Image Denoising Using Adaptive Weighted Low-Rank Matrix Recovery

This paper introduces a new image denoising method using adaptive weighted low-rank matrix recovery to tackle the challenges of separating low-rank information from noise and improving performance affected by empirical hyperparameters. We start by using image nonlocal similarity to build a low-rank denoising model, then apply the Gerschgorin theory to precisely determine the rank of the low -rank matrix. With this rank estimation, we use adaptive weighting along with singular value decomposition and weighted soft-thresholding to solve the denoising model, resulting in the denoised image. Experiments show our algorithm surpasses traditional denoising methods in average PSNR and SSIM. Specifically, for images contaminated with high-intensity noise (with a variance of 100), our algorithm achieves average PSNR and SSIM values of 24.66dB and 0.7267, respectively. Additionally, our algorithm exhibits superior performance in denoising images with real noise and is also applicable to color image denoising.