Image Restoration Model under Poisson Noise Using Sparse Representations and Split Bregman Iteration Algorithm

Abstract

Astronomical and biomedical imaging instruments are often corrupted by Poisson noise. Using the sparse representation of the underlying image in an over-complete dictionary,a sparsity regularized convex functional model is proposed to deconvolve the Poisson noisy image in the Bayesian-MAP estimate framework. The negative-log Poisson likelihood functional is used as the data fidelity term,and the non-smooth regularization term is used to constrain the sparse image representation over the dictionary. An additional term is also added to ensure the positivity of the restored image. Inspired form the split Bergman iteration method,a multi-step fast iterative algorithm is proposed to numerically solve the above model. By introducing an intermediate variable and Bergman distance,the original problem is transformed into solving two simple sub-problems iteratively,thus computational complexity is decreased greatly. Experimental results demonstrate the effiectiveness of our recovery model and numerical algorithm.