Space-Varying Coefficient Models for Diffusion Tensor Imaging using 3d Wavelets

In this paper, the space-varying coefficients model on the basis of
B-splines (Heim et al., (2006)) is adapted to wavelet basis
functions and re-examined using artificial and real data. For an
introduction to diffusion tensor imaging refer to Heim et al.
(2005, Chap. 2). First, wavelet theory is introduced and explained
by means of 1d and 2d examples (Sections 1.1 { 1.3). Section 1.4 is
dedicated to the most common thresholding techniques that serve as
regularization concepts for wavelet based models. Prior to
application of the 3d wavelet decomposition to the space-varying
coe cient elds, the SVCM needs to be rewritten. The necessary steps
are outlined in Section 2 together with the incorporation of the
positive de niteness constraint using log-Cholesky parametrization.
Section 3 provides a simulation study as well as a comparison with
the results obtained through B-splines and standard kernel
application. Finally, a real data example is presented and
discussed. The theoretical parts are based on books of Gen cay et
al. (2002, Chap. 1, 4-6), Härdle et al. (1998), Ogden (1997) and
Jansen (2001) if not stated otherwise.