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Fuzzy-Inspired Three-Dimensional DWT and GLCM Framework for Pixel Characterization of Hyperspectral Images
Published in Mohan Lal Kolhe, Kailash J. Karande, Sampat G. Deshmukh, Artificial Intelligence, Internet of Things (IoT) and Smart Materials for Energy Applications, 2023
One level of 3D DWT yields eight subbands. As recommended by previous researchers, the conventional Db2 wavelet is selected for the experiment as Db2 wavelet provides good energy compaction. Other Daubechies wavelets are avoided to minimize the computational time, as they have more number of vanishing movements. Using the wavelet coefficients, three-dimensional cooccurrence features are extracted which are listed in Table 5.1 from the eight decomposed subbands and concatenated to classify the hyperspectral data. To extract these joint spatial-spectral cooccurrence features, two different overlapping windows of size 3 × 3 × 3 are used for the Indian Pines experiment, as it contains small classes like oats, grass pasture mowed, and alfalfa. As the University of Pavia data contains large classes, medium size overlapping sliding window of 7 × 7 × 7 is used. As the contextual information can be better represented by an overlapping window than a nonoverlapping window, the overlapping sliding window is preferred.
Daubechies Wavelets
Published in Nirdosh Bhatnagar, Introduction to Wavelet Transforms, 2020
Before the construction of Daubechies wavelets is described, a quantitative definition of smoothness or regularity is given. Regularity of a function is related to its moments. As we shall see, Daubechies wavelets satisfy certain regularity conditions. Daubechies wavelets have a compact support. Therefore, the compactness of a function and its consequences, as it relates to scaling and mother wavelet functions is initially explored. Using Bezout’s theorem, Daubechies developed expressions for scaling coefficients. Using these coefficients, wavelet coefficients are determined. Finally, a scheme for computing scaling and mother wavelet functions is indicated.
Wavelet-Based Methods in Image Compression
Published in Yevgeniy V. Galperin, An Image Processing Tour of College Mathematics, 2021
This description opens the door to the use of techniques of frequency analysis - a powerful new approach towards developing more sophisticated wavelet transforms. The Daubechies wavelet transforms we will create in subsequent sections using this method will provide performance vastly superior to that of the Haar wavelet transform in such applications as image compression, edge detection, and image denoising.
Scanning the Issue
Published in IETE Journal of Research, 2023
Shiban K Koul, Arun Kumar, Ranjan K Mallik
‘Severity Analysis of Mitral Regurgitation Using Discrete Wavelet Transform” presents a computer-aided diagnosis system for the severity analysis of mitral regurgitation (MR) and evaluates the discriminatory potential of Daubechies wavelet-based texture modelling. Due to its approximate shift invariance quality, the Daubechies wavelet family has been exploited for image decomposition. Following the decomposition of the image into four layers and subsequent concatenation, seven statistical texture features are employed. Support vector machine (SVM), a supervised classifier, is applied with a 10-fold cross-validation approach.
Griffith crack analysis in nonlocal magneto-elastic strip using Daubechies wavelets
Published in Waves in Random and Complex Media, 2023
Jyotirmoy Mouley, Nantu Sarkar, Soumen De
The governing equations of the present problem are reduced to a Fredholm integral equation of the second kind using the Fourier and Abel's transformation. The integral equation has to be solved numerically as its solution cannot be found in closed form. Here, we find an approximate numerical solution of the integral equation by employing the Daubechies wavelet. Wavelets have great advantages in finding approximate numerical solutions of integral equations. Generally, the trigonometric function, exponential function or self-adjoint operator are used as the basic building block in the approximation of unknown functions. If this basic building block contains n elements, then or operations are needed in the action of a function or operator. Wavelet functions have the capability to reduce the number of operations due to its multi-resolution analysis (MRA) property. Beylkin et al. [28] employed the Haar wavelet method to solve integral equations for the first time. Though the square-shaped Haar wavelet has the simplest form among the wavelet family, discontinuity is the main technical disadvantage of the Haar wavelet. A compactly supported orthogonal wavelet basis was constructed by I. Daubechies [29] with the focus on dealing with MRA of . Moreover, Daubechies wavelets have some distinctive properties like compact support, fractal nature, unknown structure, vanishing moment condition of wavelet function, etc. As a particular case of Daubechies wavelets, the Haar wavelet is acknowledged as Db1. The knowledge of the two-scale relationship of the Daubechies family is enough to set up a numerical scheme. Daubechies wavelets avoid more complicated calculations due to the fractal nature, compact support and vanishing moment of wavelet functions. Moreover, it requires less computational time in the operation of simulation codes in MATHEMATICA, MATLAB, Phython, etc.