Abstract
The ML-EM (maximum likelihood expectation maximization) algorithm is the most popular image reconstruction method when the measurement noise is Poisson distributed. This short paper considers the problem that for a given noisy projection data set, whether the ML-EM algorithm is able to provide an approximate solution that is close to the true solution. It is well-known that the ML-EM algorithm at early iterations converges towards the true solution and then in later iterations diverges away from the true solution. Therefore a potential good approximate solution can only be obtained by early termination. This short paper argues that the ML-EM algorithm is not optimal in providing such an approximate solution. In order to show that the ML-EM algorithm is not optimal, it is only necessary to provide a different algorithm that performs better. An alternative algorithm is suggested in this paper and this alternative algorithm is able to outperform the ML-EM algorithm.
Highlights
The maximum likelihood (ML)-expectation maximization (EM) algorithm became popular in the field of medical image reconstruction in the 1980s [1][2]
The ML-EM algorithm became popular in the field of medical image reconstruction in the 1980s [1][2]
Besides Poisson noise modeling, it guarantees that the resultant image is non-negative and the total photon count of the forward projections of the resultant image is the same as the total photon count of the measured projections
Summary
The ML-EM (maximum likelihood expectation maximization) algorithm became popular in the field of medical image reconstruction in the 1980s [1][2]. This algorithm considers the Poisson noise model and finds wide applications in PET (positron emission tomography) and SPECT (single photon emission computed tomography). The ML-EM algorithm will converge to a maximum likelihood solution. The ML-EM algorithm first converges towards the true solution, and diverges away from it. The final maximum likelihood solution is too noisy to be useful. One approach is to apply a post lowpass filter on the converged noisy image, but one has to determine an ad hoc lowpass filter
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