Collaborative Computational Project in Positron Emission Tomography
and Magnetic Resonance imaging

Seminar from Michel Defrise


Title: Linear estimators for the calibration of timing offsets and timing resolution in TOF PET.


The time-of-flight (TOF) measurements in PET are usually calibrated by measuring a dedicated activity source such as a rotating rod source. Data driven calibration methods can be applied with arbitrary sources such as patient data. They are useful when a routine monitoring of the timing is desired or when the positioning or geometry of a dedicated phantom is not known with accuracy. Following Werner and Karp we consider the class of data driven methods based on the property that the non-TOF data obtained by summing all time bins are not affected by timing errors. Reconstructing and forward projecting these non-TOF data yields for each line of response (LOR) a synthetic TOF profile, which is compared with the measured TOF profile to estimate the timing offset of each detector. One approach uses a non-linear iterative estimation applied to fan-sums of LORs. A simpler and numerically more efficient approach uses a non-iterative linear least-squares fit similar to that used for the calibration with dedicated phantoms. We prove that this linear method yields an unbiased estimate of the timing offsets, which, under some conditions, achieves the Cramer-Rao lower bound (CRB) for the variance of unbiased estimators. These conditions are never strictly satisfied in practice but this result allows to identify for which type of sources the proposed method is close to optimal, as will be illustrated with simulated data. We also describe a linear estimator of the timing resolution of the detectors, and explain why this problem is very poorly conditioned


Michel Defrise received the Ph.D. degree in theoretical physics from the University of Brussels in 1981. He is currently emeritus professor in the Department of nuclear medicine of the Vrije Universiteit Brussel. His research interests include 3-D image reconstruction in nuclear medicine (PET and SPECT) and in CT. He is Fellow of the IEEE and of the Institute of Physics, and was a recipient in 2011 of the Edward J Hoffman Medical Imaging Senior Scientist Award of the IEEE and of the Edward J Hoffman Memorial Award of the Society of Nuclear Medicine.


Where: Engineering Front Executive Suite 103, UCL Engineering Front Building, TORRINGTON PLACE, London, WC1E 7JE

Remote attendance:

Friday, March 6, 2020 - 09:45 to 10:45
Seminar from Michel Defrise on Linear estimators for the calibration of timing offsets and timing resolution in TOF PET.