Joint Image Deblur and Poisson Denoising based on Adaptive Dictionary Learning

Abstract

This paper describes a blind image reconstruction algorithm for blurred image under Poisson noise. To that aim, in this work, the group sparse domain is explored to sparsely represent the image and blur kernel, and then $\ell_{1} -$norm is utilized to enforce the sparse solutions. In doing so, a joint optimization framework is developed to estimate the blur kernel matrix while removing Poisson noise. To effectively solve the developed optimization, a two-step iteration scheme involving two sub-problems is proposed. For each subproblem, the alternating direction method of multipliers (ADMM) algorithm is devised to estimate the blur or denoise. The experimental simulations demonstrate that the proposed algorithm is superior to other approaches in terms of restoration quality and performance metrics.