Design of an FPGA-Based Algorithm for Real-Time Solutions of Statistics-Based Positioning

We report on the implementation of an algorithm and hardware platform to allow real-time processing of the statistics-based positioning (SBP) method for continuous miniature crystal element (cMiCE) detectors. The SBP method allows an intrinsic spatial resolution of similar to 1.6 mm FWHM to be achieved using our cMiCE design. Previous SBP solutions have required a postprocessing procedure due to the computation and memory intensive nature of SBP. This new implementation takes advantage of a combination of algebraic simplifications, conversion to fixed-point math, and a hierarchal search technique to greatly accelerate the algorithm. For the presented seven stage, 127 x 127 bin LUT implementation, these algorithm improvements result in a reduction from > 7 x 10(6) floating-point operations per event for an exhaustive search to < 5 x 10(3) integer operations per event. Simulations show nearly identical FWHM positioning resolution for this accelerated SBP solution, and positioning differences of <0.1 mm from the exhaustive search solution. A pipelined field programmable gate array (FPGA) implementation of this optimized algorithm is able to process events in excess of 250 K events per second, which is greater than the maximum expected coincidence rate for an individual detector. In contrast with all detectors being processed at a centralized host, as in the current system, a separate FPGA is available at each detector, thus dividing the computational load. These methods allow SBP results to be calculated in real-time and to be presented to the image generation components in real-time. A hardware implementation has been developed using a commercially available prototype board.