Bilinear Constraint based ADMM for Mixed Poisson-Gaussian Noise Removal
This work addresses noise removal in imaging for applications like medical or scientific imaging, but it is incremental as it builds on existing TV-IC models with algorithmic improvements.
The authors tackled the problem of removing mixed Poisson-Gaussian noise using total variation regularized infimal convolution models by proposing new operator-splitting algorithms (BCA and BCAf) that eliminate the need for inner loops, resulting in faster convergence with comparable results to existing methods.
In this paper, we propose new operator-splitting algorithms for the total variation regularized infimal convolution (TV-IC) model [4] 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.