Learning a Secondary Source From Compressive Measurements for Adaptive Projection Design

Abstract

Recent work has established that the gradient of the mutual information (MI) in Gaussian channels with input noise can be used for projection design in a compressive sensing (CS) scenario with two independent, Gaussian mixture (GM)- distributed inputs. The resulting CS projection matrices have been shown to be capable of controlling the input-output MI terms for the two inputs. One downside of such information-theoretic strategies is their reliance on access to a priori knowledge of the input source statistics. In this paper, we assume that the GM distribution of a primary input is known and that the GM distribution of a secondary input is unknown. We derive a methodology for the online training of the distribution of the secondary input via compressive measurements and illustrate that once the distribution of this secondary source is known, we can use projection design to control the input-output MI of the system. We demonstrate through simulations the various performance trade-offs that exist within the proposed methodology.