Moments Matter: Posterior Recovery in Poisson Denoising via Log-Networks
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| Format: | Preprint |
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2025
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| _version_ | 1866915539650084864 |
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| author | Shoushtari, Shirin Chandler, Edward P. Kamilov, Ulugbek S. |
| author_facet | Shoushtari, Shirin Chandler, Edward P. Kamilov, Ulugbek S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07199 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moments Matter: Posterior Recovery in Poisson Denoising via Log-Networks Shoushtari, Shirin Chandler, Edward P. Kamilov, Ulugbek S. Signal Processing 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. |
| title | Moments Matter: Posterior Recovery in Poisson Denoising via Log-Networks |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2510.07199 |