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We investigate connections between information-theoretic andestimation-theoretic quantities in vector Poisson channel models. Inparticular, we generalize the gradient of mutual information with respect tokey system parameters from the scalar to the vector Poisson channel model. Wealso propose, as another contribution, a generalization of the classicalBregman divergence that offers a means to encapsulate under a unifyingframework the gradient of mutual information results for scalar and vectorPoisson and Gaussian channel models. The so-called generalized Bregmandivergence is also shown to exhibit various properties akin to the propertiesof the classical version. The vector Poisson channel model is drawingconsiderable attention in view of its application in various domains: as anexample, the availability of the gradient of mutual information can be used inconjunction with gradient descent methods to effect compressive-sensingprojection designs in emerging X-ray and document classification applications.

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