# 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 c c c c c c} \hline \hline \(r\) & _db1_ & _db2_ & _db3_ & _db4_ & _db5_ & _db6_ & _db7_ & _db8_ & _db9_ & _db10_ \\ \hline
7 & 0.9999 & 0.9999 & 0.9996 & 0.9994 & 0.9987 & 0.9986 & 0.9982 & 0.9970 & 0.9953 \\
8 & 1.0000 & 1.0000 & 0.9999 & 0.9999 & 0.9999 & 0.9997 & 0.9996 & 0.9997 & 0.9992 & 0.9993 \\
9 & 1.0000 & 1.0000 & 1.000 Experimental results (_SSIM_) of 3D tomographic 16-bit image \"Wmri\" DWT by using bit-width \(r\) of symlets filters coefficients. Experimental results (_PSNR_, dB) of 3D tomographic 16-bit image \"Body_1.0\" DWT by using  
\"Truf_COR\" (12-bit) and \"Body_1.0\" (16-bit) for various bit-width \(r\) and numbers \(k\) = 6, 12, 18, 24, 30 of wavelets _coif_(\(k/6\)) filters coefficients are presented in Tables 25-30. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \(r\) & _sym1_ & _sym2_ & _sym3_ & _sym4_ & _sym5_ & _sym6_ & _sym7_ & _sym8_ & _sym9_ & _sym10_ \\ \hline
9 & 0.9998 & 0.9998 & 0.9991 & 0.9990 & 0.9979 & 0.9982 & 0.9967 & 0.9954 & 0.9917 & 0.9944 \\
10 & 1.0000 & 1.0000 & 0.9998 & 0.9998 & 0.9995 & 0.9995 & 0.9992 & 0.9992 & 0.9984 & 0.9985 \\
11 & 1.0000 & 1.0000 & 1.0000 & 0.9999 & 0.9999 & 0.9999 & 0.9998 & 0.9998 & 0.9996 & 0.9995 \\
12 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 0.9999 & 1.0000 & 0.9999 & 0.9999 \\
13 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 \\ \hline \end{tabular}
\end{table} 
Table 21: Experimental results (_PSNR_, dB) of 3D tomographic 12-bit image “Trufi_COR” DWT by using bit-width \(r\) of symlets filters coefficients. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \(r\) & _sym1_ & _sym2_ & _sym3_ & _sym4_ & _sym5_ & _sym6_ & _sym7_ & _sym8_ & _sym9_ & _sym10_ \\ \hline
7 & 0.999 & 0.9999 & 0.9996 & 0.9991 & 0.9994 & 0.9990 & 0.9974 & 0.9976 & 0.9970 & 0.9969 \\
8 & 1.0000 & 1.0000 & 0.9999 & 0.9998 & 0.9998 & 0.9997 & 0.9996 & 0.9993 & 0.9994 \\
9 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 0.9999 & 1.0000 & 0.9999 & 0.9999 & 0.9998 & 0.9996 \\
12 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 \\ \hline \end{tabular}
\end{table} 
Table 22: Experimental results (_SSIM_) of 3D tomographic 12-bit image “Trufi_COR” DWT by using bit-width \(r\) of symlets filters coefficients. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \(r\) & _sym1_ & _sym2_ & _sym3_ & _sym4_ & _sym5_ & _sym6_ & _sym7_ & _sym8_ & _sym9_ & _sym10_ \\ \hline
9 & 0.9996 & 0.9995 & 0.9981 & 0.9980 & 0.9955 & 0.9964 & 0.9932 & 0.9905 & 0.9825 & 0.9886 \\
10 & 0.9999 & 0.9999 & 0.9996 & 0.9996 & 0.9990 & 0.9989 & 0.9984 & 0.9983 & 0.9966 & 0.9968 \\
11 & 1.0000 & 1.0000 & 1.0000 & 0.9999 & 0.9998 & 0.9998 & 0.9997 & 0.9997 & 0.9991 & 0.9988 \\
12 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 0.9999 & 0.9999 & 0.9998 & 0.9998 & 0.9998 \\
13 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 \\ \hline \end{tabular}
\end{table} 
Table 23: Experimental results (_PSNR_, dB) of 3D tomographic 16-bit image “Body_1.0” DWT by using bit-width \(r\) of symlets filters coefficients. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \(r\) & _sym1_ & _sym2_ & _sym3_ & _sym4_ & _sym5_ & _sym6_ & _sym7_ & _sym8_ & _sym9_ & _sym10_ \\ \hline
9 & 0.9996 & 0.9995 & 0.9981 & 0.9980 & 0.9955 & 0.9964 & 0.9932 & 0.9905 & 0.9825 & 0.9886 \\
10 & 0.9999 & 0.9999 \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(r\) & _coif1_ & _coif2_ & _coif3_ & _coif4_ & _coif5_ \\ \hline
9 & 0.9995 & 0.9976 & 0.9940 & 0.9870 & 0.9873 \\
10 & 0.9999 & 0.9995 & 0.9987 & 0.9973 & 0.9966 \\
11 & 1.0000 & 0.9998 & 0.9998 & 0.9994 & 0.9994 \\
12 & 1.0000 & 1.0000 & 1.0000 & 0.9999 & 0.9999 \\
13 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 \\ \hline \hline \end{tabular}
\end{table} 
Table 27: Experimental results (_PSNR_, dB) of 3D tomographic 12-bit image “Trufi_COR” DWT by using bit-width \(r\) of coiflets filters coefficients.