e., deblurring without knowledge of the blur kernel, is a highly ill-posed problem. The problem can be solved in two parts: i) estimate a blur kernel from the blurry image, and ii) given estimated blur kernel, de-convolve blurry input to restore the target image. In this paper, we propose a graph-based blind image deblurring algorithm by interpreting an image patch as a signal on a weighted graph. Specifically, we first argue that a skeleton image---a proxy that retains the strong gradients of the target but smooths out the details---can be used to accurately estimate the blur kernel and has a unique bi-modal edge weight distribution. Then, we design a reweighted graph total variation (RGTV) prior that can efficiently promote a bi-modal edge weight distribution given a blurry patch. Further, to analyze RGTV in the graph frequency domain, we introduce a new weight function to represent RGTV as a graph $l_1$-Laplacian regularizer. This leads to a graph spectral filtering interpretation of the prior with desirable properties, including robustness to noise and blur, strong piecewise smooth (PWS) filtering and sharpness promotion. Minimizing a blind image deblurring objective with RGTV results in a non-convex non-differentiable optimization problem. We leverage the new graph spectral interpretation for RGTV to design an efficient algorithm that solves for the skeleton image and the blur kernel alternately. Specifically for Gaussian blur, we propose a further speedup strategy for blind Gaussian deblurring using accelerated graph spectral filtering. Finally, with the computed blur kernel, recent non-blind image deblurring algorithms can be applied to restore the target image. Experimental results demonstrate that our algorithm successfully restores latent sharp images and outperforms state-of-the-art methods quantitatively and qualitatively.