Unbiased and Nonlocal Linear Regression for Video Denoising Under Multiplicative Noise

Abstract Video data from coherent systems are often corrupted by multiplicative noise, which poses a significant restoration challenge due to its inherent nonlinearity. To address this problem, we propose NL-LMURE, an unbiased and nonlocal linear regression framework for denoising video data. We derive an unbiased risk estimator for arbitrary linear denoising functions that accurately estimates the true squared Euclidean norm under multiplicative noise. By integrating this estimator with a nonlocal linear functional form, we obtain a closed-form solution that frames the denoising process as a principled ridge-regression problem. Furthermore, we introduce a robust matching criterion and a variance estimation method tailored to multiplicative noise. Theoretically, we prove that our framework is applicable to a broad class of noise distributions. Experimentally, we demonstrate the effectiveness and efficiency of our approach across diverse multiplicative noise distributions. Code is available at https://github.com/TISGroup/NL-LMURE .