Wavelets for diffusion tensor imaging

In this paper, wavelet basis functions are investigated for their suitability for processing and analysing diffusion tensor imaging (DTI) data. First, wavelet theory is introduced and explained by means of 1d and 2d examples (Section 1.1 - 1.3). General thresholding techniques, which serve as regularization concepts for wavelet based models, are presented in Section 1.4. Regularization of DTI data can be performed at two stages, either immediately after acquisition (Wirestam et al., 2006) or after tensor estimation. The latter stage of denoising is outlined in Section 6 together with the incorporation of the positive definiteness constraint using log-Cholesky parametrization. In Section 3, the procedure is examined in a simulation study and compared to standard processing and the space-varying coefficient model (SVCM) based on B-spines (Heim et al., 2007). In addition, a real data example is presented and discussed. Finally, an approach is proposed how a space-varying coefficient model could fairly be adapted to wavelet basis functions. The theoretical parts are based on books of Gencay et al. (2002, Chap. 1, 4-6), Härdle et al. (1998), Ogden (1997) and Jansen (2001) if not stated otherwise. For an introduction to diffusion tensor imaging refer to Heim et al. (2007, Chap. 2).