Iterative image reconstruction for positron emission tomography: a study of convergence and quantitation problems

Abstract

Iterative reconstruction techniques have been shown to have superior noise characteristics compared to conventional filtered backprojection (FB). The main drawbacks of the iterative methods are the increased computational burden and the difficulty in establishing a stopping criterion and ensuring proper quantitation in different imaging situations. Using a combination of techniques, we have been able to reduce the time required for iterative reconstruction to a few times that of FB. We have also compared the quantitation properties of FB to those of additive and multiplicative iteration formulas, including the Maximum Likelihood method (ML). Without acceleration, all three tested methods gave quantitative results after 40 iterations, regardless of the number of counts in the data. However, with noisy data, the best images in a leastsquares sense were obtained after typically 10-20 iterations.

Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies

“…Our results indicate a possible exception when using an MC matrix well matched to the tomograph. The results of Hoke et al [32], Llacer and Bajamonde [33], Liow and Strother [34], and Herman and Odhner [24] are all verified by our work. We find our results difficult to reconcile with those of Politte and Snyder [9].…”

“…For the highly modified MLE algorithm, they decided to stop at a fixed number of iterations. Holte et al [32] investigated the behavior of the MLE algorithm principally in cold spots. They found that noise in regions of low counts was lower than in regions of high counts, and that by iterating to a point where the high-count regions exhibited substantial noise, quantitation of cold spots was excellent.…”

Revisiting stopping rules for iterative methods used in emission tomography

“…While both theory and experiment indicate the monotonic increase of the likelihood function in the EM method, it is well-known that stopping at a smaller likelihood value, i.e. not at the maximum for the likelihood, can give a higher quality solution [6][7][8][9]. Stopping the iteration before convergence in this way is necessary but appears to conflict with the appropriate notation for PET imaging is provided.…”

Comparison of Reconstruction Methods in a Small Animal Cardiac Positron Emission Tomography Study Using a 18F-Labeled Myocardial Agent, [18F] FPTP

“…Iterative approaches include maximum likelihood-expectation maximization (ML-EM) and ordered subsets expectation maximization (OSEM). ML-EM imaging generates higher-quality images than FBP, with less noise (3)(4)(5). However, the disadvantage of ML-EM is that it requires long convergence time.…”