Poisson Noise Image Restoration Based on Bregman Proximal Gradient

In view of the fact that data item functions are not smooth in Poisson noise image restoration, while most existing first-order optimization methods require data item smoothness, a Poisson noise image restoration method based on BPG (Bregman Proximal Gradient) algorithm was proposed. Firstly, we establish a Poisson noise image recovery model using the maximum posterior estimation framework. This model aims to recover a high-quality image from noisy input data corrupted by Poisson noise. The model's data term is determined by the Kullback-Leibler (KL) divergence, which corresponds to the likelihood estimation. The KL divergence measures the difference between the probability distributions of the noisy input data and the recovered image. The regular term uses the Tikhonov regular term, which corresponds to a priori estimation. Secondly, the BPG algorithm is employed to address the model, which gives a wider and more satisfactory smoothness based on Bregman distance to replace the traditional gradient Lipschitz smoothness requirements, and maintains the convergence speed of PG (Proximal Gradient) algorithm. Finally, numerical experimental results, it proposed method outperforms the conventional algorithm by a margin of 0.01--6.94 (db) in terms of recovering Poisson noise images, and it also outperforms several algorithms in visual effects.