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Ci-Ren Jiang

2012-12-21
16:30:00 - 17:20:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Positron Emission Tomography (PET) is an imaging technique that can be used to investigate the chemical changes in human biological processes such as cancer development or neurochemical reactions. Two approaches to the analysis of PET time course data will be presented in this talk. In the first approach, the PET time course data are smoothed by borrowing information across space and accounting for this pooling through the use of a nonparametric covariate adjustment. A new model for functional data analysis, the Multiplicative Nonparametric Random Effects Model, is introduced to more accurately account for the variation in the data. This preprocessing step to smooth the data then allows subsequent analysis by methods such as Spectral Analysis to be substantially improved in terms of their mean squared error. Most dynamic PET scans are currently analyzed based on the assumption that linear first order kinetics can be used to adequately describe the system under observation. However, there has recently been strong evidence that this is not the case. Therefore, we propose a non-parametric deconvolution and analysis model for dynamic PET data based on functional principal component analysis that is free from this compartmental assumption. This yields flexibility in the possible deconvolved functions which still performing well when a linear compartmental model setup is the true data generating mechanism. As the deconvolution needs to be performed on only a relative small number of basis functions rather than voxel by voxel in the entire 3-D volume, the methodology is both robust to typical brain imaging noise levels while also being computationally efficient.