First-order primal–dual algorithm for image restoration corrupted by mixed Poisson–Gaussian noise

The total variation infimal convolution (TV-IC) model combining Kullback–Leibler and ℓ2-norm data fidelity term works well for the inverse problem of mixed Poisson–Gaussian noise. Most existing algorithms for solving the TV-IC model rely on the Newton method to solve a nonlinear optimization subproblem, which inevitably increases the computation burden. In this study, we apply the first-order primal–dual Chambolle–Pock algorithm to solve the TV-IC model. In particular, we present an effective algorithm to solve the subproblem of the joint proximal operator with the Kullback–Leibler divergence and ℓ2-norm, which is based on the bilinear constraint alternating direction multiplier method. Numerical experiment results demonstrate that the proposed algorithm outperforms the state-of-the-art methods for mixed Poisson–Gaussian denoising and deblurring problems.