# Methods for Improving Image Quality for Contour and Textures Analysis Using New Wavelet Methods
## 2 Materials and Methods
### Multiple Wiener Filter in Wavelet Domain
NCN algorithms will contribute to the reconstruction of damaged contours by using the interpolation function if the values are known only to a part of the image elements which, in most cases, are arranged irregularly, and it is necessary to obtain the missing elements by calculation. Basically, an observer who is not familiar with the original image does not even notice that the image has been restored. The output image will have the same size and resolution as the input image. At the same time, by reconstructing the contours in the images it is possible to obtain special effects, removing parts unwanted, highlighting textures, or analyzing multiresolution objects in images. In principle, there may be similarities in the way an image is processed in the case of NCN contour reconstruction and filtering. However, these two processing approaches are differentiated by the fact that in the case of restoring the contours of images with RNC the unknown portions may be larger in size, which generally do not contain any information, while in the case of noise reduction and preservation of the contours, the image pixels contain information that also includes additive noise. Conjugated Use of the Invariant Wavelet Transform in Translation and Wiener Filtering in the Wavelet Domain to Improve the Image Quality Obtained by Soft Truncation of the Wavelet Coefficients  
The obtained results show that both the use of the translation invariant wavelet transform and the Wiener filtering in the wavelet domain led to the improvement of the image quality obtained by soft truncation of the wavelet coefficients. The combined use of the two efficient filtering techniques in the wavelet domain is expected to lead to superior results of each. In this sense, we proposed and tested two schemes for combining the two methods. The first scheme (which we call scheme A) of the combined use of the two methods consists in using the image obtained by applying the soft truncation in the invariant version to translation as an estimate for the multiple Wiener filter. The second schematic scheme (which we call scheme B) consists in the implementation of the multiple Wiener filter in invariant version at translation. The results obtained are presented in Table 4. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & & & \multicolumn{3}{c}{**Wiener Filter in**} & & & \\  & & & & **Wavelet** & & & **the Wavelet** & & & & \\  & & & & **Coefficients with** & & & **Domain** & & & & \\
**Images** & \(\sigma\) & & & **Optimal** & & & **Using the Dyadic** & & & & \\  & & & & **Threshold Values** & & & & **Wavelet** & & & \\  & & & & & **Transform** & & & & & & \\ \cline{2-10}  & & **PSNR** & **C** & **PSNR** & **C** & **PSNR** & **C** & **PSNR** & **C** & **PSNR** & **C** \\  & & **(dB)** & **(\%)** & **(dB)** & **(\%)** & **(dB)** & **(\%)** & **(dB)** & **(\%)** & **(dB)** & **(\%)** \\ \hline
**Einstein** & 0.05 & 26.10 & 50.99 & 30.25 & 51.42 & 31.18 & 51.82 & 31.01 & 52.59 & 31.44 & 52.74 \\ \hline
**Goldhill** & 0.05 & 26.04 & 58.25 & 29.09 & 57.94 & 29.54 & 59.63 & 29.44 & 59.69 & 29.84 & 60.04 \\ \hline
**Aerial** & 0.05 & 20.07 & 70.83 & 28.15 & 68.82 & 28.41 & 68.90 & 28.41 & 62.89 & 28.75 & 69.85 \\ \hline
**Peppers** & 0.05 & 26.09 & 63.25 & 30.18 & 60.55 & 30.94 & 62.64 & 30.65 & 61.55 & 31.18 & 62.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results obtained by using the Wiener mediated filter. As can be seen from the data presented in Table 4, Scheme B ensures in all cases the best results, but this scheme also requires the largest number of calculations. At the same time, it is observed that in the case of rich detail images (Aerial), the use of the invariant wavelet transformation in translation leads, for an approximately equal number of calculations, to better results than the multiple Wiener filter. Instead, it ensures better results for smoother images.