A Reweighted ` Method for Image Restoration with Poisson and Mixed Poisson-gaussian Noise

We study weighted `2 fidelity in variational models for Poisson noise related image restoration problems. Gaussian approximation to Poisson noise statistic is adopted to deduce weighted `2 fidelity. Different from the traditional weighted `2 approximation, we propose a reweighted `2 fidelity with sparse regularization by wavelet frame. Based on the split Bregman algorithm introduced in [22], the proposed numerical scheme is composed of three easy subproblems that involve quadratic minimization, soft shrinkage and matrix vector multiplications. Unlike usual least square approximation of Poisson noise, we dynamically update the underlying noise variance from previous estimate. The solution of the proposed algorithm is shown to be the same as the one obtained by minimizing Kullback-Leibler divergence fidelity with the same regularization. This reweighted `2 formulation can be easily extended to mixed Poisson-Gaussian noise case. Finally, the efficiency and quality of the proposed algorithm compared to other Poisson noise removal methods are demonstrated through denoising and deblurring examples. Moreover, mixed Poisson-Gaussian noise tests are performed on both simulated and real digital images for further illustration of the performance of the proposed method. 2010 Mathematics Subject Classification. Primary: 65K10,65F22; Secondary: 94A08, 65T60.