A Novel Wavelet-Galerkin Method for Modeling Radio Wave Propagation in Tropospheric Ducts

Iqbal, Asif; Jeoti, Varun

doi:10.2528/pierb11091201

Cited by 17 publications

(9 citation statements)

References 21 publications

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“…In electromagnetics, they are essentially used because of their compression property in integral equations (Sarkar et al., 2002; Steinberg & Leviatan, 1993) and time‐domain methods (Hong & Kennett, 2002; Sarkar et al., 2002). In the domain of propagation modeling, Iqbal and Jeoti (2012a, 2012b) have used wavelets as test and approximation functions for a finite element implementation of the PWE.…”

Section: Introductionmentioning

confidence: 99%

A Local Split‐Step Wavelet Method for the Long Range Propagation Simulation in 2D

2021

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Modeling long‐range propagation of electromagnetic waves is necessary to study the performance of systems, for applications such as radar or navigation. Such models generally rely on split‐step Fourier (SSF) because large mesh sizes can be used. The split‐step wavelet method (SSW) is a recently developed method allowing to perform the same simulations as with SSF but in a shorter computation time. This method requires the pre‐computation of a free‐space propagator. Up to now, one limitation of SSW is that the steps must remain constant during the propagation. In this study, we propose an improvement of SSW in terms of memory size and versatility. This improvement relies on the use of a set of propagators, that is, the propagation of elementary wavelets. The limited support of wavelets renders the computation of the set of propagators fast, approximately as fast as one step of propagation with SSW. First, a numerical test shows the advantage in terms of computation time. Second, a numerical experience shows the advantage in terms of memory. Finally, the SSW method is applied as the direct method for a radio occultation configuration.

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Section: Introductionmentioning

confidence: 99%

A Local Split‐Step Wavelet Method for the Long Range Propagation Simulation in 2D

2021

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“…There are several different kinds of wavelets which have gained popularity throughout the development of wavelet analysis. The most important wavelet is the Harr wavelet, which is the simplest one and often the preferred wavelet in a lot of applications [25][26][27]. Equation (1) can be discretized by restraining a and b to a discrete lattice (a = 2 b & a > 0) to give the DWT, which can be expressed as follows.…”

Section: Discrete Wavelet Transformmentioning

confidence: 99%

An MR Brain Images Classifier via Principal Component Analysis and Kernel Support Vector Machine

Zhang¹,

Wu²

2012

PIER

254

146

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Abstract-Automated and accurate classification of MR brain images is extremely important for medical analysis and interpretation. Over the last decade numerous methods have already been proposed. In this paper, we presented a novel method to classify a given MR brain image as normal or abnormal. The proposed method first employed wavelet transform to extract features from images, followed by applying principle component analysis (PCA) to reduce the dimensions of features. The reduced features were submitted to a kernel support vector machine (KSVM). The strategy of Kfold stratified cross validation was used to enhance generalization of KSVM. We chose seven common brain diseases (glioma, meningioma, Alzheimer's disease, Alzheimer's disease plus visual agnosia, Pick's disease, sarcoma, and Huntington's disease) as abnormal brains, and collected 160 MR brain images (20 normal and 140 abnormal) from Harvard Medical School website. We performed our proposed methods with four different kernels, and found that the GRB kernel achieves the highest classification accuracy as 99.38%. The LIN, HPOL, and IPOL kernel achieves 95%, 96.88%, and 98.12%, respectively. We also compared our method to those from literatures in the last decade, and the results showed our DWT+PCA+KSVM with GRB kernel still achieved the best accurate classification results. The averaged processing time for a 256 × 256 size image on a laptop of P4 IBM with 3 GHz processor and 2 GB RAM is 0.0448 s. From the experimental data, our method was effective and rapid. It could be applied to the field of MR brain image classification and can assist the doctors to diagnose where a patient is normal or abnormal to certain degrees.

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“…The maximum-margin hyperplane which divides class 1 from class 2 is the support vector machine we want. Considering that any hyperplane can be written in the form of 0 b  wx (7) We want to choose the W and b to maximize the margin between the two parallel hyperplanes as large as possible while still separating the data. So we define the two parallel hyperplanes by the equations as 1 b    wx (8) Therefore, the task can be transformed to an optimization problem.…”

Section: Svmmentioning

confidence: 99%

“…By applying a wavelet transform to an image, four subbands are usually defined. They are the low-high, high-low, and high-high subbands which provide high-frequency coefficients for finer-scale image details representation, and the low-low subband whose low-frequency coefficients allow image approximation [7]. Wavelet transform have been applied in many areas of computer vision, of which image texture classification, and they have become popular for biomedical signal processing applications.…”

Section: Introductionmentioning

confidence: 99%

Automated Classification of Brain MR Images Using Wavelet-Energy and Support Vector Machines

Zhang

Wang²,

Feng³

et al. 2015

Proceedings of the 2015 International Conference on Mechatronics, Electronic, Industrial and Control Engineering

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It is of great importance to early detect abnormal brains, in order to save social resources. However, potential of wavelet decomposition is not fully explored and widely used. The wavelet-energy was a successful feature descriptor that achieved excellent performance in various applications; hence, we propose a wavelet-energy based new approach for automated classification of MR human brain images. The approach consisted of a three-stage system, including wavelet decomposition, energy extraction, and support vector machines. The results of proposed approach showed its performance was comparable with state-of-the-art algorithms. In addition, it provided a new means to detect features indicative of abnormal brains.

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A Novel Wavelet-Galerkin Method for Modeling Radio Wave Propagation in Tropospheric Ducts

Cited by 17 publications

References 21 publications

A Local Split‐Step Wavelet Method for the Long Range Propagation Simulation in 2D

A Local Split‐Step Wavelet Method for the Long Range Propagation Simulation in 2D

An MR Brain Images Classifier via Principal Component Analysis and Kernel Support Vector Machine

Automated Classification of Brain MR Images Using Wavelet-Energy and Support Vector Machines

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