Bilinear Constraint based ADMM for Mixed Poisson-Gaussian Noise Removal

In this paper, we propose new operator-splitting algorithms for the total variation regularized infimal convolution (TV-IC) model in order to remove mixed Poisson-Gaussian (MPG) noise. In the existing splitting algorithm for TV-IC, an inner loop by Newton method had to be adopted for one nonlinear optimization subproblem, which increased the computation cost per outer loop. By introducing a new bilinear constraint and applying the alternating direction method of multipliers (ADMM), all subproblems of the proposed algorithms named as BCA (short for Bilinear Constraint based ADMM algorithm) and BCAf (short for a variant of BCA with fully splitting form) can be very efficiently solved; especially for the proposed BCAf , they can be calculated without any inner iterations. Under mild conditions, the convergence of the proposed BCA is investigated. Numerically, compared to existing primal-dual algorithms for the TV-IC model, the proposed algorithms, with fewer tunable parameters, converge much faster and produce comparable results meanwhile.