Information Driven Angular Sampling for Reliable and Efficient SPECT Imaging

Low radiopharmaceutical dose and reduced scan time for molecular medical tomographic imaging are pursued for wider and safer medical applications. Towards this goal we propose an analytical approach to optimally reduce scanning duration or radiopharmaceutical dose for Single Photon Emission Computed Tomographic (SPECT) techniques, while not compromising on reconstructed image accuracy and reconstruction stability. In addition, we provide statistical guarantees to ensure generalization. This is achieved by: (a) utilizing the observation model and Fisher information driven scan strategy, (b) coordinating scanning with point spread function and prior of the reconstruction algorithm, and (c) providing statistical guarantees on reconstructed image variance through the Cramer-Rao bound. Our approach distributes the given total scanning duration optimally across scan angles to minimize Mean Square Error for a given image reconstruction algorithm. It coordinates the duration at each scan angle to ensure optimal information flow to the chosen reconstruction algorithm. For maximum likelihood (ML) estimators we derive a globally optimal closed form equation for angular sampling, and for maximum a posteriori (MAP) estimators we show the optimization problem is a difference of convex functions which can be efficiently optimized. The efficacy of the proposed scanning strategy is quantified through Monte Carlo simulations using real SPECT images and synthetic phantoms. The proposed algorithm achieves more than 2 dB PSNR improvement over conventional uniform scanning approach for real SPECT images. This improvement could be traded in to achieve more than 50% reduction in scan duration.