The Mu-Tau-Sigma model for SPECT reconstruction

Summary form only received as follows: The Mu-Tau-Sigma model accurately describes 3D SPECT imaging including the effect of constant attenuation (mu), distance-dependent collimator blurring (tau), and the intrinsic resolution of the gamma camera (sigma). An approximate analytic inversion algorithm is derived for this model that is accurate up to second order in the parameters mu and tau. The algorithm is not iterative, is explicitly 3D, and has been implemented with execution times less than 4 times those of filtered back projection (<60 seconds for 128×128×128 voxel reconstructions). The algorithm does not have the low spatial-frequency cutoff exhibited by the Tretiak-Metz algorithm and, therefore, is relatively immune to noise. Because the algorithm compensates for collimator blurring, reconstructions with equivalent resolution can be achieved with collimators of lower resolution. The extra sensitivity provided by the lower resolution collimators permits a 500% increase in counts (with resulting decrease in noise). Alternatively, one can use the current high-resolution collimators and improve the resolution of the reconstruction. For the mu-tau-sigma reconstruction, preliminary results indicate that a third possibility, increasing the angular sampling of the SPECT acquisition, may be better than decreasing the noise in each projection