# Methods for Improving Image Quality for Contour and Textures Analysis Using New Wavelet Methods
## 2 Materials and Methods
### Multiple Wiener Filter in Wavelet Domain  
The simulations performed showed that the performances obtained by using the Wiener filter in the wavelet domain, described in Section 2.3, depend on the pair of wavelet coefficients (Wiener filter estimate) used. At the same time, the use of the empirical Wiener filter in the wavelet domain leads to the improvement of the image quality obtained by soft truncation of the wavelet coefficients when it is used as an estimate both in terms of PSNR and in terms of contour conservation. However, there are cases when there is no improvement in contours. The quality of contours is especially important in the perception of images by the human visual system [43], so obtaining with the reduction of noise and an improvement in terms of contours and textures is an important goal in image processing. The fact that not the same wavelet coefficients provide the best results for all images is explainable by the fact that different signals can best be represented by different wavelet bases, an idea that underlies both compression and reduction algorithms of noise and  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{**Soft Truncation of**} & & & & & & \\  & & & & **Wavelet Coefficients** & & & & & & & \\  & & & **with Optimal** & &  
texture analysis. Likewise, different signals are poorly represented by different wavelet bases. From the analysis of the data presented in Table 1, it is possible to choose for the implementation of the Wiener filter such a wavelet base so that the signal is poorly represented with its help, in which case the performance of filtering and highlighting contours and textures will be poorer. To avoid such a situation, we propose a new Wiener filter in the wavelet domain, the structure of which is shown in Figure 2. The same estimated solution, obtained by soft modification of the wavelet coefficients, is processed in parallel by several Wiener filters in the wavelet domain. Each filter being implemented using other wavelet coefficients, and the outputs of these filters are mediated. Results obtained using this type of filter show that the use of such a filter achieves a stronger improvement in image quality while improving contours and textures, compared to the case of the Wiener empirical wavelet filter. In the implementation that was performed according to this scheme, only seven types of wavelet coefficients were used (Haar, Daubechies4, Daubechies6, Daubechies8, Daubechies12, Coifman6, and Coifman12) and dyadic wavelet transform were used. However, the simulations show that by using several types of wavelet coefficients the results obtained are better. The fact that the Wiener filter implemented using the wavelet transform in packets leads to better results in terms of preserving contours and highlighting textures compared to the Wiener filter implemented using the dyadic wavelet transform, and the latter leads to better results in PSNR terms, suggests the idea of mediation of the images obtained through the two filters. The results obtained by implementing such a filter, which we call the _mediated Wiener filter_, much more efficient in terms of computational effort than the multiple Wiener filter, are presented in Table 3. It is observed that superior results are obtained compared to those obtained by using each of the two filters that form it. As can be seen from the analysis of the data in Tables 2 and 3, the mediated Wiener filter leads to results close to those obtained by using the multiple Wiener filter but requires a much smaller volume of calculations. This can be considered an example of the trade-off between the performance of the filtering process and the computational effort required. At the output of the filter in Figure 2, for a better reconstruction of the contours and textures in the images, the result obtained after the Wiener mediated filter can be introduced in a _nonlinear cellular network (NCN) algorithm_. Figure 2: The proposed architecture for the multiple Wiener filter in the wavelet domain.