Convergent algorithms for statistical image reconstruction in emission tomography.

Emission computed tomography (ECT), including positron emission tomography (PET) and single photon emission computed tomography (SPECT), is a medical imaging technique that provides functional information about physiological processes. The goal of ECT is to reconstruct the distribution of the radioisotopes in the body by measuring the emitted photons. Statistical image reconstruction methods have shown improved image quality over conventional nonstatistical methods by using accurate physical models and appropriate noise models. However, statistical methods require huge computation and complex modeling. So computationally efficient algorithms and simple yet accurate statistical models are essential. First, we develop fast and convergent algorithms for statistical image reconstruction. Ordered subsets or incremental gradient type algorithms have been popular due to their fast initial convergence rates. However, they do not converge to a solution in general. We achieve global convergence by two methods: relaxation and incremental optimization transfer principles. Those two families of algorithms are provably convergent yet converge fast. We apply the algorithms to emission and transmission tomography and to simulation and real PET data. Secondly, we develop statistical models for randoms-precorrected PET. Accidental coincidence (AC) events, or randoms, are one of primary sources of background noise in PET. Most PET scanners are corrected for AC events by real-time subtraction of delayed window coincidences. Although the randoms-precorrection compensates in mean for AC events but destroys the usual Poisson statistics, complicating statistical reconstruction. We propose new likelihood approximations that allow negative sinogram values without requiring zero-thresholding. Analysis and simulation results show that the new statistical model is nearly free of systematic bias yet keeps low variance. Finally, we analyze the parameterization of time activity curves (TACs) in dynamic imaging. We provide approximate expressions for the covariance matrix of kinetic parameter estimators based on TAC reconstructions when TACs are modeled as a linear combination of temporal basis functions such as B-splines. The approximations are useful tools for assessing and optimizing the temporal basis functions for TACs.PhDApplied SciencesBiomedical engineeringElectrical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/124609/2/3150144.pd