Blind deconvolution via a tensor adaptive non-convex total variation prior

Blind image deconvolution is a challenging task that aims to recover sharp images from blurry ones without knowing the blur kernel. Deblurring color images is even more difficult due to three color channels. Existing deblurring methods typically tackle each channel separately, treating them as individual grayscale images and designing priors specifically for grayscale images. However, these methods need to consider the relationships between color channels, leading to the need for a more precise estimation of blur kernels. In this paper, we have observed that the total variations of the three color channels of an image exhibit low-rank characteristics, which can be effectively captured using the tensor decomposition framework. To incorporate this observation, we propose a novel prior for color image deblurring. Specifically, we define a new tensor product using an image-adaptive transform matrix and apply a non-convex function to the tensor singular values to create a novel tensor norm. Then, we present the new tensor adaptive non-convex total variation prior for image deblurring. Numerically, we develop an efficient deblurring algorithm based on the half-quadratic splitting scheme. We provide detailed solutions for each sub-problem. Experimental results demonstrate that our method accurately estimates blur kernels and produces fewer artifacts on several benchmark datasets.