Search NASA⌕ Search

SEARCH · Search NASA

Results for “wavelet basis”

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.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A unified ensemble soil moisture dataset across the continental United States

Abstract A unified ensemble soil moisture (SM) package has been developed over the Continental United States (CONUS). The data package includes 19 products from land surface models, remote sensing, reanalysis, and machine learning models. All datasets are unified to a 0.25-degree and monthly spatiotemporal resolution, providing a comprehensive view of surface SM dynamics. The statistical analysis of the datasets leverages the Koppen-Geiger Climate Classification to explore surface SM’s spatiotemporal variabilities. The extracted SM characteristics highlight distinct patterns, with the western CONUS showing larger coefficient of variation values and the eastern CONUS exhibiting higher SM values. Remote sensing datasets tend to be drier, while reanalysis products present wetter conditions. In-situ SM observations serve as the basis for wavelet power spectrum analyses to explain discrepancies in temporal scales across datasets facilitating daily SM records. This study provides a comprehensive soil moisture data package and an analysis framework that can be used for Earth system model evaluations and uncertainty quantification, quantifying drought impacts and land–atmosphere interactions and making recommendations for drought response planning.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

SU-F-BRB-12: A Novel Haar Wavelet Based Approach to Deliver Non-Coplanar Intensity Modulated Radiotherapy Using Sparse Orthogonal Collimators

Purpose: Existing efforts to replace complex multileaf collimator (MLC) by simple jaws for intensity modulated radiation therapy (IMRT) resulted in unacceptable compromise in plan quality and delivery efficiency. We introduce a novel fluence map segmentation method based on compressed sensing for plan delivery using a simplified sparse orthogonal collimator (SOC) on the 4π non-coplanar radiotherapy platform. Methods: 4π plans with varying prescription doses were first created by automatically selecting and optimizing 20 non-coplanar beams for 2 GBM, 2 head & neck, and 2 lung patients. To create deliverable 4π plans using SOC, which are two pairs of orthogonal collimators with 1 to 4 leaves in each collimator bank, a Haar Fluence Optimization (HFO) method was used to regulate the number of Haar wavelet coefficients while maximizing the dose fidelity to the ideal prescription. The plans were directly stratified utilizing the optimized Haar wavelet rectangular basis. A matching number of deliverable segments were stratified for the MLC-based plans. Results: Compared to the MLC-based 4π plans, the SOC-based 4π plans increased the average PTV dose homogeneity from 0.811 to 0.913. PTV D98 and D99 were improved by 3.53% and 5.60% of the corresponding prescription doses. The average mean and maximal OAR doses slightly increased by 0.57% and 2.57% of the prescription doses. The average number of segments ranged between 5 and 30 per beam. The collimator travel time to create the segments decreased with increasing leaf numbers in the SOC. The two and four leaf designs were 1.71 and 1.93 times more efficient, on average, than the single leaf design. Conclusion: The innovative dose domain optimization based on compressed sensing enables uncompromised 4π non-coplanar IMRT dose delivery using simple rectangular segments that are deliverable using a sparse orthogonal collimator, which only requires 8 to 16 leaves yet is unlimited in modulation resolution. This work is supported in part by Varian Medical Systems, Inc. and NIH R43 CA18339.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2012

An Adaptive Wavelet Stochastic Collocation Method for Irregular Solutions of Stochastic Partial Differential Equations

Accurate predictive simulations of complex real world applications require numerical approximations to first, oppose the curse of dimensionality and second, converge quickly in the presence of steep gradients, sharp transitions, bifurcations or finite discontinuities in high-dimensional parameter spaces. In this paper we present a novel multi-dimensional multi-resolution adaptive (MdMrA) sparse grid stochastic collocation method, that utilizes hierarchical multiscale piecewise Riesz basis functions constructed from interpolating wavelets. The basis for our non-intrusive method forms a stable multiscale splitting and thus, optimal adaptation is achieved. Error estimates and numerical examples will used to compare the efficiency of the method with several other techniques.

adaptive sparse grids↗
DOE OSTI2018

Accurate correlation energies in one-dimensional systems from small system-adapted basis functions

We propose a general method for constructing system-dependent basis functions for correlated quantum calculations. Our construction combines features from several traditional approaches: plane waves, localized basis functions, and wavelets. In a one-dimensional mimic of Coulomb systems, it requires only 2–3 basis functions per electron to achieve high accuracy, and reproduces the natural orbitals. We illustrate its effectiveness for molecular energy curves and chains of many one-dimensional atoms. Furthermore, we discuss the promise and challenges for realistic quantum chemical calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Daubechies wavelets for linear scaling density functional theory

We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10 000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Adaptive wavelet compression of large additive manufacturing experimental and simulation datasets

New manufacturing technologies such as additive manufacturing require research and development to minimize the uncertainties in the produced parts. The research involves experimental measurements and large simulations, which result in huge quantities of data to store and analyze. We address this challenge by alleviating the data storage requirements using lossy data compression. We select wavelet bases as the mathematical tool for compression. Unlike images, additive manufacturing data is often represented on irregular geometries and unstructured meshes. Thus, we use Alpert tree-wavelets as bases for our data compression method. We first analyze different basis functions for the wavelets and find the one that results in maximal compression and miminal error in the reconstructed data. We then devise a new adaptive thresholding method that is data-agnostic and allows a priori estimation of the reconstruction error. Finally, we propose metrics to quantify the global and local errors in the reconstructed data. One of the error metrics addresses the preservation of physical constraints in reconstructed data fields, such as divergence-free stress field in structural simulations. While our compression and decompression method is general, we apply it to both experimental and computational data obtained from measurements and thermal/structural modeling of the sintering of a hollow cylinder from metal powders using a Laser Engineered Net Shape process. The results show that monomials achieve optimal compression performance when used as wavelet bases. The new thresholding method results in compression ratios that are two to seven times larger than the ones obtained with commonly used thresholds. Overall, adaptive Alpert tree-wavelets can achieve compression ratios between one and three orders of magnitude depending on the features in the data that are required to preserve. Furthermore, these results show that Alpert tree-wavelet compression is a viable and promising technique to reduce the size of large data structures found in both experiments and simulations.

42 ENGINEERING↗
NASA NTRS1996

Wavelet-Based Grid Generation

Wavelets can provide a basis set in which the basis functions are constructed by dilating and translating a fixed function known as the mother wavelet. The mother wavelet can be seen as a high pass filter in the frequency domain. The process of dilating and expanding this high-pass filter can be seen as altering the frequency range that is 'passed' or detected. The process of translation moves this high-pass filter throughout the domain, thereby providing a mechanism to detect the frequencies or scales of information at every location. This is exactly the type of information that is needed for effective grid generation. This paper provides motivation to use wavelets for grid generation in addition to providing the final product: source code for wavelet-based grid generation.

HIGH PASS FILTERS↗
NASA NTRS1996

Wavelet Sparse Approximate Inverse Preconditioners

There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.

Chan, Tony F.↗
NASA NTRS2004

Planetary Transmission Diagnostics

This report presents a methodology for detecting and diagnosing gear faults in the planetary stage of a helicopter transmission. This diagnostic technique is based on the constrained adaptive lifting algorithm. The lifting scheme, developed by Wim Sweldens of Bell Labs, is a time domain, prediction-error realization of the wavelet transform that allows for greater flexibility in the construction of wavelet bases. Classic lifting analyzes a given signal using wavelets derived from a single fundamental basis function. A number of researchers have proposed techniques for adding adaptivity to the lifting scheme, allowing the transform to choose from a set of fundamental bases the basis that best fits the signal. This characteristic is desirable for gear diagnostics as it allows the technique to tailor itself to a specific transmission by selecting a set of wavelets that best represent vibration signals obtained while the gearbox is operating under healthy-state conditions. However, constraints on certain basis characteristics are necessary to enhance the detection of local wave-form changes caused by certain types of gear damage. The proposed methodology analyzes individual tooth-mesh waveforms from a healthy-state gearbox vibration signal that was generated using the vibration separation (synchronous signal-averaging) algorithm. Each waveform is separated into analysis domains using zeros of its slope and curvature. The bases selected in each analysis domain are chosen to minimize the prediction error, and constrained to have the same-sign local slope and curvature as the original signal. The resulting set of bases is used to analyze future-state vibration signals and the lifting prediction error is inspected. The constraints allow the transform to effectively adapt to global amplitude changes, yielding small prediction errors. However, local wave-form changes associated with certain types of gear damage are poorly adapted, causing a significant change in the prediction error. The constrained adaptive lifting diagnostic algorithm is validated using data collected from the University of Maryland Transmission Test Rig and the results are discussed.

Lewicki, David G.↗
DOE OSTI2017

Contextual Compression of Large-Scale Wind Turbine Array Simulations: Preprint

Data sizes are becoming a critical issue particularly for HPC applications. We have developed a user-driven lossy wavelet-based storage model to facilitate the analysis and visualization of large-scale wind turbine array simulations. The model stores data as heterogeneous blocks of wavelet coefficients, providing high-fidelity access to user-defined data regions believed the most salient, while providing lower-fidelity access to less salient regions on a block-by-block basis. In practice, by retaining the wavelet coefficients as a function of feature saliency, we have seen data reductions in excess of 94 percent, while retaining lossless information in the turbine-wake regions most critical to analysis and providing enough (low-fidelity) contextual information in the upper atmosphere to track incoming coherent turbulent structures. Our contextual wavelet compression approach has allowed us to deliver interactive visual analysis while providing the user control over where data loss, and thus reduction in accuracy, in the analysis occurs. We argue this reduced but contexualized representation is a valid approach and encourages contextual data management.

17 WIND ENERGY↗
DOE OSTI2017

Contextual Compression of Large-Scale Wind Turbine Array Simulations

Data sizes are becoming a critical issue particularly for HPC applications. We have developed a user-driven lossy wavelet-based storage model to facilitate the analysis and visualization of large-scale wind turbine array simulations. The model stores data as heterogeneous blocks of wavelet coefficients, providing high-fidelity access to user-defined data regions believed the most salient, while providing lower-fidelity access to less salient regions on a block-by-block basis. In practice, by retaining the wavelet coefficients as a function of feature saliency, we have seen data reductions in excess of 94 percent, while retaining lossless information in the turbine-wake regions most critical to analysis and providing enough (low-fidelity) contextual information in the upper atmosphere to track incoming coherent turbulent structures. Our contextual wavelet compression approach has allowed us to deliver interative visual analysis while providing the user control over where data loss, and thus reduction in accuracy, in the analysis occurs. We argue this reduced but contextualized representation is a valid approach and encourages contextual data management.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Sparse Overcomplete Denoising: Aggregation Versus Global Optimization

Denoising is often addressed via sparse coding with respect to an overcomplete dictionary. There are two main approaches when the dictionary is composed of translates of an orthonormal basis. The first, traditionally employed by techniques such as wavelet cycle spinning, separately seeks sparsity w.r.t. each translate of the orthonormal basis, solving multiple partial optimizations and obtaining a collection of sparse approximations of the noise-free image, which are aggregated together to obtain a final estimate. The second approach, recently employed by convolutional sparse representations, instead seeks sparsity over the entire dictionary via a global optimization. It is tempting to view the former approach as providing a suboptimal solution of the latter. In this letter, we analyze whether global sparsity is a desirable property, and under what conditions the global optimization provides a better solution to the denoising problem. In particular, our experimental analysis shows that the two approaches attain comparable performance in case of natural images and global optimization outperforms the simpler aggregation of partial estimates only when the image admits an extremely sparse representation. Here, we explain this phenomenon by separately studying the bias and variance of these solutions, and by noting that the variance of the global solution increases very rapidly as the original signal becomes less and less sparse.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Accurate quantum dynamics calculations using symmetrized Gaussians on a doubly dense Von Neumann lattice

In a series of earlier articles [B. Poirier, J. Theor. Comput. Chem. 2, 65 (2003); B. Poirier and A. Salam, J. Chem. Phys. 121, 1690 (2004); and ibid. 121, 1704 (2004)], a new method was introduced for performing exact quantum dynamics calculations. The method uses a 'weylet' basis set (orthogonalized Weyl-Heisenberg wavelets) combined with phase space truncation, to defeat the exponential scaling of CPU effort with system dimensionality-the first method ever able to achieve this long-standing goal. Here, we develop another such method, which uses a much more convenient basis of momentum-symmetrized Gaussians. Despite being non-orthogonal, symmetrized Gaussians are collectively local, allowing for effective phase space truncation. A dimension-independent code for computing energy eigenstates of both coupled and uncoupled systems has been created, exploiting massively parallel algorithms. Results are presented for model isotropic uncoupled harmonic oscillators and coupled anharmonic oscillators up to 27 dimensions. These are compared with the previous weylet calculations (uncoupled harmonic oscillators up to 15 dimensions), and found to be essentially just as efficient. Coupled system results are also compared to corresponding exact results obtained using a harmonic oscillator basis, and also to approximate results obtained using first-order perturbation theory up to the maximum dimensionality for which the latter may be feasibly obtained (four dimensions).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1989

Image wavelet decomposition and applications

The general problem of computer vision has been investigated for more that 20 years and is still one of the most challenging fields in artificial intelligence. Indeed, taking a look at the human visual system can give us an idea of the complexity of any solution to the problem of visual recognition. This general task can be decomposed into a whole hierarchy of problems ranging from pixel processing to high level segmentation and complex objects recognition. Contrasting an image at different representations provides useful information such as edges. An example of low level signal and image processing using the theory of wavelets is introduced which provides the basis for multiresolution representation. Like the human brain, we use a multiorientation process which detects features independently in different orientation sectors. So, images of the same orientation but of different resolutions are contrasted to gather information about an image. An interesting image representation using energy zero crossings is developed. This representation is shown to be experimentally complete and leads to some higher level applications such as edge and corner finding, which in turn provides two basic steps to image segmentation. The possibilities of feedback between different levels of processing are also discussed.

Treil, N.↗
DOE OSTI2018

Exploring the effects of climatic variables on monthly precipitation variation using a continuous wavelet-based multiscale entropy approach

Highlights: • Developed a wavelet transform entropy approach to study precipitation. • Multiscale entropy values were the basis for precipitation regionalization. • Various entropy-based bands were introduced to segregate the CWME values for each cluster. • The relationship between changes of CWME and mean monthly precipitation were investigated. • Central rain gauges of each cluster were used for further analysis. Understanding precipitation on a regional basis is an important component of water resources planning and management. The present study outlines a methodology based on continuous wavelet transform (CWT) and multiscale entropy (CWME), combined with self-organizing map (SOM) and k-means clustering techniques, to measure and analyze the complexity of precipitation. Historical monthly precipitation data from 1960 to 2010 at 31 rain gauges across Iran were preprocessed by CWT. The multi-resolution CWT approach segregated the major features of the original precipitation series by unfolding the structure of the time series which was often ambiguous. The entropy concept was then applied to components obtained from CWT to measure dispersion, uncertainty, disorder, and diversification of subcomponents. Based on different validity indices, k-means clustering captured homogenous areas more accurately, and additional analysis was performed based on the outcome of this approach. The 31 rain gauges in this study were clustered into 6 groups, each one having a unique CWME pattern across different time scales. The results of clustering showed that hydrologic similarity (multiscale variation of precipitation) was not based on geographic contiguity. According to the pattern of entropy across the scales, each cluster was assigned an entropy signature that provided an estimation of the entropy pattern of precipitation data in each cluster. Based on the pattern of mean CWME for each cluster, a characteristic signature was assigned, which provided an estimation of the CWME of a cluster across scales of 1–2, 3–8, and 9–13 months relative to other stations. The validity of the homogeneous clusters demonstrated the usefulness of the proposed approach to regionalize precipitation. Further analysis based on wavelet coherence (WTC) was performed by selecting central rain gauges in each cluster and analyzing against temperature, wind, Multivariate ENSO index (MEI), and East Atlantic (EA) and North Atlantic Oscillation (NAO), indeces. The results revealed that all climatic features except NAO influenced precipitation in Iran during the 1960–2010 period.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1985

Prospects for altimetry and scatterometry in the 90's

Current NASA plans for altimetry and scatterometry of the oceans using spaceborne instrumentation are outlined. The data of interest covers geostrophic and wind-driven circulation, heat content, the horizontal heat flux of the ocean, and the interactions between atmosphere and ocean and ocean and climate. A proposed TOPEX satellite is to be launched in 1991, carrying a radar altimeter to measure the ocean surface topography. Employing dual-wavelength operation would furnish ionospheric correction data. Multibeam instruments could also be flown on the multiple-instrument polar orbiting platforms comprising the Earth Observation System. A microwave radar scatterometer, which functions on the basis of Bragg scattering of microwave energy off of wavelets, would operate at various view angles and furnish wind speeds accurate to 1.5 m/sec and directions accurate to 20 deg.

Townsend, W. F.↗
NASA NTRS1993

On the differentiation matrix for Daubechies-based wavelets on an interval

The differentiation matrix for a Daubechies-based wavlet basis defined on an interval will be constructed. It will be shown that the differentiation matrix based on the currently available boundary constructions does not maintain the superconvergence encountered under periodic boundary conditions.

Jameson, Leland↗
DOE OSTI2017

Hybrid grid/basis set discretizations of the Schrödinger equation

We present a new kind of basis function for discretizing the Schrödinger equation in electronic structure calculations, called a gausslet, which has wavelet-like features but is composed of a sum of Gaussians. Gausslets are placed on a grid and combine advantages of both grid and basis set approaches. They are orthogonal, infinitely smooth, symmetric, polynomially complete, and with a high degree of locality. Because they are formed from Gaussians, they are easily combined with traditional atom-centered Gaussian bases. As a result, we also introduce diagonal approximations that dramatically reduce the computational scaling of two-electron Coulomb terms in the Hamiltonian.

97 MATHEMATICS AND COMPUTING↗