A maximum likelihood expectation maximization algorithm with thresholding.

The maximum likelihood expectation maximization (MLEM) algorithm has several advantages over the conventional filtered back-projection (FBP) for image reconstruction. However, the slow convergence and the high computational cost for its practical implementation have limited its clinical applications. This study proposes the incorporation of a thresholding technique in both the MLEM and ordered subsets EM (OSEM) algorithm to accelerate convergence. The threshold is set to c*m, where m is the mean pixel value of the whole image. The reconstruction time is proportional to the total number of pixels, so a thresholding technique that nullifies the value of a pixel if it falls below a threshold, can effectively remove the non-active pixels and substantially accelerate reconstruction. Preliminary tests on simulated PET data reveal that the thresholding technique accelerates the convergence rate and reduce error in the reconstructed image. The reconstruction performance improves with the increase of the threshold level and the MSE reaches minimum for c value equals to about 1.