Generalized matrix inverse reconstruction for SPECT using a weighted singular value spectrum

A method of weighting the singular value spectrum for SPECT image reconstruction with generalized matrix inverses (GMIs) has been developed, for the purpose of obtaining more localized source activity estimates than can be obtained with the use of a truncated spectrum. At each source voxel, spectral weights are computed to minimize the misfit of the resolution kernel with an ideal unit response (discretized delta function), subject to a constraint on the variance of the reconstructed source activity. This method was applied to a Monte Carlo simulated Tc-99m myocardial perfusion study and a Tc-99m myocardial perfusion phantom study acquired on a clinical scanner. GMI reconstructions using weighted and truncated spectra were compared. Resolution kernels for a weighted spectrum are narrower and have smaller sidelobes than kernels for a truncated spectrum. As a result, with the use of a weighted spectrum the resolution of reconstructed SPECT images is improved, the simulated myocardial wall thickness is better estimated and reconstructed activity is smoother in regions of uniform activity. The use of a weighted singular value spectrum is an important tool for obtaining more localized source activity estimates with GMI reconstruction.