An approximation of one-dimensional nonlinear Kortweg de Vries equation of order nine

This research presents the approximate solution of nonlinear Korteweg-de Vries equation of order nine by a hybrid staggered one-dimensional Haar wavelet collocation method. In literature, the underlying equation is derived by generalizing the bilinear form of the standard nonlinear KdV equation. The highest order derivative is approximated by Haar series, whereas the lower order derivatives are attained by integration formula introduced by Chen and Hsiao in 1997. The findings are shown in the form of tables and a figure, demonstrating the proposed technique’s convergence, robustness, and ease of application in a small number of collocation points.

Haar wavelet method for solution of variable order linear fractional integro-differential equations

<abstract><p>In this paper, we developed a computational Haar collocation scheme for the solution of fractional linear integro-differential equations of variable order. Fractional derivatives of variable order is described in the Caputo sense. The given problem is transformed into a system of algebraic equations using the proposed Haar technique. The results are obtained by solving this system with the Gauss elimination algorithm. Some examples are given to demonstrate the convergence of Haar collocation technique. For different collocation points, maximum absolute and mean square root errors are computed. The results demonstrate that the Haar approach is efficient for solving these equations.</p></abstract>

A COMPUTATIONAL ALGORITHM FOR THE NUMERICAL SOLUTION OF NONLINEAR FRACTIONAL INTEGRAL EQUATIONS

In this paper, we develop a numerical method for the solution of nonlinear fractional integral equations (NFIEs) based on Haar wavelet collocation technique (HWCT). Under certain conditions, we also prove the uniqueness and existence as well as Hyers–Ulam (HU) stability of the solution. With the help of the mentioned technique, the considered problem is transformed to a system of algebraic equations which is then solved for the required results by using Broyden algorithm. To check the validation and convergence of the proposed technique, some examples are given. For different number of collocation points (CPs), maximum absolute and mean square root errors are computed. The results show that for solving these equations, the HWCT is effective. The convergence rate is also measured for different CPs, which is nearly equal to [Formula: see text].

Ekstraksi Fitur Citra Radiografi Thorax Menggunakan DWT dan Moment Invariant

COVID-19 is an infectious disease caused by thecoronavirus family, namely severe acute respiratorysyndrome coronavirus 2 (SARS-CoV-2). The fastest methodto identify the presence of this virus is a rapid antibody or antigen test, but confirming the positive status of a COVID-19 patient requires further examination. Lung examination using chest X-ray images taken through X-rays of COVID-19patients can be one way to confirm the patient's conditionbefore/after the rapid test. This paper proposes a featureextraction model to detect COVID-19 through chestradiography using a combination of Discrete WaveletTransform (DWT) and Moment Invariant features. In thiscase, haar wavelet transform and seven Hu moments wereused to extract image features in order to find unique featuresthat represent chest radiographic images as suspectedCOVID-19, pneumonia, or normal. To find out theuniqueness of the proposed features, it is coupled with thekNN and generic ANN classification techniques. Based on theperformance parameters assessed, it turns out that thewavelet-based and moment invariant thorax radiographicimage feature model can be used as a unique featureassociated with three categories: Normal, Pneumonia, andCovid-19. This is indicated by the accuracy value of 82.7% inthe kNN classification technique and the accuracy, precision,and recall of 86%, 87%, and 86% respectively with the ANNclassification technique.

Analysis of image compression methods based on wavelet transforms for maritime applications

The purpose of the article is to develop recommendations for choosing image compression method based on wavelet transformation, depending on image type, quality and compression requirements. Among the wavelet image compression methods, Embedded Zerotree Wavelet coder (EZW) and Set Partition In Hierarchical Trees (SPIHT) are considered, and the Haar wavelet and wavelet transformation in the oriented basis with the first, third, fifth and seventh decomposition levels is used as the base wavelet transform. These compression methods were compared with each other and with the standard JPEG method on the following parameters: mean square error, maximum error, peak to noise ratio, number of bits per pixel, compression ratio, and image size. The proposed methods can be successfully applied in the transmission of seabed relief images obtained from satellites or sea buoys.

Rolling Bearing Fault Vibration Signal Denoising Based on Adaptive Morphological Wavelet Perona–Malik Filter Algorithm

This paper proposes an adaptive Perona–Malik filtering algorithm based on the morphological Haar wavelet, which is used for vibration signal denoising in rolling bearing fault diagnosis with strong noise. First, the morphological Haar wavelet operator is utilized to presmooth the noisy signal, and the gradient of the presmooth signal is estimated. Second, considering the uncertainty of gradient at the strong noise point, a strong noise point recognition operator is constructed to adaptively identify the strong noise point. Third, the two-step gradient average value of the strong noise point in the same direction is used to substitute, and the second derivative is introduced into the diffusion coefficient. Finally, diffusion filtering is performed based on the improved Perona–Malik model. The simulation experiment result indicated that not only the algorithm can denoise effectively, but also the average gradient and second derivative in the same direction can effectively suppress the back diffusion of strong noise points to improve the denoising signal-to-noise ratio. The experimental results of rolling bearing show that the algorithm can adaptively filter out strong noise points and keep the information of peak in the signal well, which can improve the accuracy of rolling bearing fault diagnosis.