Total variation regularization for Poisson vector-valued image restoration with a spatially adaptive regularization parameter selection

We propose a flexible and computationally efficient method to solve the non-homogeneous Poisson (NHP) model for grayscale and color images within the TV framework. The NHP model is relevant to image restoration in several applications, such as PET, CT, MRI, etc. The proposed algorithm uses a novel method to spatially adapt the regularization parameter; it also uses a quadratic approximation of the negative log-likelihood function to pose the original problem as a non-negative quadratic programming problem. The reconstruction quality of the proposed algorithm outperforms state of the art algorithms for grayscale image restoration corrupted with Poisson noise. Moreover, it places no prohibitive restriction on the forward operator, and to best of our knowledge, the proposed algorithm is the only one that explicitly includes the NHP model for color images and that spatially adapts its regularization parameter within the TV framework.