Scanning Linear Estimation: Improvements over Region of Interest (ROI) Methods

摘要

In tomographic medical imaging, signal activity is typically estimated by summing voxels from a reconstructed image. We introduce an alternative estimation scheme that operates on the raw projection data and offers a substantial improvement, as measured by the ensemble mean-square error (EMSE), when compared to using voxel values from a maximum-likelihood expectation-maximization (MLEM) reconstruction. The scanning-linear (SL) estimator operates on the raw projection data and is derived as a special case of maximum-likelihood (ML) estimation with a series of approximations to make the calculation tractable. The approximated likelihood accounts for background randomness, measurement noise, and variability in the parameters to be estimated. When signal size and location are known, the SL estimate of signal activity is an unbiased estimator, i.e., the average estimate equals the true value. By contrast, standard algorithms that operate on reconstructed data are subject to unpredictable bias arising from the null functions of the imaging system. The SL method is demonstrated for two different tasks: 1) simultaneously estimating a signal's size, location, and activity; 2) for a fixed signal size and location, estimating activity. Noisy projection data are realistically simulated using measured calibration data from the multi-module multi-resolution (M³R) small-animal SPECT imaging system. For both tasks the same set of images is reconstructed using the MLEM algorithm (80 iterations), and the average and the maximum value within the ROI are calculated for comparison. This comparison shows dramatic improvements in EMSE for the SL estimates. To show that the bias in ROI estimates affects not only absolute values but also relative differences, such as those used to monitor response to therapy, the activity estimation task is repeated for three different signal sizes.