Nonlinear Modeling and Processing Using Empirical Intrinsic Geometry with Application to Biomedical Imaging

Ronen Talmon, Yoel Shkolnisky, Ronald R. Coifman

Abstract: In this paper we present a method for intrinsic modeling of nonlinear filtering problems without a-priori knowledge using empirical information geometry and empirical differential geometry. We show that the inferred model is noise resilient and invariant under different random observations and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements. Based on this model, we present a Bayesian framework for nonlinear filtering, which enables to optimally process real signals without predefined statistical models. An application to biomedical imaging, in which the acquisition instruments are based on photon counters, is demonstrated; we propose to incorporate the temporal information, which is commonly ignored in existing methods, for image enhancement.