Towards analytical solution for 3D SPECT reconstruction with non-uniform attenuation and distance-dependent resolution variation: A Monte Carlo simulation study

Based on Kunyansky's and our previous work, an efficient, analytical solution to the reconstruction problem of myocardial perfusion SPECT has been developed that allows simultaneous compensation for non-uniform attenuation, scatter, and system-dependent resolution variation, as well as suppression of signal-dependent Poisson noise. To avoid reconstructed images being corrupted by the presence of Poisson noise, a Karhunen-Loeve (K-L) domain adaptive Wiener filter is applied first to suppress the noise in the primary- and scatter-window measurements. The scatter contribution to the primary-energy-window measurements is then removed by our scatter estimation method, which is based on the photon detection energy spectrum and a triple-energy-window acquisition protocol. The resolution variation is corrected by a depth-dependent deconvolution, which, being based on our central-ray approximation and a distance-frequency relation, deconvolves the scatter-free data with a measured accurate detector-response kernel in frequency domain. Finally, the deblurred projection data are analytically reconstructed with compensation for non-uniform attenuation by an algorithm based on Novikov's explicit inversion formula. The preliminary Monte Carlo simulation results using a realistic human thoracic phantom demonstrate that, for parallel-beam geometry, the proposed analytical reconstruction scheme is computationally comparable to filtered backprojection and quantitatively equivalent to iterative maximum a posteriori expectation-maximization reconstruction. Extension to other geometries is under progress.