# Methods for Improving Image Quality for Contour and Textures Analysis Using New Wavelet Methods
## 3 Results  
The results obtained by simulations show that the use of this algorithm leads to an improvement of the filtered image quality both from the PSNR point of view and visually. This can also be seen from the data presented in Table 2. The results show that the implementation of the Wiener filter in the wavelet domain by using the wavelet transformation in packets leads to weaker results in PSNR terms than the implementation using the wavelet dyadic transformation but ensures better conservation of contours. Another possible Wiener filter structure in the wavelet domain, based on the mediated Wiener filter, is shown in Figure 3. Due to its structure, we will call this structure iterated Wiener filter. Table 5 shows the results obtained by implementing the iterated Wiener filter. The gain of this filter in terms of improving the image quality evaluated in terms of PSNR is insignificant starting with the second stage of processing, but by performing several processing steps (iterations) is gained in terms of contour quality. The simulations performed on many images highlighted the efficiency of implementing the Wiener filter in the transformed domain when this domain is the wavelet domain. If better performance is achieved by using the empirical Wiener filter in the wavelet domain due to the superior properties of the wavelet transformation in terms of energy compaction in as few coefficients as possible, the success of multiple, mediated, and iterated Wiener filters is due to the possibility that the domain wavelet provides it in terms of choosing the basis for signal representation. Figure 3: Modified Wiener filter in the wavelet domain (schematic of the iterated Wiener filter). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Processing Stage**} & \multirow{2}{*}{**Wavelet Coefficients**} & \multicolumn{2}{c}{**Lena**} & \multicolumn{2}{c}{**Bridge**} \\ \cline{3-6}  & & **PSNR** & **C** & **PSNR** & **C** \\  & & **(dB)** & **(\%)** & **(dB)** & **(\%)** \\ \hline Initial & - & 26.04 & 62.97 & 26.12 & 66.41 \\ \hline Estimated & & & & & \\ solution by soft & Daubechies 4 & 29.76 & 60.49 & 27.52 & 62.45 \\ truncation & & & & & \\ \hline Stage 1 & Coifman 6 & 30.84 & 63.92 & 27.80 & 63.77 \\ \hline Stage 2 & Coifman 12 & 31.10 & 64.52 & 27.84 & 63.49 \\ \hline Stage 3 & Daubechies 6 & 31.13 & 65.15 & 27.88 & 63.86 \\ \hline Stage 4 & Daubechies 8 & 31.09 & 65.08 & 27.84 & 63.03 \\ \hline Stage 5 & Daubechies & 31.17 & 65.76 & 27.89 & 63.02 \\  & 12 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results obtained by using the iterated Wiener filter. The test images were 256 \(\times\) 256 pixels. It should be noted that in almost all images, the reduction of noise is also accompanied by an improvement of the contours of the processed image, given that usually the reduction of noise is accompanied by a degradation of the contours. Wiener filters have the property of reducing noise in images and enhancing contours, being used in deconvolution applications to remove or reduce blurring. Using together the proposed Wiener filter in the wavelet domain and a cellular neural network we obtain an adaptive improvement of the images and the restoration of the contours. The method of improving the contours and textures of images resulting from processing with the Wiener filter proposed in the article (Figure 4), followed by the application of the NCN algorithm, using the AB template, improves the contours of images by equalizing and adapting the histogram. Additionally, the evaluation of the performance of the processing process presented above can be done if we evaluate the image resulting after edge detection, for an initial image without noise but with low contrast, the image obtained by global scaling and the image obtained after preprocessing with AB template (Figures 5 and 6). Thus, it is found that edge detection is correct and robust only in the image obtained by global scaling and in the image obtained after preprocessing with the AB template.