# Methods for Improving Image Quality for Contour and Textures Analysis Using New Wavelet Methods
## 4 Conclusions  
The article presents two powerful procedures for improving images obtained by soft truncation of wavelet coefficients correlated with nonlinear cellular network. The first method consists in using the invariant wavelet transform in translation, and the second in designing Wiener filters in the wavelet domain that use as an estimate the image obtained by soft truncation of the wavelet coefficients. For both methods, the theoretical substantiation, implementation, and testing are presented. Thus, both methods are characterized based on simulations performed on many images. New filters are proposed: one based on the use of the translation invariant wavelet transform, which mediates the results obtained by repeating this procedure for several sets of wavelet coefficients and method based on Wiener filtering in the wavelet domain. The Wiener filters in the wavelet domain were called multiple Wiener filter, mediated Wiener filter and iterated Wiener filter. Although close, the results of the methods from Wiener wavelet filters differ depending on the computational effort involved. The largest computational effort requires the multiple Wiener filter, and the lowest, the mediated Wiener filter.  
The experimental results presented for testing nonlinear cellular network methods for image processing were obtained using the Matlab development environment. The proposed algorithm was tested, in a semiparallel variant, on Field Programmable Gate Array (FPGA) platform for digital emulation of the nonlinear cellular network, using FPGA Xilinx Series-7. The proposed variant, of semiparallel implementation, leads to obtaining an optimal ratio between the processing speed and the necessary hardware resources. Thus, the computation time depends only on the time constant of the hardware structure and the maximum number of steps of the algorithm (equal to the maximum displacement), being independent of the dimensions of the processed images (Figure 10).  
The obtained results showed that the unit fact frequency is only to a small extent dependent on the size of the template image, practically the fact frequency of 400 MHz can be reached. The calculation time thus estimated may be a few orders of magnitude smaller than in the case of serial implementation.  
Following the simulations performed, it was found that the proposed method leads to significant improvements both in terms of the amount of noise removed from the image, but also in terms of the quality of the contours in the filtered images.  
Considering several circular displacements so that we have approximately the same computational complexity, the Wiener filter in the wavelet domain together with the AB template in the nonlinear cellular network leads to multiresolution results, superior to those obtained by using the translation invariant wavelet transform and of classical neural networks in the case of medical images and satellite imagery.  
Figure 10: General resource requirements for implementation.  
**Author Contributions:** Conceptualization, C.D. and M.S.R.; methodology, C.D. and M.S.R.; software, C.D.; validation, C.D., M.S.R. and R.A.F.; formal analysis, C.D.; investigation, M.S.R. and R.A.F.; resources, C.D., M.S.R. and R.A.F.; data curation, C.D., M.S.R. and R.A.F.; writing--original draft preparation, M.S.R. and R.A.F.; writing--review and editing, C.D., M.S.R. and R.A.F.; visualization, C.D., M.S.R. and R.A.F.; supervision, C.D.; project administration, M.S.R.; funding acquisition, M.S.R. and R.A.F. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
This work was supported by a grant of the Romanian Ministry of Research and Innovation, CCCDI-UEFISCDI, project number PN-III-P1-1.2-PCCDI-2017-0776/No. 36 PC-CDI/15.03.2018, within PNCDI III. Acknowledgments to the National Center for Hydrogen and Fuel Cells (CNHPC)--Installations and Special Objectives of National Interest (IOSIN).  
The authors declare no conflict of interest.