The Barankin Bound for Time Estimation in TOF-PET

IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), vol. 299, pp. 1–4

Abstract

Data quality in TOF-PET depends on the accuracy of the detector time resolution (DTR). Given a model of the time distribution of the optical photons emission and of the photon transport and detection, the best achievable DTR can be obtained from a lower bound on the variance of any unbiased estimator of the interaction time of the incident annihilation photon. With current detectors hundreds of optical photons are typically detected and the Cramer-Rao bound (CRB) can be used because of its asymptotic tightness property. With some novel fast detectors involving e.g. Cerenkov photons the emission rate is low and the CRB yields an over-optimistic value of the DTR. We revisit the Barankin bound [1] (BB) originally proposed by Gorman and Hero [2] in this context. Using simulated data for a bi-exponential model of the emission we show that the BB is close to tight even when less than 10 photons are detected.

Authors 6

1. Michel Defrise

   Vrije Universiteit Brussel

   Affiliation as printed

   Vrije Universiteit,Department of Nuclear Medicine,Brussel,Belgium

   Department of Nuclear Medicine, Vrije Universiteit, Brussel, Belgium

2. Johan L. Nuyts

   KU Leuven

   Affiliation as printed

   KU Leuven, University of Leuven,Nuclear Medicine and Molecular Imaging; Medical Imaging Research Center (MIRC),Department of Imaging and Pathology,Belgium

   Department of Imaging and Pathology, Nuclear Medicine and Molecular Imaging

3. Emilie Roncali

   University of California, Davis

   Affiliation as printed

   UC Davis,Department of Biomedical Engineering and Department of Radiology,California,USA

   Department of Biomedical Engineering and Department of Radiology, UC Davis, California, USA

4. Carlotta Trigila

   University of California, Davis

   Affiliation as printed

   UC Davis,Department of Biomedical Engineering and Department of Radiology,California,USA

   Department of Biomedical Engineering and Department of Radiology, UC Davis, California, USA

5. S. Gundacker Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Germany

   RWTH Aachen University, Germany

6. Paul R. Lecoq

   Universitat Politècnica de València

   Affiliation as printed

   Polytechnic University of Valencia,Spain

   Polytechnic University of Valencia, Spain