NUMERICAL SOLUTION OF THE PROBLEM FOR POISSON’S EQUATION WITH THE USE OF DAUBECHIES WAVELET DISCRETE-CONTINUAL FINITE ELEMENT METHOD

Numerical solution of the problem for Poisson’s equation with the use of Daubechies wavelet discrete continual finite element method (specific version of wavelet-based discrete-continual finite element method) is under consideration in the distinctive paper. The operational initial continual and discrete-continual formulations of the problem are given, several aspects of finite element approximation are considered. Some information about the numerical implementation and an example of analysis are presented.

Error Minimization in ECG Signal Reconstruction Using Discrete Wavelet Transform

For clinical study and diagnosis, compression of Electro Cardio Gram (ECG) signal is a fundamental step for processing. However, the compression and reconstruction introduce errors in the signal. Therefore, error minimization is crucial before using these signals for analysis and diagnosis. This paper presents an efficient method to minimize the reconstruction error using the adaptive filtering technique. Better reconstruction was achieved based on higher value of Compression Ratio and lesser value of Percent Root mean squared difference. Daubechies Wavelet easily detects the signal spikes while keeping less error rate using Least Mean Squared Error algorithm. However, the percentage value of error appeared to be minimum when using Daubechies Wavelet because of its small coefficients other than Haar and Coiflet Wavelet. Therefore, it was concluded that Daubechies Wavelet should have been used for error minimization in the reconstructed signal.

COVID-19 Chest X-Ray Detection Performance Through Variations of Wavelets Basis Function

Our previous work regarding the X-Ray detection of COVID-19 using Haar wavelet feature extraction and the Support Vector Machines (SVM) classification machine has shown that the combination of the two methods can detect COVID-19 well but then the question arises whether the Haar wavelet is the best wavelet method. So that in this study we conducted experiments on several wavelet methods such as biorthogonal, coiflet, Daubechies, haar, and symlets for chest X-Ray feature extraction with the same dataset. The results of the feature extraction are then classified using SVM and measure the quality of the classification model with parameters of accuracy, error rate, recall, specification, and precision. The results showed that the Daubechies wavelet gave the best performance for all classification quality parameters. The Daubechies wavelet transformation gave 95.47% accuracy, 4.53% error rate, 98.75% recall, 92.19% specificity, and 93.45% precision.

Suicide cases in developed and emerging countries: an analysis using wavelets

ABSTRACT Objective The aim of this study was to use a wavelet technique to determine whether the number of suicides is similar between developed and emerging countries. Methods Annual data were obtained from World Health Organization (WHO) reports from 1986 to 2015. Discrete nondecimated wavelet transform was used for the analysis, and the Daubechies wavelet function was applied with five-level decomposition. Regarding clustering, energy (variance) was used to analyze the clusters and visualize the clustering process. We constructed a dendrogram using the Mahalanobis distance. The number of groups was set using a specific function in the R program. Results The cluster analysis verified the formation of four groups as follows: Japan, the United States and Brazil were distinct and isolated groups, and other countries (Austria, Belgium, Chile, Israel, Mexico, Italy and the Netherlands) constituted a single group. Conclusion The methods utilized in this paper enabled a detailed verification of countries with similar behaviors despite very distinct socioeconomic, geographic and climate characteristics.

Wavelet optimized upwind conservative method for traffic flow problems

Numerical schemes, namely, upwind nonconservative, upwind conservative, Lax–Friedrichs, Lax–Wendroff, MacCormack and Godunov are applied and compared on traffic flow problems. The best scheme, namely, upwind conservative is used for wavelet-optimized method using Daubechies wavelet for numerically solving the same traffic flow problems. Numerical results corresponding to the traffic flow problem with the help of wavelet-optimized, adaptive grid, upwind conservative method have been given. Moreover, the run time carried out by the developed technique have been compared to that of run time carried out by finite difference technique. It is observed that, in terms of run time, the proposed method performs better.