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

A special-purpose hardware architecture is proposed to implement the expectation-maximization algorithm to compute, in clinically useful times, the maximum-likelihood estimate of a radionuclide distribution for a positron-emission tomogram from time-of-flight measurements. Two-dimensional convolutions required for forming the estimate are converted into a series of one-dimensional convolutions that can be evaluated in parallel. Each one-dimensional convolution is evaluated using a number-theoretic transform. All numerical calculations are performed using finite-field arithmetic. To avoid the use of large finite fields and to increase parallelism, each convolution is performed by a series of convolutions with small digits in a Galois field. The hardware architecture allows a two-dimensional convolution of dimension NxN to be formed with O(N) operations, permitting one iteration of the expectation-maximization algorithm to be formed in approximately 100 ms when N=128 and the number of view angles is 32.