Spline-Based Wavelet Transforms

AbstractWe investigate the wavelet spaces $$\mathcal {W}_{g}(\mathcal {H}_{\pi })\subset L^{2}(G)$$ W g ( H π ) ⊂ L 2 ( G ) arising from square integrable representations $$\pi :G \rightarrow \mathcal {U}(\mathcal {H}_{\pi })$$ π : G → U ( H π ) of a locally compact group G. We show that the wavelet spaces are rigid in the sense that non-trivial intersection between them imposes strong restrictions. Moreover, we use this to derive consequences for wavelet transforms related to convexity and functions of positive type. Motivated by the reproducing kernel Hilbert space structure of wavelet spaces we examine an interpolation problem. In the setting of time–frequency analysis, this problem turns out to be equivalent to the HRT-conjecture. Finally, we consider the problem of whether all the wavelet spaces $$\mathcal {W}_{g}(\mathcal {H}_{\pi })$$ W g ( H π ) of a locally compact group G collectively exhaust the ambient space $$L^{2}(G)$$ L 2 ( G ) . We show that the answer is affirmative for compact groups, while negative for the reduced Heisenberg group.

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CNN-Based Classifier as an Offline Trigger for the CREDO Experiment

Sensors ◽

10.3390/s21144804 ◽

2021 ◽

Vol 21 (14) ◽

pp. 4804

Author(s):

Marcin Piekarczyk ◽

Olaf Bar ◽

Łukasz Bibrzycki ◽

Michał Niedźwiecki ◽

Krzysztof Rzecki ◽

...

Keyword(s):

Wavelet Transforms ◽

Exploratory Study ◽

Large Scale ◽

Morphological Difference ◽

Cosmic Ray ◽

Input Image ◽

Image Features ◽

The Earth ◽

Cmos Sensor ◽

Competition Process

Gamification is known to enhance users’ participation in education and research projects that follow the citizen science paradigm. The Cosmic Ray Extremely Distributed Observatory (CREDO) experiment is designed for the large-scale study of various radiation forms that continuously reach the Earth from space, collectively known as cosmic rays. The CREDO Detector app relies on a network of involved users and is now working worldwide across phones and other CMOS sensor-equipped devices. To broaden the user base and activate current users, CREDO extensively uses the gamification solutions like the periodical Particle Hunters Competition. However, the adverse effect of gamification is that the number of artefacts, i.e., signals unrelated to cosmic ray detection or openly related to cheating, substantially increases. To tag the artefacts appearing in the CREDO database we propose the method based on machine learning. The approach involves training the Convolutional Neural Network (CNN) to recognise the morphological difference between signals and artefacts. As a result we obtain the CNN-based trigger which is able to mimic the signal vs. artefact assignments of human annotators as closely as possible. To enhance the method, the input image signal is adaptively thresholded and then transformed using Daubechies wavelets. In this exploratory study, we use wavelet transforms to amplify distinctive image features. As a result, we obtain a very good recognition ratio of almost 99% for both signal and artefacts. The proposed solution allows eliminating the manual supervision of the competition process.

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Wavelet transforms: Application to data analysis - I

Resonance ◽

10.1007/bf02834969 ◽

2004 ◽

Vol 9 (11) ◽

pp. 10-22 ◽

Cited By ~ 2

Author(s):

Jatan K. Modi ◽

Sachin P. Nanavati ◽

Amit S. Phadke ◽

Prasanta K. Panigrahi

Keyword(s):

Data Analysis ◽

Wavelet Transforms

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Comparing different wavelet transforms on removing electrocardiogram baseline wanders and special trends

BMC Medical Informatics and Decision Making ◽

10.1186/s12911-020-01349-x ◽

2020 ◽

Vol 20 (S11) ◽

Author(s):

Chao-Chen Chen ◽

Fuchiang Rich Tsui

Keyword(s):

Wavelet Transforms ◽

Low Frequency ◽

Clinical Decision Support Systems ◽

Clinical Decision ◽

Temporal Position ◽

Important Indicator ◽

Real Time Processing ◽

Step Functions ◽

Baseline Wander ◽

Ecg Data

Abstract Background Electrocardiogram (ECG) signal, an important indicator for heart problems, is commonly corrupted by a low-frequency baseline wander (BW) artifact, which may cause interpretation difficulty or inaccurate analysis. Unlike current state-of-the-art approach using band-pass filters, wavelet transforms can accurately capture both time and frequency information of a signal. However, extant literature is limited in applying wavelet transforms (WTs) for baseline wander removal. In this study, we aimed to evaluate 5 wavelet families with a total of 14 wavelets for removing ECG baseline wanders from a semi-synthetic dataset. Methods We created a semi-synthetic ECG dataset based on a public QT Database on Physionet repository with ECG data from 105 patients. The semi-synthetic ECG dataset comprised ECG excerpts from the QT database superimposed with artificial baseline wanders. We extracted one ECG excerpt from each of 105 patients, and the ECG excerpt comprised 14 s of randomly selected ECG data. Twelve baseline wanders were manually generated, including sinusoidal waves, spikes and step functions. We implemented and evaluated 14 commonly used wavelets up to 12 WT levels. The evaluation metric was mean-square-error (MSE) between the original ECG excerpt and the processed signal with artificial BW removed. Results Among the 14 wavelets, Daubechies-3 wavelet and Symlets-3 wavelet with 7 levels of WT had best performance, MSE = 0.0044. The average MSEs for sinusoidal waves, step, and spike functions were 0.0271, 0.0304, 0.0199 respectively. For artificial baseline wanders with spikes or step functions, wavelet transforms in general had lower performance in removing the BW; however, WTs accurately located the temporal position of an impulse edge. Conclusions We found wavelet transforms in general accurately removed various baseline wanders. Daubechies-3 and Symlets-3 wavelets performed best. The study could facilitate future real-time processing of streaming ECG signals for clinical decision support systems.

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Influence of SiC Addition on Mechanical Behavior of Thermal Barriers with the Aid of Acoustic Emission

Journal of Composites Science ◽

10.3390/jcs5010016 ◽

2021 ◽

Vol 5 (1) ◽

pp. 16

Author(s):

David Jeronimo Busquets ◽

Carlos Bloem ◽

Amparo Borrell ◽

Maria Dolores Salvador

Keyword(s):

Acoustic Emission ◽

Mechanical Behavior ◽

Thermal Barrier Coatings ◽

Wavelet Transforms ◽

Coefficient Of Thermal Expansion ◽

Microstructural Analysis ◽

Thermal Barrier ◽

Transfer Coefficients ◽

Barrier Coatings ◽

Thermal Barriers

The improvement of high temperature materials with lower heat transfer coefficients lead to the development of thermal barrier coatings (TBCs). One of the most widely used materials for thermal barrier coatings is Y2O3 stabilized ZrO2 (Y-TZP) because of its excellent shock resistance, low thermal conductivity, and relatively high coefficient of thermal expansion. The aim of this work is to study the TBCs mechanical behavior with the addition of SiC into the suspension of Y-TZP/Al2O3 by acoustic emission (AE). Additionally, a microstructural analysis and a finite elements model were carried out in order to compare results. The coatings were made by suspension plasma spray (SPS) on metal plates of 70 × 12 × 2 mm3. An intermetallic was deposited as a bond coating, followed by a coating of Y-TZP/Al2O3 with and without 15 wt.% SiC, with thicknesses between 87 and 161 μm. The AE becomes a fundamental tool in the study of the mechanical behavior of thermal barriers. The use of wavelet transforms streamlines the study and analysis of recorded sound spectra. The crack generation arises at very low stress levels.

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