Two papers accepted on multiplicative noise removal (SIIMS and JMIV)

Our group has two papers accepted on multiplicative noise removal, spanning unsupervised neural estimation for single-image denoising and a nonlocal linear regression framework for video restoration.

1. Unbiased Risk Estimation for Multiplicative Noise Removal

Multiplicative noise removal is challenging because of its inherent nonlinearity. In this work, we derive unbiased risk estimators for the mean squared error under Gamma and normal multiplicative noise, and train neural denoisers in an unsupervised framework based on these estimators—without paired clean–noisy training data.

To make training practical, we derive computable approximations for the covariance terms and use Monte-Carlo estimation for the divergence term. We further extend the estimators to mixed multiplicative and additive noise. Theory and experiments show that the proposed criteria accurately track MSE and yield competitive or improved denoising relative to model-based and single-image unsupervised methods.

Code: github.com/TISGroup/URE-Multi-Noise

Reference: Z. Yan, T. Wang, J. Li, and C. Wang, “Unbiased Risk Estimation for Multiplicative Noise Removal,” SIAM Journal on Imaging Sciences, 2026 (to appear).

2. Unbiased and Nonlocal Linear Regression for Video Denoising under Multiplicative Noise

Video data from coherent imaging systems are often corrupted by multiplicative (speckle) noise. We propose NL-LMURE, an unbiased nonlocal linear regression framework for video denoising. By deriving an unbiased risk estimator for arbitrary linear denoisers and combining it with a nonlocal linear model, we obtain a closed-form solution that frames denoising as principled ridge regression.

We also introduce a matching criterion and variance estimation tailored to multiplicative noise. The framework applies to a broad class of noise distributions and is validated across diverse settings.

Code: github.com/TISGroup/NL-LMURE

Reference: Z. Yan, T. Wang, C. Wang, and J. Li, “Unbiased and Nonlocal Linear Regression for Video Denoising under Multiplicative Noise,” Journal of Mathematical Imaging and Vision, 2026 (to appear).