TY - GEN
T1 - Nonlinear modeling and processing using empirical intrinsic geometry with application to biomedical imaging
AU - Talmon, Ronen
AU - Shkolnisky, Yoel
AU - Coifman, Ronald R.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
KW - Intrinsic model
KW - differential geometry
KW - information geometry
KW - nonlinear dynamical systems
KW - nonparametric estimation
UR - http://www.scopus.com/inward/record.url?scp=84884943117&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-642-40020-9_48
DO - https://doi.org/10.1007/978-3-642-40020-9_48
M3 - منشور من مؤتمر
SN - 9783642400193
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 441
EP - 448
BT - Geometric Science of Information - First International Conference, GSI 2013, Proceedings
T2 - 1st International SEE Conference on Geometric Science of Information, GSI 2013
Y2 - 28 August 2013 through 30 August 2013
ER -