Adaptive updating of regularization parameters

Iterative minimization of an objective function is usually used for restoring a signal from its noisy measurements. The performance of such iterative algorithms is controlled by regularization parameters, such as Lagrange multipliers. Inappropriate choice of these parameters can either trap the algorithm in local minima and/or lead to a lower convergence rate. We propose a Noise Confidence Region Evaluation (NCRE) algorithm, which adaptively adjusts the regularization parameters. The adjustment is based on evaluation and comparison of error residuals and the considered noise statistics, at the end of each iteration. Moreover, it stops the iterations when the statistical characteristics of the residual match those of the considered noise. NCRE can be used with different algorithms, such as: wavelet soft thresholding, Total Variation denoising, Iterative Soft Thresholding compressed sensing recovery, that have been explained in this paper. In addition, NCRE enables Block Matching and 3D filtering denoising method to be used in an iterative scheme applied on low dose computed tomography images. Simulation results showed advantages of the NCRE in improving the performance of the discussed methods in sense of image quality and mean squared error. Moreover, NCRE enables these algorithms to converge in fewer iterations.