# Gaussian Surrogates for Poisson Imaging: Some Theoretical and Empirical Results

arXiv: https://arxiv.org/abs/2602.17274 · HTML: https://mlsanity.com/paper/2602.17274/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 26 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Builds on (most cited first, 2 of 2)

- [On bayesian estimation and proximity operators](https://mlsanity.com/paper/1807.04021/) (2018)
- [Multiview Attenuation Estimation and Correction](https://mlsanity.com/paper/1701.02615/) (2017)

## Abstract (arXiv)

In imaging inverse problems with Poisson-distributed measurements, it is common to use objectives derived from the Poisson likelihood. But performance is often evaluated by mean squared error (MSE), which raises a practical question: how much does a Poisson objective matter for MSE, even at low dose? We analyze the MSE of Poisson and Gaussian surrogate reconstruction objectives under Poisson noise. In a stylized diagonal model, we show that the unregularized Poisson maximum-likelihood estimator can incur large MSE at low dose, while Poisson MAP mitigates this instability through regularization. We then study two Gaussian surrogate objectives: a heteroscedastic quadratic objective motivated by the normal approximation of Poisson data, and a homoscedastic quadratic objective that yields a simple linear estimator. We show that both surrogates can achieve MSE comparable to Poisson MAP in the low-dose regime, despite departing from the Poisson likelihood. Numerical computed tomography experiments indicate that these conclusions extend beyond the stylized setting of our theoretical analysis.