Nonparametric Response Function Estimation via FPCA with an Application to Dynamic Pet Data

• Activity Number: 108
• Type: Invited
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ci-Ren Jiang*+ and John Aston and Jane-Ling Wang
• Companies: Academia Sinica and University of Warwick and UC Davis
• Keywords: deconvolution ; functional principal component analysis ; positron emission tomography imaging ; smoothing

Abstract

In dynamic PET data analysis, injected radioactive tracer concentrations are measured over time to help understand functional processes in the body. Traditionally, parametric forms are assumed for the implied impulse response functions while estimating the concentration; however, these parametric assumptions are difficult to verify and may not hold. Therefore, we propose a nonparametric approach to estimate the response functions and thus the concentration. First, we employ FPCA with a multiplicative structure to represent the signal function for each voxel. As convolution can be viewed as a linear operator, we secondly apply deconvolution to the mean and eigenfunctions of the voxel signals. Then, the response function for each voxel can be represented as a linear combination of deconvolved mean function and deconvolved eigenfunctions where the linear coefficients are identical to the multiplicative coefficients and principal component scores in the first step. Therefore, the integral of the concentration in a finite time interval (a quantity of particular interest) can be obtained easily. This approach is demonstrated with simulation studies and real data analysis.