Variational Regularized Bayesian Estimation for Joint Blur Identification and Edge-Driven Image Restoration

The paper presents a novel method for joint blur identification and edge-driven image restoration in variational double regularized Bayesian estimation. The motivation is that the degradation of images includes not only additive, random noises but also multiplicative, spatial degradations, i.e., blur. Traditional nonlinear filtering techniques are observed in underutilization of blur identification techniques, and vice versa. To improve blur identification and image restoration, a designed nonlinear diffusion operator and a point spread function (PSF) learning term are needed to integrate the proposed approach. A newly introduced prior solution space provides prior information to the PSF learning. The cost functions are optimized iteratively in an alternate minimization with respect to the estimation of images and PSFs. Numerical experiments show that the proposed algorithm is efficient and robust, handling images that are formed in different environments with different types and amounts of blur and noise.