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 ~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 × 127 bin LUT implementation, these algorithm improvements result in a reduction from > 7 × 10
⁶
floating-point operations per event for an exhaustive search to < 5 × 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.