Blind image deblurring using both L0 and L1 regularization of Max-min prior

Abstract

Image deblurring involves estimating the blur kernel from intermediate latent images to recover their corresponding sharp, deblurred versions. In recent years, sophisticated priors such as dark channel, extreme channel, local maximum gradient, and patch-wise minimal pixels have demonstrated promising effectiveness. In this study, we propose a Max-min (Mm) prior for effective blind image deblurring. This work is motivated by the observation that the 1−Mm map of blurred images is less sparse than that of the corresponding clean images. The difference between the highest and lowest intensities around dominant edges is greater than in smooth areas. We theoretically and empirically demonstrate that blurring greatly diminishes this inherent characteristic. This property enables us to establish a new energy function and propose a blur kernel estimation model using L0 and L1 regularization of the Mm prior. The proposed method employs a linear operator to compute the Mm map, combined with an efficient optimization scheme to handle various specific scenarios. Through visual and quantitative experiments, we show that the proposed algorithm outperforms state-of-the-art algorithms. In terms of deblurring quality, robustness, and computational efficiency, the developed model surpasses comparable methods. The implemented code is available at https://github.com/eqtedaei/mm-prior-deblur