Variance Reduction on Randoms from delayed coincidence histograms for the HRRT

Abstract

A new algorithm for variance reduction on random coincidences (VRR) has been validated for the HRRT. VRR i s crucial to achieve quantitation for low statistics dynamic studies reconstructed with iterative methods based on ordinary Poisson model. On HRRT, VRR cannot be performed in projection space since individual LOR's are mixed after histogramming in parallel projection space using nearest neighbor approximation and axial compression. The proposed algorithm uses the classical random rate equation on the 4.5 1 0 9 LOR's. However, crystal singles are registered at block level and have lower deadtime than coincidences. Variations in layer identification with countrate were reported biasing random estimation from block singles. Our method overcomes these problems by estimating the singles per crystal from delayed coincidences. A singles map is created histogramming every delayed event into 2 singles. Each element represents the number of coincidences between that crystal and the ones in the 5 opposite coincident heads. The algorithm finds iteratively the crystal singles rates compatible with the delayed coincidence events. The method has been validated on decaying phantoms. We compared estimated and measured block singles to identify deadtime difference between singles and coincidences. Comparison of measured and estimated random at plane level in sinogram space confirms that the method is quantitative. The current HRRT software distribution implements the algorithm.