# Generalized Bregman Divergence and Gradient of Mutual Information for Vector Poisson Channels

arXiv: https://arxiv.org/abs/1301.6648 · HTML: https://mlsanity.com/paper/1301.6648/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2013.

## Built on by (most cited first, 2 of 2)

- [Information-Theoretic Diffusion](https://mlsanity.com/paper/2302.03792/) (2023)
- [ItDPDM: Information-Theoretic Discrete Poisson Diffusion Model](https://mlsanity.com/paper/2505.05082/) (2025)

## Abstract (arXiv)

We investigate connections between information-theoretic and estimation-theoretic quantities in vector Poisson channel models. In particular, we generalize the gradient of mutual information with respect to key system parameters from the scalar to the vector Poisson channel model. We also propose, as another contribution, a generalization of the classical Bregman divergence that offers a means to encapsulate under a unifying framework the gradient of mutual information results for scalar and vector Poisson and Gaussian channel models. The so-called generalized Bregman divergence is also shown to exhibit various properties akin to the properties of the classical version. The vector Poisson channel model is drawing considerable attention in view of its application in various domains: as an example, the availability of the gradient of mutual information can be used in conjunction with gradient descent methods to effect compressive-sensing projection designs in emerging X-ray and document classification applications.