Phys. Med. Biol. 42 (1997) 433–439. Printed in the UK PII: S0031-9155(97)75575-1 Validation of the central-ray approximation for attenuated depth-dependent convolution in quantitative SPECT reconstruction Zhengrong Liang, Juihsi Cheng and Jinghan Ye Departments of Radiology, Electrical Engineering and Computer Science, State University of New York, Stony Brook, NY 11794, USA Received 3 June 1996, in final form 20 August 1996 Abstract. In order to model photon attenuation and detector resolution variation as a depth-dependent convolution for efficient reconstruction of quantitative SPECT, a central-ray approximation is necessary. This work investigates the impact of the approximation upon reconstruction accuracy and computational efficiency. A patient chest CT image was acquired and converted into an object-specific attenuation map. From a segmentation of the map, an emission thorax phantom was constructed with a cardiac insert. To generate a system-specific resolution-variant kernel, a point source was measured at several depths from the surface of a low-energy, high-resolution, parallel-hole collimator of a SPECT system. Projections of parallel- beam geometry were simulated from the phantom, the map, and the kernel on an elliptical orbit. Reconstruction was performed by the ML-EM algorithm with and without the central-ray approximation. The approximation cuts down dramatically (more than 100 fold) the computing time with a negligible loss (less than 1%) of reconstruction accuracy. 1. Introduction Compensation for photon attenuation and detector resolution variation is a major component in reconstruction of quantitative SPECT (single-photon emission computed tomography) (Jaszczak 1988). While photon transportation within an attenuating body and photon detection by a collimator/detector SPECT system can be modelled by a projection equation (Liang 1992), inversion of the equation is very difficult (Riauka and Gortel 1994). Some assumptions and approximations are necessary for the inversion in order to implement quantitative SPECT for clinical use. A central-ray approximation has been implicitly assumed when analytical inversion of the projection equation was attempted for uniform attenuating media and depth-dependent detector response (Appledorn 1989, van Elmbt and Walrand 1993). We have applied the approximation for iterative inversion of the projection equation in the cases of non-uniform attenuating media (for example the chest) and variable detector response (Liang et al 1988, 1989). A very simple ray-tracing model was used to study the approximation. The model assumed a zero contribution to a detection bin if the centre of a voxel is out of the view of that bin, and otherwise a whole-voxel contribution to that bin. Although the central-ray approximation seems reasonable (less than 1% error by the simple model), it has been argued for a while whether the approximation has a significant impact on the reconstruction accuracy for a more realistic ray-tracing model. This work aims to use an accurate ray-tracing model for both the object-specific attenuation and the system-specific detector response to investigate the approximation on the reconstruction accuracy. 0031-9155/97/020433+07$19.50 c  1997 IOP Publishing Ltd 433