Generalized Bregman Divergence and Gradient of Mutual Information for Vector Poisson Channels
This work provides tools for optimizing compressive-sensing projections in applications like X-ray imaging and document classification, representing an incremental advancement in information theory for specific domains.
The authors generalized the gradient of mutual information from scalar to vector Poisson channel models and proposed a generalized Bregman divergence to unify gradient results across Poisson and Gaussian channels, showing it retains classical properties.
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.