Comparison of 2D Wavelets 3D Wavelets and JPEG

This section presents some compression results using two 3D image data sets. The first is a 3D MR brain data set obtained with a GE 5x Sigma Scanner with 26 images and a slice distance of 6 mm. Each image is 256 x 256 x 12 bits. The second set is a 3D CT spine from a GE CT scanner with 69 images and a slice distance of 3 mm. Each image is 512 x 512 x 12 bits. The 3D wavelet, 2D wavelet, and JPEG compression were applied to

FIGURE 8 Compression ratio versus RMSE for three different filter banks in the slice direction. (a) CT knee image set with 1-mm slice distance. (b) CT knee image set with 5-mm slice distance.

each data set. The 2D wavelet compression was implemented with the 9/7 filter bank in x and y, applied to each slice. Figures 9a and 9b compare the performance of 3D wavelet and JPEG algorithms, and Figs 9c and 9d compare the 3D and 2D wavelet compression. In these curves, the compression ratio is given as a function of equivalent peak signal-to-noise ratio (EPSNR), defined as

FIGURE 8 Compression ratio versus RMSE for three different filter banks in the slice direction. (a) CT knee image set with 1-mm slice distance. (b) CT knee image set with 5-mm slice distance.

where fwin is the display window width of the image that depends on its modality and type of image.

Figure 10 shows the original and decompressed images of the CT spine compressed at a 20:1 ratio using the 3D wavelet, the 2D wavelet, and JPEG methods. Figures 11a, 11b, and 11c show the difference images between the original and the decompressed images for the 3D wavelet, 2D wavelet, and JPEG, respectively. In order to emphasize the differences, a window in the spine region is used (Fig. 10a). The difference images shown here have been processed by adding a gray level of 128 and multiplying by 5. The 3D difference image has the smallest visual discrepancy. The 2D difference image (Fig. 11b) shows granular noise similar to that in the 3D difference image, but with larger granules and higher amplitude. The JPEG difference image (Fig. 11c) has larger errors in high frequency regions (spine regions) than the 3D wavelet difference image. Also, the JPEG difference image clearly shows block artifacts that are typical at relatively high compression ratios with JPEG.

In general, the difference image of a wavelet-compressed image has uniform error in all regions. This is due to the fact that wavelets operate at multiple resolutions and the filters can accommodate the representation of small textural elements, edges as well as homogeneous regions. The 3D wavelet compression has better performance than the 2D wavelet compression because the former utilizes information in three orientations and can take advantage of the data structure and redundancies in the z direction as well.

FIGURE 9 3D wavelet compression vs JPEG: (a) MR brain image set with 6-mm slice distance, (b) CT spine image set with 3-mm slice distance. 3D wavelet compression vs 2D wavelet compression: (c) MR brain image set, (d) CT spine image set.

Original

FIGURE 10 One slice of a CT image set compressed at ratio of 20:1 using the 3D and 2D wavelet algorithms and JPEG. (a) Original image, (b) compressed with the 3D wavelet method, (c) compressed with the 2D wavelet method, (d) compressed with JPEG.

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FIGURE 11 The spinal column portion of the difference images obtained after compression using (a) the 3D wavelet method, (b) the 2D wavelet method, (c) JPEG. The original image is shown in Fig. 10a within the rectangle.
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