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52 Three-Dimensional Image Compression with Wavelet Transforms TABLE 3 Five best wavelet filters for CT and MR image compression"

Filter banks Filter coefficients

9/7 ho 0.026749, - 0.016864, - 0.078223,0.266864,0.602949,0.266864, - 0.078223, - 0.016864,0.026749

g0 0.045636, - 0.028772, - 0.295636,0.557543, - 0.295636, - 0.028772,0.045636

13/11 h0 - 0.00599119,0.00265816,0.03343325, - 0.02367046, - 0.04870418,0.27101229,0.54252426,0.27101229,

- 0.04870418, - 0.02367046,0.03343325,0.00265816, - 0.00599119 g0 0.01002830,0.00444934, - 0.07688893, - 0.04890542,0.31686063,0.58891216,0.31686063, - 0.04890542, - 0.07688893, 0.00444934, 0.01002830

17/11 h0 0.00134975, - 0.00135360, - 0.01201420,0.00843901,0.03516647, - 0.05463331, - 0.06650990,0.29754791,0.58401575,0.29754791,

- 0.06650990, - 0.05463331,0.03516647,0.00843901, - 0.01201420, - 0.00135360,0.00134975

0.01020092,0.01023007, - 0.05566486, - 0.02854447,0.29546394,0.53662880,0.29546394, - 0.02854447, - 0.05566486,0.01023007, 0.01020092

Daubechies20 0.026670057901, 0.188176800078, 0.527201188932, 0.688459039454, 0.281172343661, - 0.249846424327, - 0.195946274377,

0.127369340336, 0.093057364604, - 0.071394147166, - 0.029457536822, 0.033212674059, 0.003606553567, - 0.010733175483, 0.001395351747, 0.001992405295, - 0.000685856695, - 0.000116466855, 0.000093588670, - 0.000013264203

Coiflet 6 - 0.00169185102, - 0.00348787622, 0.01919116068, 0.02167109464, - 0.09850721332, - 0.05699742448, 0.45678712217, 0.78931940900,

0.38055713085, - 0.07043874879, - 0.056514193868,0.03640996261,0.00876013071, - 0.01119475927, - 0.001921335414, 0.00204138098, 0.00044583040, - 0.00021625728, 0.0004458303975, - 0.00021625728

"The first three are biorthogonal and the last two are orthogonal.

coefficients. The first three filter banks are biorthogonal, and the last two are orthogonal. The second column in Table 3 presents the filter coefficients. For the biorthogonal filter banks, both low-pass h0 and high-pass g0 filters are listed. For the orthogonal filter banks, only the low-pass coefficients are given since the high-pass filter can be easily obtained from the low-pass filter using the orthogonality property as follows:

The performance of the wavelet filters listed in Table 3 was evaluated using the sample images described in Tables 1 and 2. The quality of the compression is often measured with the root-mean-square error (RMSE) between the original image f(x, y, z) and the image f.(x, y, z) reconstructed after compression such that i E Lf(x> y>z) -fc(x> y> z)]2>|1/2

where — is the total number of pixels in the image.

The comparative study indicated that compression was similar with all five filters, but the three biorthogonal filter banks slightly outperformed the orthogonal filter banks.

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