{"ID":2858885,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.07199","arxiv_id":"2510.07199","title":"Moments Matter: Posterior Recovery in Poisson Denoising via Log-Networks","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 $\\mathbb{E}[x \\mid y]$. When the noise is Gaussian, 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}[x \\mid 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}[x \\mid y] $, the log-network is trained to learn $\\mathbb{E}[\\log x \\mid y]$, 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.","short_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 $\\mathbb{E}[x \\mid y]$. When the noise is...","url_abs":"https://arxiv.org/abs/2510.07199","url_pdf":"https://arxiv.org/pdf/2510.07199v1","authors":"[\"Shirin Shoushtari\",\"Edward P. Chandler\",\"Ulugbek S. Kamilov\"]","published":"2025-10-08T16:30:26Z","proceeding":"eess.SP","tasks":"[\"eess.SP\"]","methods":"[]","has_code":false}