Fast, accurate and shift-varying line projections for iterative reconstruction using the GPU

Maximum-Likelihood Estimation With a Contracting-Grid Search Algorithm

A fast search algorithm capable of operating in multi-dimensional spaces is introduced. As a sample application, we demonstrate its utility in the 2D and 3D maximum-likelihood position-estimation problem that arises in the processing of PMT signals to derive interaction locations in compact gamma cameras. We demonstrate that the algorithm can be parallelized in pipelines, and thereby efficiently implemented in specialized hardware, such as field-programmable gate arrays (FPGAs). A 2D implementation of the algorithm is achieved in Cell/BE processors, resulting in processing speeds above one million events per second, which is a 20× increase in speed over a conventional desktop machine. Graphics processing units (GPUs) are used for a 3D application of the algorithm, resulting in processing speeds of nearly 250,000 events per second which is a 250× increase in speed over a conventional desktop machine. These implementations indicate the viability of the algorithm for use in real-time imaging applications.

Bayesian reconstruction of photon interaction sequences for high-resolution PET detectors

Realizing the full potential of high-resolution positron emission tomography (PET) systems involves accurately positioning events in which the annihilation photon deposits all its energy across multiple detector elements. Reconstructing the complete sequence of interactions of each photon provides a reliable way to select the earliest interaction because it ensures that all the interactions are consistent with one another. Bayesian estimation forms a natural framework to maximize the consistency of the sequence with the measurements while taking into account the physics of gamma-ray transport. An inherently statistical method, it accounts for the uncertainty in the measured energy and position of each interaction. An algorithm based on maximum a posteriori (MAP) was evaluated for computer simulations. For a high-resolution PET system based on cadmium zinc telluride detectors, 93.8% of the recorded coincidences involved at least one photon multiple-interactions event (PMIE). The MAP estimate of the first interaction was accurate for 85.2% of the single photons. This represents a two-fold reduction in the number of mispositioned events compared to minimum pair distance, a simpler yet efficient positioning method. The point-spread function of the system presented lower tails and higher peak value when MAP was used. This translated into improved image quality, which we quantified by studying contrast and spatial resolution gains.