Differential attenuation method for simultaneous estimation of activity and attenuation in multiemission single...

A penalized weighted least squares reconstruction algorithm is described that 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 single photon emission computed tomography imaging isotope with emissions at two or more distinct energies, after accurate compensation 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 201T1 projection data from a single-slice numerical cardiac phantom with and without cold myocardial defects. 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 reduce the sensitivity of the solution to noise in the projection data. These included: (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 data. The combined effect of these techniques substantially reduced the compute time required for the reconstruction.