# Analysis of the Quantization Noise in Discrete Wavelet Transform Filters for 3D Medical Imaging
## 3 Results
### Experiments of the 3D Medical Tomographic Images DWT
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(r\) & _coif1_ & _coif2_ & _coif3_ & _coif4_ & _coif5_ \\ \hline
10 & 58.14 & 52.30 & 48.76 & 46.38 & 45.24 \\
11 & **62.21** & 56.20 & 56.34 & 52.78 & 53.00 \\
12 & 67.16 & **62.90** & **64.06** & **60.82** & 59.41 \\
13 & 75.02 & 71.54 & 68.84 & 65.25 & **64.93** \\
14 & 85.17 & 77.12 & 74.73 & 72.81 & 72.40 \\
15 & 99.11 & 87.99 & 83.32 & 81.23 & 80.64 \\
16 & 126.33 & 103.94 & 95.26 & 92.00 & 88.75 \\
17 & \(\infty\) & \(\infty\) & 121.68 & 109.44 & 101.44 \\
18 & \(\infty\) & \(\infty\) & \(\infty\) & \(\infty\) & \(\infty\) \\ \hline \hline \end{tabular}
\end{table} 
Table 28: Experimental results (_SSIM_) of 3D tomographic 12-bit image “Trufi_COR” DWT by using bit-width \(r\) of coiflets filters coefficients. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(r\) & _coif1_ & _coif2_ & _coif3_ & _coif4_ & _coif5_ \\ \hline
9 & 33.91 & 27.72 & 24.02 & 20.62 & 21.25 \\
10 & **40.58** & 34.26 & 30.54 & 27.99 & 27.35 \\
11 & 44.93 & 38.35 & 38.25 & 34.55 & 35.28 \\
12 & 50.59 & **45.41** & **46.59** & **43.00** & **41.96** \\
13 & 61.35 & 55.11 & 52.12 & 48.07 & 48.21 \\
14 & \(\infty\) & 66.81 & 58.76 & 56.43 & 56.52 \\
15 & \(\infty\) & \(\infty\) & \(\infty\) & 99.82 & 96.81 \\
16 & \(\infty\) & \(\infty\) & \(\infty\) & \(\infty\) & \(\infty\) \\ \hline \hline \end{tabular}
\end{table} 
Table 25: Experimental results (_PSNR_, dB) of 3D tomographic 8-bit image “wmri” DWT by using bit-width \(r\) of coiflets filters coefficients. Experimental results (\(PSNR\), dB) of various 3D tomographic 12-bit grayscale images DWT by wavelet \(db4\) with bit-width \(r=11\) of filters coefficients are presented in Table 34 and in Figure 8. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**BPC** & **PSNR, dB** & **Results** & _cof1_ & _cof2_ & _cof3_ & _cof4_ & _cof5_ \\ \hline \multirow{4}{*}{8} & \multirow{4}{*}{40} & Calculation & 12 & 13 & 13 & 14 & 14 \\  & & Experimental & 10 & 12 & 12 & 12 & 12 \\  & & Difference & 2 & 1 & 1 & 2 & 2 \\ \cline{2-8}  & & \multirow{4}{*}{\(\infty\)} & Calculation & 14 & 15 & 15 & 16 & 16 \\  & & Experimental & 14 & 15 & 15 & 16 & 16 \\  & & Difference & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{12} & \multirow{4}{*}{60} & Calculation & 15 & 16 & 17 & 17 \\  & & Experimental & 11 & 12 & 12 & 12 & 13 \\  & & Difference & 4 & 4 & 5 & 5 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 33: Minimum values of \(r\), at which the result of 3D tomographic images DWT by coiflets reaches high and maximum quality. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**BPC** & **PSNR, dB** & **Results** & _sym1_ & _sym2_ & _sym4_ & _sym6_ & _sym8_ & _sym10_ \\ \hline \multirow{4}{*}{8} & \multirow{4}{*}{40} & Calculation & 11 & 11 & 12 & 13 & 13 \\  & & Experimental & 10 & 10 & 11 & 11 & 12 & 12 \\  & & Difference & 1 & 1 & 1 & 2 & 1 & 1 \\ \cline{2-8}  & \multirow{4}{*}{\(\infty\)} & Calculation & 13 & 13 & 14 & 15 & 15 & 15 \\  & & Experimental & 13 & 13 & 14 & 15 & 15 & 15 \\  & & Difference & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{12} & \multirow{4}{*}{60} & Calculation & 14 & 14 & 15 & 16 & 17 & 17 \\  & & Experimental & 10 & 10 & 11 & 12 & 12 & 13 \\  & & Difference & 4 & 4 & 4 & 4 & 5 & 4 \\ \hline \multirow{4}{*}{16} & \multirow{4}{*}{\(\infty\)} & Calculation & 16 & 17 & 18 & 19 & 19 & 19 \\  & & Experimental & 16 & 16 & 16 & 17 & 18 & 18 \\  & & Difference & 0 & 1 & 2 & 2 & 1 & 1 \\ \hline \multirow{4}{*}{16} & \multirow{4}{*}{80} & Calculation & 17 & 18 & 19 & 20 & 20 & 20 \\  & & Experimental & 8 & 8 & 9 & 9 & 10 & 10 \\  & & Difference & 9 & 10 & 10 & 11 & 10 & 10 \\ \hline \multirow{4}{*}{16} & \multirow{4}{*}{\(\infty\)} & Calculation & 20 & 21 & 22 & 23 & 23 & 24 \\  & & Experimental & 16 & 16 & 16 & 17 & 18 & 18 \\ \cline{1-1}  & & Difference & 4 & 5 & 6 & 6 & 5 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 32: Minimum values of \(r\), at which the result of 3D tomographic images DWT by symlets reaches high and maximum quality. results. This confirms the accuracy of theoretical analysis.