An Improved Variational Method for Image Denoising
Jing-En Huang, Jia-Wei Liao, Ku-Te Lin, Yu-Ju Tsai, Mei-Heng Yueh
TL;DR
The paper tackles image denoising under mixed noise by proposing a mixed-norm TV model with the objective $||D_x u||_1 + ||D_y u||_1 + μ||u-f||_1 + α||u-f||_2^2$, solved via a convergence-guaranteed split-Bregman algorithm. It establishes the uniqueness of the minimizer and proves convergence of the algorithm to this minimizer, then demonstrates superior denoising performance across Gaussian, S&P, Poisson, speckle, and uniform noises on standard images. The experimental results show that the mixed-norm TV method yields higher PPS scores than classic TV variants and often rivals or exceeds the performance of DnCNN in mixed-noise scenarios, highlighting both theoretical guarantees and practical effectiveness. Overall, the approach provides a robust, edge-preserving denoising framework for complex noise with publicly available code.
Abstract
The total variation (TV) method is an image denoising technique that aims to reduce noise by minimizing the total variation of the image, which measures the variation in pixel intensities. The TV method has been widely applied in image processing and computer vision for its ability to preserve edges and enhance image quality. In this paper, we propose an improved TV model for image denoising and the associated numerical algorithm to carry out the procedure, which is particularly effective in removing several types of noises and their combinations. Our improved model admits a unique solution and the associated numerical algorithm guarantees the convergence. Numerical experiments are demonstrated to show improved effectiveness and denoising quality compared to other TV models. Such encouraging results further enhance the utility of the TV method in image processing.