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

Area of Science:

• Medical Imaging
• Detector Physics
• Computational Science

Background:

• Statistics-based positioning (SBP) offers intrinsic spatial resolution for continuous miniature crystal element (cMiCE) detectors.
• Previous SBP methods required postprocessing due to high computational and memory demands.

Purpose of the Study:

• To implement a real-time processing algorithm and hardware platform for SBP in cMiCE detectors.
• To overcome computational limitations of existing SBP techniques.

Main Methods:

• Developed an accelerated SBP algorithm using algebraic simplifications, fixed-point math, and hierarchical search.
• Implemented the optimized algorithm on a pipelined field-programmable gate array (FPGA).
• Utilized a commercially available prototype board for hardware implementation.

Main Results:

• Reduced computational load from >7 × 10^6 floating-point operations to < 5 × 10^3 integer operations per event.
• Achieved nearly identical FWHM positioning resolution (~1.6 mm) compared to exhaustive search methods.
• FPGA implementation processes >250 K events/second, exceeding detector coincidence rates.

Conclusions:

• The optimized SBP algorithm and FPGA platform enable real-time processing for cMiCE detectors.
• This advancement facilitates immediate data availability for image generation components.
• Distributed processing across individual detectors reduces computational load.