Mixed Fractional-Order and High-Order Adaptive Image Denoising Algorithm Based on Weight Selection Function

Abstract

In this paper, a mixed-order image denoising algorithm containing fractional-order and high-order regularization terms is proposed, which effectively suppresses the staircase effect generated by the TV model and its variants while better preserving the edges and details of the image. Adding different regularization penalties in different regions is fundamental to improving the denoising performance of the model. Therefore, a weight selection function is designed using the structure tensor to achieve a more effective selection of regularization terms in different regions. In each iteration, the regularization parameters are adaptively adjusted according to the Morozov discrepancy principle to promote the performance of the algorithm. Based on the primal–dual theory, the original algorithm is improved by using the predictor–corrector scheme to obtain a more accurate approximate solution while ensuring the convergence of the algorithm. The effectiveness of the proposed algorithm is demonstrated through simulation experiments.