A differential attenuation method for simultaneous estimation of SPECT activity and attenuation distributions

A penalized weighted least squares (PWLS) reconstruction algorithm is described which simultaneously estimates activity and attenuation distributions from emission sinogram data alone. This estimation technique is based on differential attenuation information and is applicable to any SPECT imaging isotope with emissions at two or more distinct energies, after compensating for Compton scatter. A rotation-based forward projector is used to efficiently model photon attenuation at multiple emission energies, as well as distance-dependent spatial resolution. The algorithm was tested using simulated scatter-free ²⁰¹Tl projection data from a single-slice numerical cardiac phantom with a large cold myocardial defect. Poisson noise was added to the projection data to mimic clinically realistic count densities. The activity estimates resulting from the proposed method had fewer artifacts and were substantially more accurate than images reconstructed with filtered backprojection without compensation for attenuation. Several techniques were employed to reduce the time required for the iterative routine to converge and to improve the stability of the solution, including: (1) a preconditioning image variable transformation; (2) a coarse-to-fine grid initialization schedule; and (3) a convex hull image mask determined directly from the projection data. The combined effect of these techniques was a reduction in compute time by a factor of ~200