Year: 2026
Type: conference-paper
Abstract: Poisson denoising plays a central role in photon-limited imaging applications such as microscopy, astronomy, and medical imaging. It is common to train deep learning models for denoising using the mean-squared error (MSE) loss, which corresponds to computing the posterior mean ${\mathbb{E}}[{\mathbf{x}}\mid {\mathbf{y}}]$. When the noise is Gaussian, the Tweedie’s formula enables approximation of the posterior distribution through its higher-order moments. However, this connection no longer holds for Poisson denoising: while ${\mathbb{E}}[{\mathbf{x}}\mid {\mathbf{y}}]$ still minimizes MSE, it fails to capture posterior uncertainty. We propose a new strategy for Poisson denoising based on training a log-network. Instead of predicting the posterior mean ${\mathbb{E}}[{\mathbf{x}}\mid {\mathbf{y}}]$, the log-network is trained to learn ${\mathbb{E}}\left[ {\log {\mathbf{x}}|{\mathbf{y}}} \right]$, leveraging the logarithm as a convenient parameterization for the Poisson distribution. We provide a theoretical proof that the proposed log-network enables recovery of higher-order posterior moments and, thus supports posterior approximation. Experiments on simulated data show that our method matches the denoising performance of standard MMSE models, while providing access to the posterior.
Institution: University of Wisconsin–Madison
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415318170
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