A three-dimensional ray-driven attenuation, scatter and geometric responsecorrection technique for SPECT in inhomogeneous media

The qualitative and quantitative accuracy of SPECT images is degraded by ph ysical factors of attenuation, Compton scatter and spatially varying collim ator geometric response. This paper presents a 3D ray-tracing technique for modelling attenuation, s catter and geometric response for SPECT imaging in an inhomogeneous attenua ting medium. The model is incorporated into a three-dimensional projector-b ackprojector and used with the maximum-likelihood expectation-maximization algorithm for reconstruction of parallel-beam data. A transmission map is u sed to define the inhomogeneous attenuating and scattering object being ima ged. The attenuation map defines the probability of photon attenuation betw een the source and the scattering site, the scattering angle at the scatter ing site and the probability of attenuation of the scattered photon between the scattering site and the detector. The probability of a photon being sc attered through a given angle and being detected in the emission energy win dow is approximated using a Gaussian function. The parameters of this Gauss ian function are determined using physical measurements of parallel-beam sc atter line spread functions from a non-uniformly attenuating phantom. The 3 D ray-tracing scatter projector-backprojector produces the scatter and prim ary components. Then, a 3D ray-tracing projector-backprojector is used to m odel the geometric response of the collimator. From Monte Carlo and physical phantom experiments, it is shown that the bes t results are obtained by simultaneously correcting attenuation, scatter an d geometric response, compared with results obtained with only one or two o f the three corrections. It is also shown that a 3D scatter model is more a ccurate than a 2D model. A transmission map is useful for obtaining measurements of attenuation and scatter in SPECT data, which can be used together with a model of the geome tric response of the collimator to obtain corrected images with quantitativ e and diagnostically accurate information.