Fast optimization for multichannel total variation minimization with non-quadratic fidelity

Total variation (TV) has been proved very successful in image processing, and it has been combined with various non-quadratic fidelities for non-Gaussian noise removal. However, these models are hard to solve because TV is non-differentiable and nonlinear, and non-quadratic fidelity term is also nonlinear and even non-differentiable for some special cases. This prevents their widespread use in practical applications. Very recently, it was found that the augmented Lagrangian method is extremely efficient for this kind of models. However, only the single-channel case (e.g., gray images) is considered. In this paper, we propose a general computational framework based on augmented Lagrangian method for multichannel TV minimization with non-quadratic fidelity, and then show how to apply it to two special cases: L1 and Kullback–Leibler (KL) fidelities, two common and important data terms for blurry images corrupted by impulsive noise or Poisson noise, respectively. For these typical fidelities, we show that the sub-problems either can be fast solved by FFT or have closed form solutions. The experiments demonstrate that our algorithm can fast restore high quality images.