A Fast Reconstruction Algorthm for Stationary Positron Emission Tomography Based on a Modified EM Algorithm

Abstract
An efficient iterative reconstruction method for positron emission tomography (PET) is presented. The algorithm is basically an enhanced EM (expectation maximization) algorithm with improved frequency response. High-frequency components of the ratio of measured to calculated projections are extracted and are taken into account for the iterative correction of image density in such a way that the correction is performed with a uniform efficiency over the image plane and with a flat frequency response. As a result, the convergence speed is not so sensitive to the image pattern or matrix size as the standard EM algorithm, and nonuniformity of the spatial resolution is significantly improved. Nonnegativity of the reconstructed image is preserved. Simulation studies have been made assuming two PET systems: a scanning PET with ideal sampling and a stationary PET with sparse sampling. In the latter, a "bank array" of detectors is employed to improve the sampling in the object plane. The new algorithm provides satisfactory images by two or three iterations starting from a flat image in either case. The behavior of convergence is monitored by evaluating the root mean square of C(b)-1 where C(b) is the correction factor for pixel b in the EM algorithm. The value decreases rapidly and monotonically with iteration number. Although the theory is not accurate enough to assure the stability of convergence, the algorithm is promising to achieve significant saving in computation compared to the standard EM algorithm.