A Simplified EM Reconstruction Algorithm for TOFPET

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Abstract
A simplified expectation-maximization (EM) algorithm for image reconstruction in positron emission tomography with time-of-flight information (TOFPET) has been developed. This new method requires substantially less computation time than the estimated posterior-density weighting (EPDW) method developed by Snyder and Politte [1,2]. Mathematically, the integration of TOFPET images at different angles yields a 2-D image which is the convolution of the true image and a rotationally symmetric point spread function (PSF). The new method uses this PSF to construct the probability functions and employs the summed TOFPET image as the incomplete data set in the expectation step of the EM algorithm; thus, the time-costly angle-by-angle operations required in EPDW are reduced to a single operation, cutting the processing time by a factor of approximately l/M for an image reconstruction using M projection angles. Results from computer simulation studies suggest that this new method may offer image quality superior to that produced by other algorithms.