Wavelet Filters for the Interslice Direction

Sample Images for Evaluation of Wavelet Filters

Since the pixel sizes in the x and y directions are very different from the slice distances, the best filter bank used in the slice direction may be different from that of the x and y directions. The best filters for the interslice direction were determined using 12 different 3D image data sets from various anatomical and imaging modalities as described in Table 4. The first column in the table is the name for each image set where the first two letters represent the image modality and the next two letters represent the anatomy. The last letter, a or c, in the MR sets stands for axial or coronal, respectively. As indicated in the fourth column, the slice distance varies from 1 to 7 mm.

Evaluation of Wavelet Filter Banks

With a fixed filter bank in the x and y directions, for example, the 9/7, the performance of different wavelet filters can be evaluated by applying them to the z-direction of the 3D image sets described in Table 4. The three best filters for the z direction were the 9/7, Daubechies4 (D4) [1], and Haar [11]. Figure 8 shows an example of the compression results for two different CT knee image sets at 1-mm and 5-mm slice distances. The two image sets were from the same patient, but two different studies. The compression ratios obtained by applying the 9/7 wavelet to the image set with a 1-mm slice distance were better than those of the D4 and Haar (Fig. 8a). In contrast, the Haar wavelet seems to perform better for image sets with 5-mm slice distances (Fig. 8b). This figure also indicates that for the same RMSE, thinner slice distances yield a higher compression ratio.

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