Designed measurements for vector count data

Journal Article

We consider design of linear projection measurements for a vector Poisson signal model. The projections are performed on the vector Poisson rate,X ∈ ℝ+n, and the observed data are a vector of counts, Y ∈ ℤ +m. The projection matrix is designed by maximizing mutual information between Y and X, I(Y;X). When there is a latent class label C ∈ {1; : : : ;L} associated with X, we onsider the mutual information with respect to Y and C, I(Y ;C). New analytic expressions for the gradient of I(Y ;X) and I(Y ;C) are presented, with gradient performed with respect to the measurement matrix. Connections are made to the more widely studied Gaussian measurement model. Example results are presented for compressive topic modeling of a document corpora (word counting), and hyperspectral compressive sensing for chemical classification (photon counting).

Duke Authors

Cited Authors

  • Wang, L; Carlson, D; Rodrigues, MD; Wilcox, D; Calderbank, R; Carin, L

Published Date

  • January 1, 2013

Published In

International Standard Serial Number (ISSN)

  • 1049-5258

Citation Source

  • Scopus