The High-Resolution Wavelet Transform: A Generalization of the Discrete Wavelet Transforms.
Abstract not provided.
Jimenez Aparicio, Miguel↗
SEARCH · Engineering Papers
Results for “Discrete wavelet transform”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
The High-Resolution Wavelet Transform: A Generalization of the Discrete Wavelet Transforms.
Abstract not provided.
Jimenez Aparicio, Miguel↗
Use of switched capacitor filters to implement the discrete wavelet transform
This paper analyzes the use of IIR switched capacitor filters to implement the discrete wavelet transform and the inverse transform, using quadrature mirror filters (QMF) which have the necessary symmetry for reconstruction of the data. This is done by examining the sensitivity of the QMF transforms to the manufacturing variance in the desired capacitances. The performance is evaluated at the outputs of the separate filter stages and the error in the reconstruction of the inverse transform is compared with the desired results.
Kaiser, Kraig E.↗
Entanglement Renormalization for Quantum Field Theories with Discrete Wavelet Transforms
We propose an adaptation of Entanglement Renormalization for quantum field theories that, through the use of discrete wavelet transforms, strongly parallels the tensor network architecture of the Multiscale Entanglement Renormalization Ansatz (a.k.a. MERA). Our approach, called wMERA, has several advantages of over previous attempts to adapt MERA to continuum systems. In particular, (i) wMERA is formulated directly in position space, hence preserving the quasi-locality and sparsity of entanglers; and (ii) it enables a built-in RG flow in the implementation of real-time evolution and in computations of correlation functions, which is key for efficient numerical implementations. As examples, we describe in detail two concrete implementations of our wMERA algorithm for free scalar and fermionic theories in (1+1) spacetime dimensions. Possible avenues for constructing wMERAs for interacting field theories are also discussed.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Performance of a Discrete Wavelet Transform for Compressing Plasma Count Data and its Application to the Fast Plasma Investigation on NASA's Magnetospheric Multiscale Mission
Plasma measurements in space are becoming increasingly faster, higher resolution, and distributed over multiple instruments. As raw data generation rates can exceed available data transfer bandwidth, data compression is becoming a critical design component. Data compression has been a staple of imaging instruments for years, but only recently have plasma measurement designers become interested in high performance data compression. Missions will often use a simple lossless compression technique yielding compression ratios of approximately 2:1, however future missions may require compression ratios upwards of 10:1. This study aims to explore how a Discrete Wavelet Transform combined with a Bit Plane Encoder (DWT/BPE), implemented via a CCSDS standard, can be used effectively to compress count information common to plasma measurements to high compression ratios while maintaining little or no compression error. The compression ASIC used for the Fast Plasma Investigation (FPI) on board the Magnetospheric Multiscale mission (MMS) is used for this study. Plasma count data from multiple sources is examined: resampled data from previous missions, randomly generated data from distribution functions, and simulations of expected regimes. These are run through the compression routines with various parameters to yield the greatest possible compression ratio while maintaining little or no error, the latter indicates that fully lossless compression is obtained. Finally, recommendations are made for future missions as to what can be achieved when compressing plasma count data and how best to do so.
Particles↗
Fast Traveling-Wave Detection and Identification Method for Power Distribution Systems Using Discrete Wavelet Transform
Explore the source record for details and available documents.
Jimenez Aparicio, Miguel↗
The Use of the Discrete Wavelet Transform to Perform High Level Data Compression for Applications in Telemedicine
The document includes an executive summary of the program activities; questions regarding tiling that have yet to be addressed; and the impact of the grants received which include MDACC Infrastructure development, support of technology transfer, and the technical accomplishments of the program.
Schomer, Donald F.↗
The Application of Time-Frequency Methods to HUMS
This paper reports the study of four time-frequency transforms applied to vibration signals and presents a new metric for comparing them for fault detection. The four methods to be described and compared are the Short Time Frequency Transform (STFT), the Choi-Williams Distribution (WV-CW), the Continuous Wavelet Transform (CWT) and the Discrete Wavelet Transform (DWT). Vibration data of bevel gear tooth fatigue cracks, under a variety of operating load levels, are analyzed using these methods. The new metric for automatic fault detection is developed and can be produced from any systematic numerical representation of the vibration signals. This new metric reveals indications of gear damage with all of the methods on this data set. Analysis with the CWT detects mechanical problems with the test rig not found with the other transforms. The WV-CW and CWT use considerably more resources than the STFT and the DWT. More testing of the new metric is needed to determine its value for automatic fault detection and to develop methods of setting the threshold for the metric.
Pryor, Anna H.↗
Detailed Vibration Analysis of Pinion Gear with Time-Frequency Methods
In this paper, the authors show a detailed analysis of the vibration signal from the destructive testing of a spiral bevel gear and pinion pair containing seeded faults. The vibration signal is analyzed in the time domain, frequency domain and with four time-frequency transforms: the Short Time Frequency Transform (STFT), the Wigner-Ville Distribution with the Choi-Williams kernel (WV-CW), the Continuous Wavelet' Transform (CWT) and the Discrete Wavelet Transform (DWT). Vibration data of bevel gear tooth fatigue cracks, under a variety of operating load levels and damage conditions, are analyzed using these methods. A new metric for automatic anomaly detection is developed and can be produced from any systematic numerical representation of the vibration signals. This new metric reveals indications of gear damage with all of the time-frequency transforms, as well as time and frequency representations, on this data set. Analysis with the CWT detects changes in the signal at low torque levels not found with the other transforms. The WV-CW and CWT use considerably more resources than the STFT and the DWT. More testing of the new metric is needed to determine its value for automatic anomaly detection and to develop fault detection methods for the metric.
Mosher, Marianne↗
Method and system for progressive mesh storage and reconstruction using wavelet-encoded height fields
Systems and methods are provided for progressive mesh storage and reconstruction using wavelet-encoded height fields. A method for progressive mesh storage includes reading raster height field data, and processing the raster height field data with a discrete wavelet transform to generate wavelet-encoded height fields. In another embodiment, a method for progressive mesh storage includes reading texture map data, and processing the texture map data with a discrete wavelet transform to generate wavelet-encoded texture map fields. A method for reconstructing a progressive mesh from wavelet-encoded height field data includes determining terrain blocks, and a level of detail required for each terrain block, based upon a viewpoint. Triangle strip constructs are generated from vertices of the terrain blocks, and an image is rendered utilizing the triangle strip constructs. Software products that implement these methods are provided.
Baxes, Gregory A.↗
Method and system for progressive mesh storage and reconstruction using wavelet-encoded height fields
Systems and methods are provided for progressive mesh storage and reconstruction using wavelet-encoded height fields. A method for progressive mesh storage includes reading raster height field data, and processing the raster height field data with a discrete wavelet transform to generate wavelet-encoded height fields. In another embodiment, a method for progressive mesh storage includes reading texture map data, and processing the texture map data with a discrete wavelet transform to generate wavelet-encoded texture map fields. A method for reconstructing a progressive mesh from wavelet-encoded height field data includes determining terrain blocks, and a level of detail required for each terrain block, based upon a viewpoint. Triangle strip constructs are generated from vertices of the terrain blocks, and an image is rendered utilizing the triangle strip constructs. Software products that implement these methods are provided.
Baxes, Gregory A.↗
Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's
We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.
Cai, Wei↗
Automated Framework for Groundwater Monitoring Using DWT with LSTM and Transformers
Environmental monitoring is critical for safeguarding public health and ecological well-being. Traditional data structuring and workflow monitoring methods consume significant time and effort, hindering timely insights and effective decision-making. Our study addresses this challenge by presenting an AI framework that automates data cleaning, structuring, and modeling processes, specifically targeting applications in groundwater monitoring. By leveraging automation for data processing and model training, our framework establishes a novel and efficient paradigm for environmental monitoring, with its potential application to the vast network of over a hundred Department of Energy Environmental Management (DoE-EM) cleanup sites across the country. It analyzes data streams from a network of groundwater Internet-of-Things (IoT) sensors deployed at the Savannah River Site (SRS) for prediction modeling. This allows human experts to focus on analysis and decision-making, ultimately leading to better environmental outcomes.The framework employs multivariate time-series forecasting methods to study and model the behavior of varying chemical analytes. The continuous learning process is enabled by utilizing deep learning techniques. It allows the framework to become more nuanced in its analysis over time, adapting to the specific characteristics of the environmental site and the evolving nature of contaminant behavior. Deep learning models known for sequence modeling, LSTM, and Transformers are employed for time series forecasting. Data processing and structuring are essential components significantly impacting the final model's performance. This hypothesis was proven by presenting a comparative analysis of model performance with processed and unprocessed data. The feature engineering approach utilized was the Discrete Wavelet Transform, which works well with time series data.
Discrete Wavelet Transform (DWT)↗
A generalized machine learning workflow to visualize mechanical discontinuity
Accurate detection and mapping of mechanical discontinuity in materials has widespread industrial and research applications. Herein, we developed a generalized machine-learning framework for visualizing single mechanical discontinuity embedded in material of any composition, velocity, density, porosity, and size with limited data. The proposed visualization of discontinuity requires accurate estimations of the length, location, and orientation of the embedded discontinuity by processing multipoint wave-transmission measurements. k-Wave simulator is used to create a large dataset of elastic waveforms recorded during multi-point wave-transmission measurements through materials containing single mechanical discontinuity. k-Wave simulator considers the wave attenuation, dispersion, and mode conversion in wave motion. Discrete wavelet transform (DWT) and statistical feature extraction are essential for data preprocessing prior to the data-driven model development. DWT also minimizes the effect of noise. Using hyper-parameter tuning and cross validation, gradient boosting regression can visualize the mechanical discontinuity with an accuracy of 0.85, in terms of coefficient of determination. A double-layered neural network-based regression has better performance with an accuracy of 0.95. Use of convolutional neural network converts the predictive task from a waveform processing to an image processing problem. Convolutional neural network achieved a generalization performance of 0.91. The proposed generalized workflow requires robust simulation of wave propagation, signal processing, feature engineering, and model evaluation. Sensors closest to the source and those located opposite the source are the most significant for the desired visualization. Notably, the sensors closest to the source capture the non-linear associations, whereas the sensor on the border opposite to the source capture the linear associations between the measured waveforms and the properties of the mechanical discontinuity.
42 ENGINEERING↗
Wavelet compression techniques for hyperspectral data
Hyperspectral sensors are electro-optic sensors which typically operate in visible and near infrared bands. Their characteristic property is the ability to resolve a relatively large number (i.e., tens to hundreds) of contiguous spectral bands to produce a detailed profile of the electromagnetic spectrum. In contrast, multispectral sensors measure relatively few non-contiguous spectral bands. Like multispectral sensors, hyperspectral sensors are often also imaging sensors, measuring spectra over an array of spatial resolution cells. The data produced may thus be viewed as a three dimensional array of samples in which two dimensions correspond to spatial position and the third to wavelength. Because they multiply the already large storage/transmission bandwidth requirements of conventional digital images, hyperspectral sensors generate formidable torrents of data. Their fine spectral resolution typically results in high redundancy in the spectral dimension, so that hyperspectral data sets are excellent candidates for compression. Although there have been a number of studies of compression algorithms for multispectral data, we are not aware of any published results for hyperspectral data. Three algorithms for hyperspectral data compression are compared. They were selected as representatives of three major approaches for extending conventional lossy image compression techniques to hyperspectral data. The simplest approach treats the data as an ensemble of images and compresses each image independently, ignoring the correlation between spectral bands. The second approach transforms the data to decorrelate the spectral bands, and then compresses the transformed data as a set of independent images. The third approach directly generalizes two-dimensional transform coding by applying a three-dimensional transform as part of the usual transform-quantize-entropy code procedure. The algorithms studied all use the discrete wavelet transform. In the first two cases, a wavelet transform coder was used for the two-dimensional compression. The third case used a three dimensional extension of this same algorithm.
Evans, Bruce↗
Denoising Seismic Waveforms Using a Wavelet-Transform-Based Machine-Learning Method
Seismic waveform data recorded at stations can be thought of as a superposition of the signal from a source of interest and noise from other sources. Frequency‐based filtering methods for waveform denoising do not result in desired outcomes when the targeted signal and noise occupy similar frequency bands. Recently, denoising techniques based on deep‐learning convolutional neural networks (CNNs), in which a recorded waveform is decomposed into signal and noise components, have led to improved results. These CNN methods, which use short‐time Fourier transform representations of the time series, provide signal and noise masks for the input waveform. These masks are used to create denoised signal and designaled noise waveforms, respectively. However, advancements in the field of image denoising have shown the benefits of incorporating discrete wavelet transforms (DWTs) into CNN architectures to create multilevel wavelet CNN (MWCNN) models. The MWCNN model preserves the details of the input due to the good time–frequency localization of the DWT. In this report we use a data set of over 382,000 constructed seismograms recorded by the University of Utah Seismograph Stations network to compare the performance of CNN and MWCNN‐based denoising models. Evaluation of both models on constructed test data shows that the MWCNN model outperforms the CNN model in the ability to recover the ground‐truth signal component in terms of both waveform similarity and preservation of amplitude information. Model evaluation of real‐world data shows that both the CNN and MWCNN models outperform standard band‐pass filtering (BPF; average improvement in signal‐to‐noise ratio of 9.6 and 19.7 dB, respectively, with respect to BPF). Evaluation of continuous data suggests the MWCNN denoiser can improve both signal detection capabilities and phase arrival time estimates.
58 GEOSCIENCES↗
Context Modeler for Wavelet Compression of Spectral Hyperspectral Images
A context-modeling sub-algorithm has been developed as part of an algorithm that effects three-dimensional (3D) wavelet-based compression of hyperspectral image data. The context-modeling subalgorithm, hereafter denoted the context modeler, provides estimates of probability distributions of wavelet-transformed data being encoded. These estimates are utilized by an entropy coding subalgorithm that is another major component of the compression algorithm. The estimates make it possible to compress the image data more effectively than would otherwise be possible. The following background discussion is prerequisite to a meaningful summary of the context modeler. This discussion is presented relative to ICER-3D, which is the name attached to a particular compression algorithm and the software that implements it. The ICER-3D software is summarized briefly in the preceding article, ICER-3D Hyperspectral Image Compression Software (NPO-43238). Some aspects of this algorithm were previously described, in a slightly more general context than the ICER-3D software, in "Improving 3D Wavelet-Based Compression of Hyperspectral Images" (NPO-41381), NASA Tech Briefs, Vol. 33, No. 3 (March 2009), page 7a. In turn, ICER-3D is a product of generalization of ICER, another previously reported algorithm and computer program that can perform both lossless and lossy wavelet-based compression and decompression of gray-scale-image data. In ICER-3D, hyperspectral image data are decomposed using a 3D discrete wavelet transform (DWT). Following wavelet decomposition, mean values are subtracted from spatial planes of spatially low-pass subbands prior to encoding. The resulting data are converted to sign-magnitude form and compressed. In ICER-3D, compression is progressive, in that compressed information is ordered so that as more of the compressed data stream is received, successive reconstructions of the hyperspectral image data are of successively higher overall fidelity.
Kiely, Aaron↗
Engineering Relaxor Behavior in (BaTiO 3 ) n /(SrTiO 3 ) n Superlattices
Complex-oxide superlattices provide a pathway to numerous emergent phenomena because of the juxtaposition of disparate properties and the strong interfacial interactions in these unit-cell-precise structures. This is particularly true in superlattices of ferroelectric and dielectric materials, wherein new forms of ferroelectricity, exotic dipolar textures, and distinctive domain structures can be produced. Here, in this study, relaxor-like behavior, typically associated with the chemical inhomogeneity and complexity of solid solutions, is observed in (BaTiO 3 ) n /(SrTiO 3 ) n (n = 4–20 unit cells) superlattices. Dielectric studies and subsequent Vogel–Fulcher analysis show significant frequency dispersion of the dielectric maximum across a range of periodicities, with enhanced dielectric constant and more robust relaxor behavior for smaller period n. Bond-valence molecular-dynamics simulations predict the relaxor-like behavior observed experimentally, and interpretations of the polar patterns via 2D discrete-wavelet transforms in shorter-period superlattices suggest that the relaxor behavior arises from shape variations of the dipolar configurations, in contrast to frozen antipolar stripe domains in longer-period superlattices (n = 16). Moreover, the size and shape of the dipolar configurations are tuned by superlattice periodicity, thus providing a definitive design strategy to use superlattice layering to create relaxor-like behavior which may expand the ability to control desired properties in these complex systems.
36 MATERIALS SCIENCE↗