This section includes the results from homomorphic filtering experiments performed on the PD-Weighted MRI volume of Data Set 1 (see Chapter 8). The goal of the experiments is to determine the suitability of homomorphic filtering using a low pass filter for RF correction. To this end, qualitative and quantitative measures are used.
The qualitative measure takes the form of a ``before and after'' sequence of images. The purpose of this sequence is to highlight artifacts (if any) introduced by the filtering technique.
The quantitative measures include a tissue intensity profile graph and a tissue intensity variance. These measures were described in Section 2.3.
Filtering should flatten the intensity profile in all dimensions so that the average voxel intensity for each tissue type is close to constant. Consequently the variance should be reduced.
The WiT igraph shown in Figure 6.4 was used to homomorphic filter Data Set 1. The function of each operator in the igraph is listed in Table 6.1.
Figure 6.4: Spatial domain homomorphic filter
using a low pass filter.
Table 6.1: A brief description of
the operators used in the homomorphic filtering igraph.
Figure 6.5 shows slice 14 of Data Set 1 before and after homomorphic filtering using low pass filtering. The intensity variation due to RF inhomogeneity appears to have been reduced.
Figure 6.5: Results of homomorphic
filtering. (a) before, (c) after. (b) shows the output of mriBlurVolume for 
.
Figure 6.6 shows the tissue intensity profiles before and after homomorphic filtering. The intensity variances have obviously been reduced. Table 6.2 shows the actual change in variances.
Figure 6.6: Tissue intensity profiles before
and after homomorphic filtering.
Table 6.2: Tissue intensity variances
before and after homomorphic filtering.
Operating on Data Set 1, the igraph of Figure 6.4 ran in about 4 minutes on a Sun SPARC 5 with 16 MBytes of RAM.