An iterative lagrange multiplier method for constrained total-variation-based image denoising

Various effective algorithms have been proposed in the past two decades for nonlinear PDEs arising from the unconstrained total-variation-based image denoising problem regularizing the total variation constrained minimization model. Such algorithms can be used to obtain a satisfactory result as long as a suitable regularization parameter balancing the trade-off between a good fit to the data and a regular solution is given. However, it is generally difficult to obtain a suitable regularization parameter without which restored images can be unsatisfactory: if it is too large, then the resulting solution is still contaminated by noise, while if too small, the solution is a poor approximation of the true noise-free solution. To provide an automatic method for the regularization parameter when the noise level is known a priori, one way is to address the coupled Karush-Kuhn-Tucker (KKT) systems from the constrained total variation optimization problem. So far much less work has been done on this problem. This paper presents an iterative update algorithm for a Lagrange multiplier to solve the KKT conditions, and our proposed method can adaptively deal with noisy images with different variances σ2. Numerical experiments show that our model can effectively find a highly accurate solution and produce excellent restoration results in terms of image quality.