An alternating multiple residual Wasserstein regularization model for Gaussian image denoising

Abstract

Abstract Residual histograms can provide meaningful statistical information in low-level visual research. However, the existing image denoising methods do not deeply explore the potential of alternate multiple residual histograms for overall optimization constraints. Considering this deficiency, this paper presents a novel unified framework of the alternating multiple residual Wasserstein regularization model (AMRW), which can tactfully embrace multiple residual Wasserstein constraints and different image prior information for image denoising. Specifically, AMRW focuses on solving the practical and meaningful problem of restoring a clean image from multiple frame degraded images. Utilizing the Wasserstein distance in the optimal transport theory, the residual histograms of the multiple degraded images are as close as possible to the referenced Gaussian noise histogram to enhance the noise estimation accuracy. Further, the proposed concrete AMRW combines the triple residual Wasserstein distance with the image total variation prior information for Gaussian image denoising. More importantly, through the alternating implementation of residual Wasserstein regularization from different image frames, the beneficial information of the image is essentially transmitted in each cycle, continuously improving the quality of the output image. Synchronously, the alternate iterative algorithm of histogram matching and Chambolle dual projection has high implementation efficiency. AMRW provides a new research idea for other visual processing tasks such as image inpainting and image deblurring. Finally, extensive numerical experiments substantiate that our AMRW can greatly boost the subjective and objective performance of the restored images compared with some popular image denoising algorithms in recent years.