Use of geometric prior information in Bayesian tomographic image reconstruction: a preliminary report

Jorge Llacer; Bart M. ter Haar Romeny; Max A. Viergever

doi:10.1117/12.130892

9 December 1992 Use of geometric prior information in Bayesian tomographic image reconstruction: a preliminary report

Jorge Llacer, Bart M. ter Haar Romeny, Max A. Viergever

Proceedings Volume 1768, Mathematical Methods in Medical Imaging; (1992) https://doi.org/10.1117/12.130892
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

In this paper we examine the possibility of using pure geometrical information from a prior image to assist in the reconstruction of tomographic data sets with lower number of counts. The situation can arise in dynamic studies, for example, in which the sum image from a number of time frames is available, defining desired regions-of-interest (ROFs) with good accury, and the time evolution of uptake in those ROl's needs to be obtained from the low count individual data sets. The prior information must be purely geometrical in such a case, so that the activity in the ROFs of the prior does not influence the estimated uptake from the individual time frames. It is also desired that the prior does not impose any other conditions on the reconstructions, i.e., no smoothness or deviation from a known set of values is desired. We amKk this problem in the framework of Vision Response Functions (VRFs), based on the work done by JJ. Koenderink inUtrecht. WeshowthatthereareassembliesofVRFsthatcanbepresentedinaformthatisinvariantwithrespecttorotations and translations and that some functions of those invariants can convey the desired geometric prior information independent of the level of ativity in the ROFs, except at very low levels. Preliminary results based on a one-dimensional reconstruction problem will be presented. Using the zero crossings of the Gaussian derivative form of the LaplaCian of a prior image at different scales, a variant of the EM algorithm has been found that allows the reconstruction of low count data sets with those priors. At this time, this involves using a modified Conjugate Gradient (CG) maximization method for the M-step of the algorithm. The results show that the distorted shapes of reconstructions of data sets with low counts are effectively corrected by the method, although many questions exist at this time about basic and computational issues.

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Jorge Llacer, Bart M. ter Haar Romeny, and Max A. Viergever "Use of geometric prior information in Bayesian tomographic image reconstruction: a preliminary report", Proc. SPIE 1768, Mathematical Methods in Medical Imaging, (9 December 1992); https://doi.org/10.1117/12.130892

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