Spectral Norm Regularization for Blind Image Deblurring

Blind image deblurring is a well-known ill-posed inverse problem in the computer vision field. To make the problem well-posed, this paper puts forward a plain but effective regularization method, namely spectral norm regularization (SN), which can be regarded as the symmetrical form of the spectral norm. This work is inspired by the observation that the SN value increases after the image is blurred. Based on this observation, a blind deblurring algorithm (BDA-SN) is designed. BDA-SN builds a deblurring estimator for the image degradation process by investigating the inherent properties of SN and an image gradient. Compared with previous image regularization methods, SN shows more vital abilities to differentiate clear and degraded images. Therefore, the SN of an image can effectively help image deblurring in various scenes, such as text, face, natural, and saturated images. Qualitative and quantitative experimental evaluations demonstrate that BDA-SN can achieve favorable performances on actual and simulated images, with the average PSNR reaching 31.41, especially on the benchmark dataset of Levin et al.