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 [6] 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 al-gorithm) and BCA_f (short for a variant of BCA with fully splitting form) can be very efficiently solved. Especially for the proposed BCA_f, they can be calculated without any inner iterations. The convergence of the proposed algorithms are investigated, where particularly, a Huber type TV regularizer is adopted to guarantee the convergence of BCA_f. 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.