Statistically regulated and adaptive EM reconstruction for emission computed tomography

Iterative algorithms such as MLEM are rapidly becoming the standard for reconstruction in emission computed tomography. However, such algorithms require arbitrary stopping criteria, are sensitive to noise artifacts, and require accelerated implementations that may not work well for all imaging situations. We have investigated several new iterative algorithms with likelihood-based objective functions that use the concepts of statistically adaptive subsetting and spatially adaptive updates. The resulting statistically regulated expectation maximization (StatREM) algorithms are closely related to OSEM with the following exceptions: they apply spatially adaptive regularization and use statistically adaptive subsets to accelerate convergence in a controlled manner. Projection data are processed sequentially and internal statistically adaptive subsets are formed. When accumulated statistical power merits an update, e.g., determined by paired sample t-test, then spatially adaptive updates are applied and the corresponding test statistics and subset accumulations are reset. Reconstruction continues iteratively until no further statistically significant errors remain. The following properties were observed for clinical, phantom and simulated data: (1) user-defined test levels can provide statistically based stopping criteria; (2) recovery of spatial resolution is accelerated in high-count regions while low-count regions are regulated to reduce noise artifacts; (3) notable acceleration is achieved for large, sparse datasets [such as fully 3-D positron emission tomography (PET)]; and (4) resolution and contrast are superior to conventional OSEM at much lower noise levels. Statistically regulated expectation maximization algorithms may potentially provide a new archetype for PET and SPECT reconstruction.