This work applies a previously developed analytical algorithm to the reconstruction problem in a rotating multi-segment slant-hole (RMSSH) SPECT system. The RMSSH collimator has greater detection efficiency than the parallel-hole collimator with comparable spatial resolution at the expense of limited common volume-of-view (CVOV) and is therefore suitable for detecting low-contrast lesions in breast, cardiac and brain imaging. The absorption of gamma photons in both the human breast and brain can be assumed to follow an exponential rule with a constant attenuation coefficient. In this work, 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 backprojection followed by a finite weighted inverse Hilbert transform. The projection data are first differentiated along a specific direction in the projection space and then backprojected to the image space. The result from this 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 CVOV of the RMSSH collimator, the detector captures gamma photon emissions from the breast and from parts of the torso. The simulation results show that the DBH method is capable of exactly reconstructing the activity within a well-defined region-of-interest (ROI) within the breast if the activity is confined to the breast or if the activity outside the CVOV is uniformly attenuated for each measured projection, while a conventional filtered backprojection algorithm only reconstructs the high frequency components of the activity function in the same geometry.
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