We consider design of linear projection measurements for a vector Poisson signal model. The projections are performed on the vector Poisson rate, and the observed data are a vector of counts. The projection matrix is designed
by maximizing mutual information between the observed data and the underlying Poisson rate. When there is a latent class label associated with the Poisson rate, we consider the mutual information with respect to the observed data and that label. New analytic expressions for the gradient of mutual are presented, with gradient performed with respect to the measurement matrix. Example results are presented for compressive
topic modeling of a document corpora (word counting), and hyperspectral compressive sensing for chemical classification (photon counting).