PDF (5143 kByte) - WIAS

a) b) c) d)
FIGURE 4. Color coded FA maps for example 1 a) for noise-free data, b) for
noisy data, c) after smoothing the noisy data with the proposed method but using
non-adaptive weights only, d) after position-orientation adaptive smoothing
the noisy data as proposed here.
a) b)
c) d)
FIGURE 5. Estimated tensor mixture model [Tabelow et al., 2012] a) for noisefree
data, b) for noisy data, c) after position-orientation adaptive smoothing as
proposed in this paper, d) after smoothing with structural adaptation as proposed
previously [Tabelow et al., 2008].
Experimental data. Due to the very high resolution of the experimental diffusion weighted data
the SNR for this data set is very low, see Figure 6(a) for a color coded FA map of some axial slice
for one subject. However, the position-orientation adaptive smoothing method proposed in this
paper using the described choices of parameters (see example code in Appendix B for explicit
values) and k ⋆ = 12 iteration steps results in an apparent improvement of the tensor estimates
without blurring the fine structures observed in diffusion weighted imaging, see Figure 6(b). The
previous version of our method explicitly based on the diffusion tensor model [Tabelow et al.,
2008] is not able to remove much of the noise in this data set, see Figure 6(c). The reason
is that the former algorithm relies on the diffusion tensor model known to be wrong for large
parts of the brain. It obviously fails for very low SNR. For comparison of the results of the
smoothing algorithm with a kind of ground truth the measured data set contains four repeated
measurements which can lead to a largely improved SNR, see Figure 6(d). This data set with
repeated measurements can also be smoothed using the proposed method (Figure 6(e)) and
the DTI based algorithm (Figure 6(f)) with apparent improvements. By visual inspection, the
11