LURE: An Unsupervised Denoising Framework for Multiplicative Lognormal Noise
Monalisa Bakshi, Gayathri Venkat, Nikhil Bisen, Chandra Sekhar Seelamantula, Thierry Blu · SIAM Journal on Imaging Sciences · 2025
Abstract. Most image denoising problems focus on additive white Gaussian noise. In real-world imaging scenarios such as ultrasound, synthetic aperture radar, and optical-coherence tomography, the noise is multiplicative. Multiplicative noise has an extreme degradation effect compared to additive noise of the same variance. Further, in a practical imaging setting, one does not have access to the ground-truth clean images to train a deep neural network in a supervised fashion for image denoising. In this paper, we propose an unsupervised image denoising method for multiplicative noise. Specifically, we consider lognormal noise and develop an unbiased risk estimator of the mean-square error (MSE). We show that the resulting lognormal noise unbiased risk estimate, which we abbreviate as LURE, is an accurate estimator of the Oracle MSE. Computation of LURE involves the weighted trace of the Jacobian, which we estimate using a stochastic/Monte Carlo approximation method that is not only fast but also results in an accurate estimate of the MSE. The framework is flexible enough to accommodate a wide spectrum of denoisers—from wavelet denoising techniques to state-of-the-art deep learning techniques, subject to certain smoothness conditions on the denoiser. We deploy modern deep learning models such as U-Net, dilated-residual U-Net (DRUNet), and gradient step denoiser with DRUNet (GS-DRUNet) to establish the reliability of LURE. The performance measures used are peak signal-to-noise ratio (PSNR) and structural similarity index metric (SSIM). We show that minimizing Monte Carlo LURE in an unsupervised setting gives results that are on par with and sometimes even better than those obtained using the Oracle MSE loss in the supervised setting. We also provide comparisons with unsupervised despeckling techniques such as SAR2SAR, SAR-CNN, and Speckle2Void on real-world noisy images.