# External Division of Two Bregman Proximity Operators for Poisson Inverse Problems

arXiv: https://arxiv.org/abs/2602.11482 · HTML: https://mlsanity.com/paper/2602.11482/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 20 references that are in the map.
- First posted on arXiv 12 Feb 2026.

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

- [First Order Methods beyond Convexity and Lipschitz Gradient Continuity with Applications to Quadratic Inverse Problems](https://mlsanity.com/paper/1706.06461/) (2017)
- [Convergent Bregman Plug-and-Play Image Restoration for Poisson Inverse Problems](https://mlsanity.com/paper/2306.03466/) (2023)

## Abstract (arXiv)

This paper presents a novel method for recovering sparse vectors from linear models corrupted by Poisson noise. The contribution is twofold. First, an operator defined via the external division of two Bregman proximity operators is introduced to promote sparse solutions while mitigating the estimation bias induced by classical ℓ1-norm regularization. This operator is then embedded into the already established NoLips algorithm, replacing the standard Bregman proximity operator in a plug-and-play manner. Second, the geometric structure of the proposed external-division operator is elucidated through two complementary reformulations, which provide clear interpretations in terms of the primal and dual spaces of the Poisson inverse problem. Numerical tests show that the proposed method exhibits more stable convergence behavior than conventional Kullback-Leibler (KL)-based approaches and achieves significantly superior performance on synthetic data and an image restoration problem.