Wavelet-based Method Research Articles

Wavelet-based collocation methods for solving multi-dimensional integro-differential systems

This paper presents a comprehensive investigation of wavelet-based collocation methods for solving multi-dimensional integro-differential systems. The research addresses the challenging problem of finding numerical solutions to integro-differential equations (IDEs) that are essential in various scientific and engineering applications. We propose novel numerical approximations for infinitely dimensional problems, including fractional Cattaneo-Rayleigh waves and nonlinear diffusion problems defined on unbounded domains. The study introduces a unified computational strategy that directly applies to IDEs without discretization, particularly focusing on the integer and fractional-order Cattaneo-Rayleigh model of thermoelasticity in one-dimensional zonal regions. Through numerical experiments, we demonstrate that our wavelet collocation approach achieves high efficiency and superior accuracy compared to traditional methods. The results show particularly strong performance in handling systems with differential physical singularities, functional physical singularities, and vector-valued physical singularities. Our approach provides a valuable toolbox for addressing complex modeling challenges in biology, mechanical signal processing, and digital communications where partial integro-differential equations naturally arise.

Uncovering Displacement between Nuclear and Renewable Electricity Generation for G7 Countries by Novel Wavelet-Based Methods

ABSTRACT Under the pressure of climate-related issues, importance of clean electricity generation (EG) has been developing in ensuring sustainable environment. Accordingly, countries have been trying to increase clean EG. Although increasing clean EG is important, it is also critical that clean EG alternatives should not cause displacement. Otherwise, there may not be certain progress in stimulating clean EG. So, this study aims to investigate displacement between nuclear and renewable EG types. In this context, the study considers four clean EG sources (i.e. nuclear, hydro, solar, and wind), analyzes G7 countries, uses high-frequency daily data between 1 January 2019 to 30 December 2023, applies novel Wavelet Local Multiple Correlation (WLMC) method as the main model, and performs Wavelet Transform Coherence (WTC) for the robustness check. The study defines that (i) hydro and wind EG have a displacement (supporting) effect on nuclear EG at short (long) term; (ii) solar EG has a supporting (displacement) effect on nuclear EG at short (long) term; (iii) the most critical EG source is nuclear for France and United States and hydro for Great Britain and Japan; (iv) the WTC method reveals the robustness. The study determines that renewable EG has a displacement (supporting) effect on nuclear EG in short (long) term. Therefore, there are certain conflict between nuclear and renewable EG in the short term, whereas they support each other in the long term. Thus, there is a need for comprehensive and balanced energy transition policy so that choices should not cause a displacement among alternatives.

Enhanced Wavelet-Based Medical Image Denoising with Bayesian-Optimized Bilateral Filtering.

Medical image denoising is essential for improving the clarity and accuracy of diagnostic images. In this paper, we present an enhanced wavelet-based method for medical image denoising, aiming to effectively remove noise while preserving critical image details. After applying wavelet denoising, a bilateral filter is utilized as a post-processing step to further enhance image quality by reducing noise while maintaining edge sharpness. The bilateral filter's effectiveness heavily depends on its parameters, which must be carefully optimized. To achieve this, we employ Bayesian optimization, a powerful technique that efficiently identifies the optimal filter parameters, ensuring the best balance between noise reduction and detail preservation. The experimental results demonstrate a significant improvement in image denoising performance, validating the effectiveness of our approach.

Artifact Management for Cerebral Near-Infrared Spectroscopy Signals: A Systematic Scoping Review.

Artifacts induced during patient monitoring are a main limitation for near-infrared spectroscopy (NIRS) as a non-invasive method of cerebral hemodynamic monitoring. There currently does not exist a robust "gold-standard" method for artifact management for these signals. The objective of this review is to comprehensively examine the literature on existing artifact management methods for cerebral NIRS signals recorded in animals and humans. A search of five databases was conducted based on the Preferred Reporting Items for Systematic Reviews and Meta-Analysis guidelines. The search yielded 806 unique results. There were 19 articles from these results that were included in this review based on the inclusion/exclusion criteria. There were an additional 36 articles identified in the references of select articles that were also included. The methods outlined in these articles were grouped under two major categories: (1) motion and other disconnection artifact removal methods; (2) data quality improvement and physiological/other noise artifact filtering methods. These were sub-categorized by method type. It proved difficult to quantitatively compare the methods due to the heterogeneity of the effectiveness metrics and definitions of artifacts. The limitations evident in the existing literature justify the need for more comprehensive comparisons of artifact management. This review provides insights into the available methods for artifact management in cerebral NIRS and justification for a homogenous method to quantify the effectiveness of artifact management methods. This builds upon the work of two existing reviews that have been conducted on this topic; however, the scope is extended to all artifact types and all NIRS recording types. Future work by our lab in cerebral NIRS artifact management will lie in a layered artifact management method that will employ different techniques covered in this review (including dynamic thresholding, autoregressive-based methods, and wavelet-based methods) amongst others to remove varying artifact types.

Stand-alone segmentation of blood flow pulsatility measured with diffuse correlation spectroscopy.

We present a stand-alone blood flow index (BFI) pulse segmentation method for diffuse correlation spectroscopy that uses a wavelet-based representation of the BFI signal at the cardiac frequency in place of an exogenous physiological reference. We use this wavelet-based segmentation method to quantify BFI waveform morphology in a cohort of 30 healthy adults. We demonstrate that the waveform morphology features obtained with the wavelet approach strongly agree with those obtained using an exogenous blood pressure reference signal. These results suggest the promise of stand-alone wavelet-based BFI segmentation for quantifying BFI waveform morphological features.

Identifying Halos in Cosmological Simulations with Continuous Wavelet Analysis: The 2D Case

Continuous wavelet analysis is gaining popularity in science and engineering for its ability to analyze data across both spatial and scale domains simultaneously. In this study, we introduce a wavelet-based method for halo identification and assess its feasibility in two-dimensional (2D) scenarios. We begin by generating four pseudo-2D data sets from the SIMBA dark matter simulation by compressing thin slices of three-dimensional (3D) data into 2D. Subsequently, we calculate the continuous wavelet transform (CWT) directly from the particle distributions, identify local maxima that represent actual halos, and segment the CWT to delineate halo boundaries. A comparison with the traditional friends-of-friends (FOF) method shows that while our CWT-identified halos contain slightly fewer particles, they have smoother boundaries and are more compact in dense regions. In contrast, the CWT method can link particles over greater distances to form halos in sparse regions due to its spatial segmentation scheme. The spatial distribution and halo power spectrum of both CWT and FOF halos demonstrate substantial consistency, validating the 2D applicability of CWT for halo detection. While our identification scheme has been tested solely in a limited 2D context and has shown some performance limitations, its linear time complexity of O(N) and consistency with the FOF method suggest its suitability for analyzing significantly larger data sets in the future and its potential to be extended to the 3D case.

A comparison of tonal-broadband decomposition algorithms for propeller noise

The usage of propellers is increasing as an alternative to traditional aircraft and has become the primary option for new urban mobility vehicles. However, noise emissions from rotating blades can be a challenge for the certification of these new vehicles. The acoustic sources from a propeller can be decomposed into deterministic and random components. Therefore, academic research has focused on developing methods to separate these components. This study compares the performance of several methods available in the literature to decompose propeller noise signals into tonal and broadband components. Initially, the methods were applied to synthetic data that represents the main characteristics of rotating blade noise. Later, the methods were tested on realistic acoustic data collected from an isolated propeller test rig. The results showed that methods based on phase-averaging recorded signals satisfactorily detected harmonic components. The method based on cross-correlation between data blocks effectively extracted the broadband spectra, but it performed poorly on harmonic detection. Additionally, the wavelet transform and Proper Orthogonal Decomposition methods were capable of reconstructing time series related to both deterministic and random parts. However, further investigation is required regarding the separation of POD modes, as unexpected trends were observed with the wavelet-based method.

Ocean Wave Directional Distribution from GPS Buoy Observations off the West Coast of Ireland: Assessment of a Wavelet-Based Method

Abstract Knowledge of the directional distribution of a wave field is crucial for a better understanding of complex air–sea interactions. However, the dynamic and unpredictable nature of ocean waves, combined with the limitations of existing measurement technologies and analysis techniques, makes it difficult to obtain precise directional information, leading to a poor understanding of this important quantity. This study investigates the potential use of a wavelet-based method applied to GPS buoy observations as an alternative approach to the conventional methods for estimating the directional distribution of ocean waves. The results indicate that the wavelet-based estimations are consistently good when compared to the framework of widely used parameterizations for the directional distribution. The wavelet-based method presents advantages in comparison with the conventional methods, including being purely data-driven and not requiring any assumptions about the shape of the distribution. In addition, it was found that the wave directional distribution is narrower at the spectral peak and broadens asymmetrically at higher and lower scales, particularly sharply for frequencies below the peak. The directional spreading appears to be independent of the wave age across the entire range of frequencies, implying that the angular width of the directional spectrum is primarily controlled by nonlinear wave–wave interactions rather than by wind forcing. These results support the use of the wavelet-based method as a practical alternative for the estimation of the wave directional distribution. In addition, this study highlights the need for continued innovation in the field of ocean wave measuring technologies and analysis techniques to improve our understanding of air–sea interactions. Significance Statement This study presents a wavelet-based technique for obtaining the directional distribution of ocean waves applied to GPS buoy. This method serves as an alternative to conventional methods and is relatively easy to implement, making it a practical option for researchers and engineers. The study was conducted in a highly energetic environment characterized by high wind speeds and large waves, providing a valuable dataset for understanding the dynamics of marine environment in extreme conditions. This research has implications for improving our understanding of directional characteristics of ocean waves, which is crucial for navigation, offshore engineering, weather forecasting, and coastal hazard mitigation. This study also highlights the challenges associated with understanding wave directionality and emphasizes a need for further observations.

Active few-shot learning for rare bioacoustic feature annotation

The collection and annotation of bioacoustic data present several challenges to researchers. Bioacoustic monitoring of rare (sparse) or cryptic species generally encounter two main issues. The cost of collecting and processing field data and a lack of labelled datasets for the target species. The detection of invasive species incursions and probability of absence testing is especially challenging due to these species having population densities at or close to zero. We present a methodology specifically designed to aid in the analysis of rare acoustic events within long-term field recordings. This approach combines a wavelet-based segmentation method that automatically extracts transient features from within-field recordings. A few-shot active learning recommender system in a human-in-the-loop process prioritises the annotation of low-certainty samples. This process combines the accuracy of human classification and the speed of computational tools to greatly reduce the presence of non-target features in field recordings. We evaluate this approach using an invasive species identification case study. This methodology achieves a test accuracy of 98.4% as well as 81.2% test accuracy using 2-shot, 2-way prototypical learning without fine-tuning, demonstrating high performance at varying data availability contexts. Active learning using low-certainty samples achieves >90% test accuracy using only 20 training samples compared to 80 samples without active learning. This approach allows users to train custom audio classification models for any application with rare features. The model can be easily exported for use in the field making real-time bioacoustic monitoring of less-vocal species a possibility. All code and data are available at https://github.com/Listening-Lab/Annotator.

Image Deconvolution and Point-spread Function Reconstruction with STARRED: A Wavelet-based Two-channel Method Optimized for Light-curve Extraction

We present starred, a point-spread function (PSF) reconstruction, two-channel deconvolution, and light-curve extraction method designed for high-precision photometric measurements in imaging time series. An improved resolution of the data is targeted rather than an infinite one, thereby minimizing deconvolution artifacts. In addition, starred performs a joint deconvolution of all available data, accounting for epoch-to-epoch variations of the PSF and decomposing the resulting deconvolved image into a point source and an extended source channel. The output is a high-signal-to-noise-ratio, high-resolution frame combining all data and the photometry of all point sources in the field of view as a function of time. Of note, starred also provides exquisite PSF models for each data frame. We showcase three applications of starred in the context of the imminent LSST survey and of JWST imaging: (i) the extraction of supernovae light curves and the scene representation of their host galaxy; (ii) the extraction of lensed quasar light curves for time-delay cosmography; and (iii) the measurement of the spectral energy distribution of globular clusters in the “Sparkler,” a galaxy at redshift z = 1.378 strongly lensed by the galaxy cluster SMACS J0723.3-7327. starred is implemented in jax, leveraging automatic differentiation and graphics processing unit acceleration. This enables the rapid processing of large time-domain data sets, positioning the method as a powerful tool for extracting light curves from the multitude of lensed or unlensed variable and transient objects in the Rubin-LSST data, even when blended with intervening objects.

Literature Review of Wavelet-Based Image Filtering Methods

Abstract: Noise is a random signal that corrupts the quality of an image. For many decades, eliminating it or reducing its intensity in the image has been a major concern for many scientists. To this end, several studies on image processing (with the aim of eliminating or reducing the intensity of noise) have been carried out. Although a multitude of filtering methods emerged from these studies, numerous works have shown the effectiveness of the wavelet transform in image filtering. Thus, several wavelet-based methods (for image filtering purposes) have been illustrated in the literature. Some methods involve performing wavelet decomposition followed by thresholding and other methods involve combining wavelet decomposition with various filtering methods. This combination can have two or more methods. After filtering, the effectiveness of the filter can be evaluated. It is measured in terms of qualitative and/or quantitative parameters. Indeed, a filtering method is said to be efficient when the PSNR parameter (parameter most used in the literature) obtained has a minimum value of 30dB. This article presents a literature review of wavelet-based image filtering methods. Emphasis is placed on works presenting a better PSNR value (wavelet type, combination carried out, mother wavelet, decomposition number). In the end, this article gives a panoramic view of the choices of tools to use by a reader who would like to get involved in image filtering

Wavelet-based digital pulse-shape method for discrimination between neutron and gamma-rays with organic scintillation detectors

Organic scintillator detectors are central instruments in many applications involving fast neutrons. Many organic scintillator detectors exhibit pulse-shape discrimination (PSD) properties and are widely used to discriminate between neutron events and background gamma rays. PSD methods have been traditionally implemented using analog electronic circuits; however, in recent years, digital techniques have proven to outperform analog methods in areas such as count rate capability. Many digital PSD algorithms with various levels of achievement have been proposed, and those based on the wavelet transform of digitized scintillation pulses have shown great promise for operation at high event rates, where the pulse pile-up effect limits the performance of PSD methods. However, the proposed wavelet-based PSD methods involve intricate calculations that limit their practical use. In this work, we describe a modified version of the wavelet-based PSD methods that offers significant simplification of the PSD process while still producing excellent PSD performance. The method employs the Haar wavelet transform, which is the simplest available wavelet function and is easily implemented on digital hardware, such as field-programmable gate arrays (FPGA). We describe the details of the method, and different aspects of its performance are experimentally demonstrated using an experimental setup comprising a NE213 liquid scintillation detector. A figure-of-merit (FOM) of 1.47 ± 0.07 is achieved with an energy threshold of 500 keVee (electron equivalent energy). An excellent FOM value (1.32) is achieved with a short pulse processing window of only 26 ns, indicating the resilience of the method against the pulse pile-up effect.

Scale-3 Haar wavelet-based method of fractal-fractional differential equations with power law kernel and exponential decay kernel

Abstract In this study, wavelet method has been proposed to solve fractal-fractional differential equations (FFDEs) with power law kernel (FFDPL) and exponential decay kernel (FFDED). The proposed method is based on scale 3 Haar wavelets with collocation method, and fractional integral operational matrices for derivatives of Caputo and Caputo–Fabrizio sense are derived to solve FFDPL and FFDED. The applicability of the proposed method is shown by solving some numerical examples, and the obtained results are compared with available solutions in the literature. The solutions are presented in the graphical and tabular forms also.

An adaptive Morlet wavelet-based iterative filtering method for locating informative frequency band

Locating the informative frequency band of rolling bearing fault signals is of great significance for feature extraction and fault diagnosis. Benefiting from the adjustable center frequency and bandwidth as well as the similarity to impulse-like characteristics induced by bearing failures, Morlet wavelets are commonly used in resonance demodulation. However, fault impulses are highly susceptible to contamination by strong noise, which impedes the efficacy of existing wavelet parameter selection strategies and frequency band optimization methods. In this paper, an adaptive Morlet wavelet-based iterative filtering (AMIF) method is proposed for frequency band optimization under strong noise. The resonance frequency band is pinpointed based on adaptive Morlet wavelet filter banks, with off-band noise being canceled and fault features being refined during the level-by-level filtering process. Additional iterative operations are leveraged to enhance fault features of in-band signals to facilitate the optimization of the filtering parameters. Effectiveness of the proposed AMIF method and its superiority over the wavelet packet transform-based kurtogram and minimum entropy deconvolution are verified through simulation and experimental analysis. The results demonstrate that AMIF can accurately localize the informative frequency band, thereby extracting high-quality fault features, making it suitable for bearing fault diagnosis under strong noise condition with different fault types.

Modification of wavelet-based downsampling method to reduce computational error in nonlinear dynamic analysis

One of the significant obstacles in conducting linear and non-linear time history analysis is its time-consuming nature. In this article, a new downsamlping method based on discrete wavelet transform (DWT) and smoothing is proposed to overcome this problem. In order to assess the precision of this approach, 50,000 linear and non-linear dynamic analyses of single degree of freedom (SDOF) systems and 300 nonlinear dynamic analyses of frame structures have been performed. One hundred Fema440 records were utilized to generate approximate waves up to the third level and the outcomes of this method were then contrasted with those of DWT. It has been demonstrated that the third-level approximate wave produced by DWT, previously considered dependable in other research, generates significant errors in results and the average error (absolute error percentage of the acceleration spectrum) of its third-level approximate wave is approximately 17.5%. On the other hand, the proposed method generated approximate waves with an average error of less than 4.5% across all behavior coefficients and periods and the error rate decreases as the period and behavior coefficient increase. Analysis of steel moment-resisting frames indicated that the lowest error in both methods is achieved for the base shear and across different engineering demand parameters, the average error rate for the proposed method was below 7.5%. Furthermore, caution must be exercised when employing the proposed method for structures with periods shorter than 0.5 s.

Error analysis of Haar wavelet-based Galerkin numerical method with application to various nonlinear optimal control problems

ABSTRACT First, this paper defines a general nonlinear optimal control problem with state/control constraints and its approximation problem as the Haar wavelet Galerkin optimal control problem (HWGOCP). Then, a Haar wavelet-based Galerkin numerical method has been developed, which converts it to a nonlinear optimization problem. We theoretically prove that a Haar wavelet feasible solution of HWGOCP will exist. We also show that the approximate solutions of HWGOCP are consistent and converge to the optimal solution of the problem. A variety of application problems have been considered, which include optimal control of tumour growth using Chemotherapy drugs, optimal control of infection via the SIS model using treatment, the Brachistochrone problem in mechanics, optimal control of mold using a fungicide, optimal control of pH value of a chemical reaction to determine the quality of a product, etc.

Entropy Wavelet-Based Method to Increase Efficiency in Highway Bridge Damage Identification

Highway bridges are crucial civil constructions for the transport infrastructure, which require proper attention from the corresponding institutions of each country and constant financing for their adequate maintenance; this is important because different types of damage can be generated within these structures, caused by natural disasters, among other sources, and the heavy loads they transport every day. Therefore, the development of simple, efficient, and low-cost methods is of vital importance, allowing us to identify damage in a timely manner and avoid bridges collapsing. As reported in a previous work, the wavelet energy accumulation method (WEAM) and its corresponding application in the Rio Papaloapan Bridge (RPB) represented an important advance within the field. Despite identifying damage in bridges with precision and at a low cost, there are several aspects to improve in that method. Therefore, in this work, that method was improved, eliminating several steps, and meaningfully reducing the computational burden by implementing an algorithm based on the Shannon entropy, thus giving way to the new entropy wavelet-based method (EWM). This new method was applied directly with regard to the real-life RPB, in both its healthy and damaged conditions. Also, its corresponding numerical model based on the finite element method in its healthy condition and different damage scenarios were carried out. The results indicate that the new EWM retains the advantages of WEAM, and it allows for damage identification to be completed more efficiently, increasing the precision by approximately 0.11%, and significantly reducing the computing time required to obtain results by 5.67 times.

Literature Review on Digital Image Processing and Its Techniques

Purpose: Understand the current state of knowledge in the field of digital image processing. Identify key concepts, theories, and methodologies that have been explored in previous research. Explore the various techniques and algorithms used in digital image processing. Evaluate the strengths and weaknesses of existing methods. Identify gaps or limitations in current techniques. Provide a context for the research by summarizing and synthesizing relevant studies. Show how different studies contribute to the overall understanding of digital image processing. Identify gaps in the existing literature that your research can address. Determine areas where further investigation is needed. Offer a foundation for discussion and interpretation of your results in the context of existing literature. Enable you to relate your findings to the broader field of digital image processing. Design/Methodology/Approach: Clearly define the scope of your literature review (e.g., specific techniques, applications, or periods). State the objectives of the literature review, such as identifying trends, evaluating methodologies, or addressing research gaps. Develop a comprehensive search strategy to identify relevant literature. Utilize academic databases, journals, conferences, and other reputable sources. Use a combination of keywords, Boolean operators, and controlled vocabulary (e.g., MeSH terms) to refine search queries. Systematically review and select relevant literature based on the established criteria. Document the process, including databases searched, keywords used, and reasons for inclusion/exclusion. Identify gaps in the existing literature and propose potential avenues for future research. Discuss the implications of these gaps for the advancement of knowledge in the field Findings/Results: Literature often discusses various image enhancement techniques such as histogram equalization, contrast stretching, and spatial filtering. Researchers explore the effectiveness of these techniques in improving image quality for different applications. Segmentation methods, including thresholding, region-based segmentation, and clustering algorithms, are frequently discussed. Object recognition and classification techniques using features like texture, color, and shape are common topics. Different image compression algorithms, such as JPEG, JPEG2000, and various wavelet-based methods, are often compared in terms of compression ratio and quality. The literature might address real-time image processing challenges and solutions, especially in applications like video surveillance, autonomous vehicles, and augmented reality. Originality/Value: Ensure that the literature review comprehensively covers key and recent works in digital image processing. This includes foundational theories, algorithms, and applications. Identify seminal papers, landmark studies, and recent advancements to create a timeline of the field's development. Paper Type: Review of existing literature

Economic extremes steering renewable energy trajectories: A time-frequency dissection of global shocks

The impact between time series may differ at different frequencies and time periods, and certain external events may cause sharp fluctuations in new financial markets. It is essential to conduct additional analyses on the extreme relationships in the time-frequency domain. However, extreme causal relationships and time-varying characteristics under various shocks usually cannot be detected simultaneously. Therefore, we reveal the extreme impacts and dynamic changes in global economic conditions on renewable energy by extending a fresh extreme wavelet-based method. Our results reveal significant extreme asymmetric impacts of economic conditions on renewable energy. Moreover, this effect was reinforced by extreme events such as the outbreak of the global financial crisis and the Russia–Ukraine conflict. This paper provides a deep analysis of economic conditions and renewable energy from a time-frequency domain perspective, which can aid investors and policy-makers in making relevant decisions under extreme conditions.

What Matters for Comovements among Gold, Bitcoin, CO2, Commodities, VIX and International Stock Markets during the Health, Political and Bank Crises?

This paper analyzes the connectedness between gold, wheat, and crude oil futures, Bitcoin, carbon emission futures, and international stock markets in the G7, BRICS, and Gulf regions with the outbreak of exogenous and unexpected shocks related to health, banking, and political crises. To this end, we use a wavelet-based method on the returns of different assets during the period 2 January 2019, to 21 April 2023. The empirical findings show that the existence of time-varying linkages between markets is well documented and appears stronger during the COVID-19 pandemic. However, it seems to diminish for some associations with the advent of the Russia-Ukraine War. The empirical results also show that investor risk perceptions measured by the VIX are negatively and substantially linked to stock markets in different regions. Other interesting findings emerge from the connectedness analysis with the outbreak of Silicon Valley bankruptcy. In particular, Bitcoin tends to regain its role as a safe-haven asset against some G7 stock markets during the bank crisis. Such findings can provide valuable insights for investors and policymakers concerning the relationship between different markets during different crises.