Reconstructing uniformly attenuated rotating slant-hole SPECT projection data using the DBH method

This work applies a previously developed analytical algorithm to the reconstruction in a rotating multi-segment slant-hole (RMSSH) SPECT system. The RMSSH SPECT data of a digital NCAT phantom with breast attachment are modeled as the uniformly attenuated Radon transform of the activity distribution. These data are reconstructed using an analytical algorithm called the DBH method, which is an acronym for the procedure of differentiation and backprojection followed by a finite weighted Hilbert transform. The projection data are first differentiated along a specific direction and then backprojected to the image space. The result from the first step is equal to a one-dimensional finite weighted Hilbert transform of the object; this transform is then numerically inverted to obtain the reconstructed image. With the limited common volume-of-view (CVOV) of the RMSSH collimator, the detector captures gamma photon emissions from the breast and from parts of the torso. A conventional filtered backprojection algorithm only reconstructs the high frequency components of the activity function. The DBH method is capable of exactly reconstructing the activity within a well defined region-of-interest (ROI) within the breast. Quantitative accuracy is shown in this ROI from the simulation results.