AN ANALYTICAL APPROACH TO QUANTITATIVE RECONSTRUCTION OF NONUNIFORM ATTENUATED BRAIN SPECT

An analytical approach to quantitative brain SPECT (Single-photon-emis sion computed tomography) with non-uniform attenuation is developed. T he approach formulates accurately the projection-transform equation as a summation of primary- and scatter-photon contributions. The scatter contribution can be estimated using the multiple-energy-window sample s and removed from the primary-energy-window data by subtraction. The approach models the primary contribution as a convolution of the atten uated source and the detector-response kernel at a constant depth from the detector with the central-ray approximation. The attenuated Radon transform of the source can be efficiently deconvolved using the dept h-frequency relation. The approach inverts exactly the attenuated Rado n transform by Fourier transforms and series expansions. The performan ce of the analytical approach was studied for both uniform- and non-un iform-attenuation cases, and compared to the conventional FBP (filtere d-backprojection) method by computer simulations. A patient brain x-ra y image was acquired by a CT (computed-tomography) scanner and convert ed to the object-specific attenuation map for 140 keV energy. The math ematical Hoffman brain phantom was used to simulate the emission sourc e and was resized such that it was completely surrounded by the skull of the cr attenuation map. The detector-response kernel was obtained f rom measurements of a point source at several depths in air from a par allel-hole collimator of a SPECT camera. The projection data were simu lated from the object-specific attenuating source including the depth- dependent detector response. Quantitative improvement (>5%) in reconst ructing the data was demonstrated with the nonuniform attenuation comp ensation, as compared to the uniform attenuation correction and the co nventional FBP reconstruction. The commuting time was less than 5 min on an HP/730 desktop computer for an image array of 128(2) x 32 from 1 28 projections of 128 x 32 size.