The removal of Poisson noise is essential in medical and astronomical imaging.In the framework of Bayesian-MAP estimation

a sparsity regularized convex functional model is proposed to denoise Poisson noisy image in terms of the sparse representation of the underlying image in an over-complete dictionary.The negative-log Poisson likelihood functional is used for data fidelity term and non-smooth regularization term constrains the sparse representations of the underlying image over the dictionary.An additional term is also added in the functional to ensure the non-negative of the denoised image.Based on the Split Bergman iteration method

a multi-step fast iterative algorithm is proposed to solve the above model numerically.By introducing an intermediate variable and Bergman distance

the original problem is transformed into solving two simple sub-problems iteratively

thus the computational complexity is decreased rapidly.Experimental results demonstrate the effectiveness of our recovery model and the numerical iteration algorithm.