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Clinical Imaging of Microwave Mammography

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A hardware architecture using finite-field arithmetic for computing maximum-likelihood estimates in emission

H R Klotz¹, D L Snyder

¹McDonnell Douglas Astronaut. Co., St. Louis, MO.

IEEE Transactions on Medical Imaging

|January 1, 1988

Summary

A novel hardware architecture speeds up positron-emission tomography (PET) image reconstruction using the expectation-maximization algorithm. This innovation enables faster computation of maximum-likelihood estimates from time-of-flight measurements for clinical applications.

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Area of Science:

Medical Imaging
Computer Architecture
Signal Processing

Background:

Positron-emission tomography (PET) imaging requires computationally intensive algorithms for accurate radionuclide distribution estimation.
Existing methods for maximum-likelihood estimation (MLE) using the expectation-maximization (EM) algorithm can be time-consuming, limiting clinical utility.
Time-of-flight (TOF) measurements in PET offer improved image quality but increase computational demands.

Purpose of the Study:

To propose a specialized hardware architecture for accelerating the EM algorithm in PET image reconstruction.
To enable computation of MLE from TOF measurements within clinically relevant timeframes.
To optimize the calculation of 2D convolutions through parallel processing and number-theoretic transforms.

Main Methods:

The proposed architecture converts 2D convolutions into parallelizable 1D convolutions.
Number-theoretic transforms (NTTs) are employed for efficient evaluation of 1D convolutions.
Finite-field arithmetic, specifically using small digits in a Galois field, is utilized for numerical calculations to enhance parallelism and manage field size.

Main Results:

The hardware architecture achieves O(N) operations for an NxN 2D convolution.
A single iteration of the EM algorithm can be computed in approximately 100 ms for N=128 with 32 view angles.
The approach effectively balances computational efficiency with the complexity of PET image reconstruction.

Conclusions:

The developed hardware architecture significantly accelerates PET image reconstruction by optimizing the EM algorithm.
This acceleration is achieved through parallelized 1D convolutions, NTTs, and finite-field arithmetic.
The proposed system has the potential to significantly improve the clinical workflow and diagnostic capabilities of TOF-PET imaging.