Statistical image reconstruction algorithms using paraboloidal surrogates for PET transmission scans.

Positron Emission Tomography (PET) is a diagnostic imaging tool that provides images of radioactive substances injected into the body to trace biological functions. The radioactive substance emits a positron which annihilates with an electron to produce two 511 keV photons traveling in approximately opposite directions to be coincidentally detected by two detectors. Many photons are absorbed or scattered, reducing the number of detected emission events. Attenuation correction is crucial for quantitatively accurate PET reconstructions. PET transmission scans are performed to estimate attenuation parameters which are in turn used to correct the emission scans for attenuation effects. The noise in estimating the attenuation parameters propagates to the emission images affecting their quality and quantitative correctness. Thus, attenuation image reconstruction is extremely important in PET. Conventional methods of attenuation correction are suboptimal and ignore the Poisson nature of the data. We propose to use penalized likelihood Image reconstruction techniques for transmission scans. Current algorithms for transmission tomography have two important problems: (1) they are not guaranteed to converge, (2) if they converge, the convergence is slow. We develop new fast and monotonic optimization algorithms for penalized likelihood image reconstruction based on a novel paraboloidal surrogates principle. We present results showing the speed of the new optimization algorithms as compared to previous ones. We apply the algorithms to PET data obtained from an anthropomorphic thorax phantom and real patient data. A transmission scan performed after the patient is injected is called a post-injection transmission scan. Post-injection transmission scans are desirable since the patient throughput is increased and motion artifacts are reduced as compared to pre-injection scans. However, there are emission counts contaminating the measurements. We include emission contamination in the post-injection transmission measurement statistical model and obtain better images as compared to conventional subtraction based approaches. We also present a joint estimation technique to estimate attenuation and emission images simultaneously from transmission and emission scans. We analyze noise propagation from transmission scans to emission images for some sequential image reconstruction methods. The results show that transmission noise affects emission image quality heavily, especially when short transmission scans are utilized.Ph.D.Applied SciencesBiomedical engineeringElectrical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/132124/2/9959750.pd