applied sciences Article Methods for Improving Image Quality for Contour and Textures Analysis Using New Wavelet Methods Catalin Dumitrescu 1 , Maria Simona Raboaca 2,3,4 and Raluca Andreea Felseghi 3,4,* 1 Department Telematics and Electronics for Transports, University “Politehnica” of Bucharest, 060042 Bucharest, Romania; [email protected] 2 ICSI Energy, National Research and Development Institute for Cryogenic and Isotopic Technologies, 240050 Ramnicu Valcea, Romania; [email protected] 3 Faculty of Electrical Engineering and Computer Science, “¸Stefancel Mare” University of Suceava, 720229 Suceava, Romania 4 Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania * Correspondence: [email protected] Abstract: The fidelity of an image subjected to digital processing, such as a contour/texture high- lighting process or a noise reduction algorithm, can be evaluated based on two types of criteria: objective and subjective, sometimes the two types of criteria being considered together. Subjective criteria are the best tool for evaluating an image when the image obtained at the end of the processing is interpreted by man. The objective criteria are based on the difference, pixel by pixel, between the original and the reconstructed image and ensure a good approximation of the image quality perceived by a human observer. There is also the possibility that in evaluating the fidelity of a remade (reconstructed) image, the pixel-by-pixel differences will be weighted according to the sensitivity of the human visual system. The problem of improving medical images is particularly important Citation: Dumitrescu, C.; Raboaca, in assisted diagnosis, with the aim of providing physicians with information as useful as possible M.S.; Felseghi, R.A. Methods for in diagnosing diseases. Given that this information must be available in real time, we proposed Improving Image Quality for Contour a solution for reconstructing the contours in the images that uses a modified Wiener filter in the and Textures Analysis Using New Wavelet Methods. Appl. Sci. 2021, 11, wavelet domain and a nonlinear cellular network and that is useful both to improve the contrast of 3895. https://doi.org/10.3390/ its contours and to eliminate noise. In addition to the need to improve imaging, medical applications app11093895 also need these applications to run in real time, and this need has been the basis for the design of the method described below, based on the modified Wiener filter and nonlinear cellular networks. Academic Editor: Athanasios Nikolaidis Keywords: wavelet adaptive methods; contours preservation; wavelet multiresolution analysis Received: 30 March 2021 Accepted: 22 April 2021 Published: 25 April 2021 1. Introduction Norbert Wiener’s theory of optimal filtering of continuous signals is the basis of linear Publisher’s Note: MDPI stays neutral least squares linear error filters dependent on input data. Wiener studied in his 1949 with regard to jurisdictional claims in paper “Extrapolation, Interpolation and Smoothing of Stationary Time Series”, considering published maps and institutional affil- stationary signals, the problem of estimation in terms of the least squares error in the iations. continuous case of time series. The extension of Wiener’s theory to the discrete case is simple and has a great practical utility because it led to the implementation of this type of filter using digital signal processors or specialized circuits in this class. Wiener filters play an important role in a wide range of applications [1] such as linear prediction, signal encoding, Copyright: © 2021 by the authors. echo cancellation, signal recovery, channel equalization, signal identification or additive Licensee MDPI, Basel, Switzerland. noise suppression, a number of studies focusing on their use in practical applications. The This article is an open access article coefficients of the Wiener filter are calculated so as to minimize the average square error distributed under the terms and between the filter output and the useful signal. Randy Gomez, Tatsuya Kawahara and conditions of the Creative Commons Kazuhrio Nakadai [2] are researching with the purpose of improving the late reflection, Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ noise power and the speech from a contaminated signal and improve it with a novel 4.0/). Appl. Sci. 2021, 11, 3895. https://doi.org/10.3390/app11093895 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 3895 2 of 23 scheme. The solutions include an acoustic model (AM) and proves its robustness and effectiveness through experimental evaluation. The system proposed by Saeed Ayat, M. T. Manzuri-Shalmani and Roohollah Di- anat [3] involves a WaveShrink module and proposed an improved system of wavelet- based enhancement with a thresholding algorithm and a novel method for the selection of the threshold. The results are presenting, comparatively with similar approaches, an improvement in the system performances. Israel Cohen [4] presents a new approach with an improved minima controlled re- cursive averaging (IMCRA) for noise estimation, low input signal to noise ratio (SNR) weak speech components. The IMCRA method proved to be effective and it has a lower estimation error compared with other methods, provides a lower residual noise and better speech quality. Boll, S. [5] is using a stand-alone noise suspension algorithm to reduce spectral effects of added noise. This system can be used for speech recognition systems, speaker authentication systems or narrow band voice as a pre-processor. Babul Islam, Hamidul Islam and Monsor Rahman [6] are using Wiener filter to identify and estimate the mel frequency axis Mel-LPC spectra in a medium with additive noises. After the filter is applied, the transform of inverse wavelet is applied and it obtains the signal of enhanced time domain speech. The result has presented an improvement on the word accuracy by 17.22%. S. G. Mallat [7] uses a pyramidal algorithm with quadrature mirror filters. The representation presents several spatial orientations. This representation of the application may be used in fractal analysis, texture discrimination and image coding. M. Kivanc Mihcak, I. Kozintsev and K. Ramchandran [8] want to apply first the maximum likelihood (ML) rule and then the estimation procedure MMSE—minimum mean squared error. Comparative with other results from literature, this method presents favorable result. P. Moulin and Juan Liu [9] research on thresholding and minimax/global wavelet shrinkage methods has proven to be very good in different scenarios. They are introducing a new group of priors with the base on Rissanen universal prior on integers. The theoretical and experimental results are presenting the robustness of some wrong specifications of others on image processing. Eero P. Simoncelli and Edward H. Adelson [10] are analyzing the noise removing problem starting from its solution, the Wiener solution and develop its extension, a Bayesian estimator. This estimator is nonlinear and performs a “coring” operation. Based on steerable wavelet pyramid, they create for subband statistics a simple model semiblind noise-removal algorithm. Martin J. Wainwright and Eero P. Simoncelli [11] proposed for the modeling of natural images the Gaussian scale mixture. Using multiscale bases are two surprising types of non-Gaussian behavior. A procedure of nonlinear “normalization” can be used as Gaussian coefficients. M. Kazubek [12] presents an error occurring on the approximate analysis in the empirical Wiener. They observed that the performance of the filter Wiener can be increased fixing the problems produced by the thresholding operation. Shi Zhong and Vladimir Cherkassky [13] are analyzing under the framework of the theory of statistical learning the image denoising to present the wavelet thresholding. They propose a tree structure based on spatial location, scale and magnitude. Dohono, D. L. [14] is using an empirical wavelet transform and proves two results: smooth and adapt. The first one has high probability and the second has precision. This method highlights new information about abstract statistical inference and the possibility of connecting it with an optimal recovery model. H. Zhang, A. Nosratinia and R.O. Wells [15] are developing an extension of the Minim Mental State Examination (MMSE) pixel wise wavelet denoising. For autocorrelations they Appl. Sci. 2021, 11, 3895 3 of 23 use an exponential decay model and for Fir Wiener filtering a parametric solution in the wavelet domain. This filter proves a notable denoising performance. H.G. Senel, R.A. Peters and B. Dawant [16] are using a novel median filter. They are combining in fuzzy connectedness already existing ideas and new ones in order to improve the extraction of edges. The edge detection proved, through qualitative and statistical analyses, to have better accuracy. Suresh Kumar et al. [17] want to remove the noise captured in images among the capturing or those injected during image transmission. Their attention is centered on the salt and pepper noise, Gaussian noise and speckle noise through the Wiener and performance comparison of median filters. Mei-Sen Pan, Jing-Tian Tang and Xiao-Li Yang [18] are applying a filter method in order to improve the quality of the image and to remove the noise. The medical images are analyzed and when noises are identified the noise granularity function (NGF) is applied, the size of the filtering window is adaptively adjusted and then with the median filter are eliminated from the MI—median the current noise marked pixel, amid with the noise mark cancellation. This method is efficient in the imagine preservation and to remove the noises [19]. San-li Yi, Zhen-Cheng Chen and Hong-li Ling [20] are proposing a modified Wiener fil- ter that uses diffusion weighted images (DWIs) with multiboundary. This modified Wiener and the classical Wiener filter are compared and analyzed in detail. The modified method has lower mean square error, more accurate DTIs and a lower nonpositive percentage. Hosseini, H.; Hessar, F. and Marvasti, F. [21] are presenting a method to reduce noise suppression with a high-density impulse in real-time.