Wavelet Signal Processing: A Review for Recent Applications

Kumar, Amit

doi:10.29126/23951303/ijet-v6i6p7

Cited by 4 publications

(3 citation statements)

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“…Our goal in this contribution is to use custom-built wavelet bases to detect mass-like abnormalities (mass-like pattern) in mammograms. The signal representation and analysis using basis functions such as wavelets has been a booming research topic for more than 20 years due to their attractive properties for various purposes [13][14][15]. Pattern recognition and detection belong to this field.…”

Section: Introductionmentioning

confidence: 99%

A New Method for 2D-Adapted Wavelet Construction: An Application in Mass-Type Anomalies Localization in Mammographic Images

Valdés-Santiago,

León-Mecías,

Baguer Díaz-Romañach

et al. 2024

Applied Sciences

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This contribution presents a wavelet-based algorithm to detect patterns in images. A two-dimensional extension of the DST-II is introduced to construct adapted wavelets using the equation of the tensor product corresponding to the diagonal coefficients in the 2D discrete wavelet transform. A 1D filter was then estimated that meets finite energy conditions, vanished moments, orthogonality, and four new detection conditions. These allow, when performing the 2D transform, for the filter to detect the pattern by taking the diagonal coefficients with values of the normalized similarity measure, defined by Guido, as greater than 0.7, and α=0.1. The positions of these coefficients are used to estimate the position of the pattern in the original image. This strategy has been used successfully to detect artificial patterns and localize mass-like abnormalities in digital mammography images. In the case of the latter, high sensitivity and positive predictive value in detection were achieved but not high specificity or negative predictive value, contrary to what occurred in the 1D strategy. This means that the proposed detection algorithm presents a high number of false negatives, which can be explained by the complexity of detection in these types of images.

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Section: Introductionmentioning

confidence: 99%

A New Method for 2D-Adapted Wavelet Construction: An Application in Mass-Type Anomalies Localization in Mammographic Images

Valdés-Santiago,

León-Mecías,

Baguer Díaz-Romañach

et al. 2024

Applied Sciences

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“…The proposed method allows the limitations of the Fourier analysis to be overcome. The Fourier analysis is based on time-frequency methods [7] that were used in the last few decades, namely the fractional [8][9][10], short time [11][12][13], windowed FT [14,15], Gabor [16][17][18], wavelet [19][20][21], Hilbert-Huang [22][23][24], and Fourier-Bessel transformations [25,26], and even decomposition over empirical modes [27,28].…”

Section: Introductionmentioning

confidence: 99%

Approximation of Aperiodic Signals Using Non-Integer Harmonic Series: The Generalized NAFASS Approach

2023

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In this paper, the non-orthogonal amplitude-frequency analysis of smoothed signals (NAFASS) method) is used to approximate discrete aperiodic signals from various complex systems with the non-integer harmonic series (NIHS). When approximating by the NIHS, there is a problem in determining the dispersion law for harmonic frequencies. In the original version of the NAFASS approach, the frequency dispersion law was determined from a linear-difference equation. However, many complex systems in nature have frequency distributions that differ from the linear law, which is used in the conventional Fourier analysis of periodic signals. This paper proposes a generalization of the NAFASS method for describing aperiodic signals by the NIHS with a frequency distribution that satisfies a recursive formula, which coincides with the local generalized geometric mean (GGM). The methodology of the generalized NAFASS method is demonstrated using descriptions of financial data (prices for metals) and sound data (sounds of insects) as examples. The results show the effectiveness of the generalized NAFASS approach for describing real-world time data. This discovery allows us to propose a new classification scheme for smoothed and aperiodic signals captured as responses and envelopes from various complex systems.

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“…W AVELET transforms [1] play an essential role in signal analysis and processing for a variety of applications [2]- [7], which has enabled its widespread use in microscopy [8], [9], magnetic resonance spectroscopy [10], denoising [11]- [15], noise filtering [16], compression [17], [18], and fault diagnosis [19], among others. Signal averaging [20], on the other hand, is the backbone of noise reduction in physical signals [21]- [26] to obtain high fidelity signals, especially in spectroscopy and microscopy [27]- [30].…”

Section: Introductionmentioning

confidence: 99%

Signal Averaging in Wavelet Domain

Woldemariam¹,

Srivastava²

2022

Preprint

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<p>We present a method to implement signal averaging using wavelet transforms. Signal averaging plays an essential role in reducing noise from physical experiments, but is currently performed outside wavelet transforms and removes the information of individual data points or experimental scans. We introduce the conditions that need to be satisfied to implement signal averaging using wavelet transforms, showing that only the Haar wavelet can be used to obtain signal-averaged information. Our method identifies the wavelet component that contains the signal-averaged value and develops a procedure to recover it. The method is tested on model data using varied amounts of Gaussian and Poisson noise at different data lengths as well as experimental data from the Electron Spin Resonance (ESR) spectroscopy. While the Haar wavelet is successful in obtaining the mean, other wavelets yield weighted averages. The incorporation of this method enables signal averaging and analysis to be carried out simultaneously in the wavelet domain, expanding the application of wavelet transforms and improving wavelet analysis. The code is available via GitHub and denoising.cornell.edu, as well as the corresponding author's group website (signalsciencelab.com).</p>

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Wavelet Signal Processing: A Review for Recent Applications

Cited by 4 publications

References 0 publications

A New Method for 2D-Adapted Wavelet Construction: An Application in Mass-Type Anomalies Localization in Mammographic Images

A New Method for 2D-Adapted Wavelet Construction: An Application in Mass-Type Anomalies Localization in Mammographic Images

Approximation of Aperiodic Signals Using Non-Integer Harmonic Series: The Generalized NAFASS Approach

Signal Averaging in Wavelet Domain

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