Adapting total generalized variation for blind image restoration

Abstract

AbstractIn this paper, a fast blind deconvolution approach is proposed for image deblurring by modifying a recent well-known natural image model, i.e., the total generalized variation (TGV). As a generalization of total variation, TGV aims at reconstructing a higher-quality image with high-order smoothness as well as sharp edge structures. However, when it turns to the blind issue, as demonstrated either empirically or theoretically by several previous blind deblurring works, natural image models including TGV actually prefer the blurred images rather than their counterpart sharp ones. Inspired by the discovery, a simple, yet effective modification strategy is applied to the second-order TGV, resulting in a novel L0–L1-norm-based image regularization adaptable to the blind deblurring problem. Then, a fast numerical scheme is deduced with O(NlogN) complexity for alternatingly estimating the intermediate sharp images and blur kernels via coupling operator splitting, augmented Lagrangian and also fast Fourier transform. Experiment results on a benchmark dataset and real-world blurred images demonstrate the superiority or comparable performance of the proposed approach to state-of-the-art ones, in terms of both deblurring quality and speed. Another contribution in this paper is the application of the newly proposed image prior to single image nonparametric blind super-resolution, which is a fairly more challenging inverse imaging task than blind deblurring.\n In spite of that, we have shown that both blind deblurring and blind super-resolution (SR) can be formulated into a common regularization framework. Experimental results demonstrate well the feasibility and effectiveness of the proposed blind SR approach, and also its advantage over the recent method by Michaeli and Irani in terms of estimation accuracy.\n