Non-iterative quantitative SPECT reconstructions with a reduced-size system matrix

Our research objective is to design a clinically viable computational procedure that will provide quantitative activity distribution to be used in dosimetry calculations for internal radiotherapy (IRT). To this end, we studied the accuracy of images reconstructed with the qSPECT method which includes CT-based attenuation correction, 3D resolution recovery, and analytical scatter calculation. During these investigations we found that determination of object boundaries is often difficult due to the substantial edge "smoothing" caused by the MLEM reconstruction process which also created distortions in voxelized activity distributions. By contrast, methods based on direct matrix inversion may reconstruct sharper images. In parallel, it is well known fact that some tumor SPECT studies are characterized by an intense tracer uptake which is localized in a relatively small area, while the remaining parts of the body have only low background. That fact served as a motivation/justification for developing and testing of the non-iterative reconstruction technique based on solving the reduced system of equations. Special algorithm was designed to extract only this part of the initial system matrix which corresponds to the volume of interest (VOI) to be reconstructed. The penalized least squares approach with Tikhonov-type regularizer was employed to solve this reduced system. Preliminary comparison of our partial penalized least squares (PPLS) method with MLEM using Monte Carlo and analytical simulations of hot object with no or low (up to 11%) background shows improved accuracy of the activity estimation when using PPLS. In experiments with 11% background, this method, however, produces artifacts at the boundaries of the VOI. Nevertheless, even in these unfavorable situations it could be employed as an element (hidden from the clinical user) of quantitative data processing.