Maximum-Likelihood Estimation With a Contracting-Grid Search Algorithm

Abstract

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.