Slices Correlation Regularization for Attenuation Map Reconstruction Using Only Emission Data with Data Consistency Conditions and a “knowledge Set”

Previously we developed algorithm to obtain transmission reconstructions from emission data without transmission measurements. The optimal basis set of “knowledge set” was used to create an approximate attenuation map, and the expansion coefficients were estimated using optimization algorithm. Since a truncated expansion does not represent an image precisely, the estimated coefficients can be unstable in the presence of systematic errors. This problem is illposed. Therefore, regularization methods are necessary for reconstruction. Previously a constraint, based on distribution of the expansion coefficients of single slice, was explored. Additional information can be extract from the fact that adjacent transmission slices have a similar structure. In this paper, a constraint based on this similarity of expansion coefficients is considered, making the reconstruction problem fully 3D. It was shown that slices correlation can further improve the quality of emission images.