Predictive Modeling of Wavelet Coefficients for Physical Processes.
Abstract not provided.
Khalil, Mohammad↗
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Wavelet-Based Spot Detection Algorithms for Low Signal-to-Noise Ratios.
Abstract not provided.
Anthony, Stephen Michael↗
Wavelet-Based Spot Detection for Low Signal-to-Noise Ratios.
Abstract not provided.
Anthony, Stephen Michael↗
Detecting multi‐scale riverine topographic variability and its influence on Chinook salmon habitat selection
Abstract Quantifying geomorphic conditions that impact riverine ecosystems is critical in river management due to degraded riverine habitat, changing flow and thermal conditions, and increasing anthropogenic pressure. Geomorphic complexity at different scales directly impacts habitat heterogeneity and affects aquatic biodiversity resilience. Here we showed that the combination of continuous spatial survey at high resolution, topobathymetric light detection and ranging (LiDAR), and continuous wavelet analysis can help identify and characterize that complexity. We used a continuous wavelet analysis on 1‐m resolution topobathymetry in three rivers in the Salmon River Basin, Idaho (USA), to identify different scales of topographic variability and the potential effects of this variability on salmonid redd site selection. On each river, wavelet scales characterized the topographic variability by portraying repeating patterns in the longitudinal profile. We found three major representative spatial wavelet scales of topographic variability in each river: a small wavelet scale associated with local morphology such as pools and riffles, a mid‐wavelet scale that identified larger channel unit features, and a large wavelet scale related to valley‐scale controls. The small wavelet scale was used to identify pools and riffles along the entire lengths of each river as well as areas with differing riffle‐pool development. Areas along the rivers with high local topographic variability (high wavelet power) at all wavelet scales contained the largest features (i.e., deepest or longest pools) in the systems. By comparing the wavelet power for each wavelet scale to Chinook salmon redd locations, we found that higher small‐scale wavelet power, which is related to pool‐riffle topography, is important for redd site selection. The continuous wavelet methodology objectively identified scales of topographic variability present in these rivers, performed efficient channel‐unit identification, and provided geomorphic assessment without laborious field surveys.
Duffin, Jenna↗
SWinzip v. 2.0
SWinzip is a Matlab and C++ library for scientific lossy data compression and reconstruction using compressed sensing and tree-wavelets transforms. These methods are known for their large compression and usefulness in data analytics such as features extraction. Compressed sensing and wavelets methods rely heavily on sparse and dense linear algebra operations implemented through the Boost codes in our library. SWinzip accommodates data represented on both regular grids (e.g. image data) and point-clouds (e.g. unstructured meshes). In SWinzip v2.0, there is more focus on wavelet compression and the following features are added: - The matrix-free (direct) wavelet transform is implemented in both C++ and Matlab. A threshold-based compression can now be used. Examples for distributed compression are also added. - Python implementation of Alpert wavelet transforms - Field data comparison using wavelets in Matlab with global and local metrics
Solloum, Maher↗
Multiresolution edge detection using enhanced fuzzy c-means clustering for ultrasound image speckle reduction
Purpose: Speckle suppression in ultrasound (US) images of various anatomic structures via a novel speckle noise reduction algorithm. Methods: The proposed algorithm employs an enhanced fuzzy c-means (EFCM) clustering and multiresolution wavelet analysis to distinguish edges from speckle noise in US images. The edge detection procedure involves a coarse-to-fine strategy with spatial and interscale constraints so as to classify wavelet local maxima distribution at different frequency bands. As an outcome, an edge map across scales is derived whereas the wavelet coefficients that correspond to speckle are suppressed in the inverse wavelet transform acquiring the denoised US image. Results: A total of 34 thyroid, liver, and breast US examinations were performed on a Logiq 9 US system. Each of these images was subjected to the proposed EFCM algorithm and, for comparison, to commercial speckle reduction imaging (SRI) software and another well-known denoising approach, Pizurica's method. The quantification of the speckle suppression performance in the selected set of US images was carried out via Speckle Suppression Index (SSI) with results of 0.61, 0.71, and 0.73 for EFCM, SRI, and Pizurica's methods, respectively. Peak signal-to-noise ratios of 35.12, 33.95, and 29.78 and edge preservation indices of 0.94, 0.93, and 0.86 were found for the EFCM, SIR, and Pizurica's method, respectively, demonstrating that the proposed method achieves superior speckle reduction performance and edge preservation properties. Based on two independent radiologists’ qualitative evaluation the proposed method significantly improved image characteristics over standard baseline B mode images, and those processed with the Pizurica's method. Furthermore, it yielded results similar to those for SRI for breast and thyroid images significantly better results than SRI for liver imaging, thus improving diagnostic accuracy in both superficial and in-depth structures. Conclusions: A new wavelet-based EFCM clustering model was introduced toward noise reduction and detail preservation. The proposed method improves the overall US image quality, which in turn could affect the decision-making on whether additional imaging and/or intervention is needed.
60 APPLIED LIFE SCIENCES↗
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↗
A Galerkin method with two-dimensional Haar basis functions for the computation of the Karhunen–Loève expansion
We study the numerical approximation of a homogeneous Fredholm integral equation of second kind associated with the Karhunen–Loève expansion of Gaussian random fields. We develop, validate, and discuss an algorithm based on the Galerkin method with two-dimensional Haar wavelets as basis functions. The shape functions are constructed from the orthogonal decomposition of tensor-product spaces of one-dimensional Haar functions, and a recursive algorithm is employed to compute the matrix of the discrete eigenvalue system without the explicit calculation of integrals, allowing the implementation of a fast and efficient algorithm that provides considerable reduction in CPU time, when compared with classical Galerkin methods. Numerical experiments confirm the convergence rate of the method and assess the approximation error and the sparsity of the eigenvalue system when the wavelet expansion is truncated. We illustrate the numerical solution of a diffusion problem with random input data with the present method. In this problem, accuracy was retained after dropping the coefficients below a threshold value that was numerically determined. A similar method with scaling functions rather than wavelet functions does not need a discrete wavelet transform and leads to eigenvalue systems with better conditioning but lower sparsity.
97 MATHEMATICS AND COMPUTING↗
A novel coupling of noise reduction algorithms for particle flow simulations
Proper orthogonal decomposition (POD) and its extension based on time-windows have been shown to greatly improve the effectiveness of recovering smooth ensemble solutions from noisy particle data. However, to successfully de-noise any molecular system, a large number of measurements still need to be provided. In order to achieve a better efficiency in processing time-dependent fields, we have combined POD with a well-established signal processing technique, wavelet-based thresholding. In this novel hybrid procedure, the wavelet filtering is applied within the POD domain and referred to as WAVinPOD. The algorithm exhibits promising results when applied to both synthetically generated signals and particle data. In this work, the simulations compare the performance of our new approach with standard POD or wavelet analysis in extracting smooth profiles from noisy velocity and density fields. Numerical examples include molecular dynamics and dissipative particle dynamics simulations of unsteady force- and shear-driven liquid flows, as well as phase separation phenomenon. Simulation results confirm that WAVinPOD preserves the dimensionality reduction obtained using POD, while improving its filtering properties through the sparse representation of data in wavelet basis. This paper shows that WAVinPOD outperforms the other estimators for both synthetically generated signals and particle-based measurements, achieving a higher signal-to-noise ratio from a smaller number of samples. The new filtering methodology offers significant computational savings, particularly for multi-scale applications seeking to couple continuum informations with atomistic models. It is the first time that a rigorous analysis has compared de-noising techniques for particle-based fluid simulations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
The discrete Kalman filtering approach for seismic signals deconvolution
Seismic signals are a convolution of reflectivity and seismic wavelet. One of the most important stages in seismic data processing is deconvolution process; the process of deconvolution is inverse filters based on Wiener filter theory. This theory is limited by certain modelling assumptions, which may not always valid. The discrete form of the Kalman filter is then used to generate an estimate of the reflectivity function. The main advantage of Kalman filtering is capability of technique to handling continually time varying models and has high resolution capabilities. In this work, we use discrete Kalman filter that it was combined with primitive deconvolution. Filtering process works on reflectivity function, hence the work flow of filtering is started with primitive deconvolution using inverse of wavelet. The seismic signals then are obtained by convoluting of filtered reflectivity function with energy waveform which is referred to as the seismic wavelet. The higher frequency of wavelet gives smaller wave length, the graphs of these results are presented.
58 GEOSCIENCES↗
Rapid production of large-area deep sub-wavelength hybrid structures by femtosecond laser light-field tailoring
The goal of creation of large-area deep sub-wavelength nanostructures by femtosecond laser irradiation onto various materials is being hindered by the limited coherence length. Here, we report solution of the problem by light field tailoring of the incident beam with a phase mask, which serves generation of wavelets. Direct interference between the wavelets, here the first-order diffracted beams, and interference between a wavelet and its induced waves such as surface plasmon polariton are responsible for creation of microgratings and superimposed nanogratings, respectively. The principle of wavelets interference enables extension of uniformly induced hybrid structures containing deep sub-wavelength nanofeatures to macro-dimension.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
ON THE FLARE-INDUCED SEISMICITY IN THE ACTIVE REGION NOAA 10930 AND RELATED ENHANCEMENT OF GLOBAL WAVES IN THE SUN
A major flare (of class X3.4) occurred on 2006 December 13 in the active region NOAA 10930. This flare event has remained interesting to solar researchers for studies related to particle acceleration during the flare process and the reconfiguration of magnetic fields as well as fine-scale features in the active region. The energy released during flares is also known to induce acoustic oscillations in the Sun. Here, we analyze the line-of-sight velocity patterns in this active region during the X3.4 flare using the Dopplergrams obtained by the Global Oscillation Network Group (GONG) instrument. We have also analyzed the disk-integrated velocity observations of the Sun obtained by the Global Oscillation at Low Frequency (GOLF) instrument on board the Solar and Heliospheric Observatory spacecraft as well as full-disk collapsed velocity signals from GONG observations during this flare to study any possible connection between the flare-related changes seen in the local and global velocity oscillations in the Sun. We apply wavelet transform to the time series of the localized velocity oscillations as well as the global velocity oscillations in the Sun spanning the flare event. The line-of-sight velocity shows significant enhancement in some localized regions of the penumbra of this active region during the flare. The affected region is seen to be away from the locations of the flare ribbons and the hard X-ray footpoints. The sudden enhancement of this velocity seems to be caused by the Lorentz force driven by the 'magnetic jerk' in the localized penumbral region. Application of wavelet analysis to these flare-induced localized seismic signals shows significant enhancement in the high-frequency domain (5 <{nu} < 8 mHz) and a feeble enhancement in the p-mode oscillations (2 <{nu} < 5 mHz) during the flare. On the other hand, the wavelet analysis of GOLF velocity data and the full-disk collapsed GONG velocity data spanning the flare event indicates significant post-flare enhancements in the high-frequency global velocity oscillations in the Sun, as evident from the wavelet power spectrum and the corresponding scale-average variance. The present observations of the flare-induced seismic signals in the active region in context of the driving force are different as compared to previous reports on such cases. We also find indications of a connection between flare-induced localized seismic signals and the excitation of global high-frequency oscillations in the Sun.
79 ASTRONOMY AND ASTROPHYSICS↗
Coherent structure in solar wind C{sup 6+}/C{sup 4+} ionic composition data during the quiet-sun conditions of 2008
This analysis offers evidence of characteristic scale sizes in solar wind charge state data measured in situ for 13 quiet-Sun Carrington rotations in 2008. Using a previously established novel methodology, we analyze the wavelet power spectrum of the charge state ratio C{sup 6+}/C{sup 4+} measured in situ by ACE/SWICS for 2 hr and 12 minute cadence. We construct a statistical significance level in the wavelet power spectrum to quantify the interference effects arising from filling missing data in the time series, allowing extraction of significant power from the measured data to a resolution of 24 minutes. We analyze each wavelet power spectrum for transient coherency and global periodicities resulting from the superposition of repeating coherent structures. From the significant wavelet power spectra, we find evidence for a general upper limit on individual transient coherency of ∼10 days. We find evidence for a set of global periodicities between 4-5 hr and 35-45 days. We find evidence for the distribution of individual transient coherency scales consisting of two distinct populations. Below the ∼2 day timescale, the distribution is reasonably approximated by an inverse power law, whereas for scales ≳2 days, the distribution levels off, showing discrete peaks at common coherency scales. In addition, by organizing the transient coherency scale distributions by wind type, we find that these larger, common coherency scales are more prevalent and well defined in coronal hole wind. Finally, we discuss the implications of our results for current theories of solar wind generation and describe future work for determining the relationship between the coherent structures in our ionic composition data and the structure of the coronal magnetic field.
79 ASTRONOMY AND ASTROPHYSICS↗
Multi-resolution anisotropy studies of ultrahigh-energy cosmic rays detected at the Pierre Auger Observatory
Here, we report a multi-resolution search for anisotropies in the arrival directions of cosmic rays detected at the Pierre Auger Observatory with local zenith angles up to 80(o) and energies in excess of 4 EeV (4 × 10 18 eV). This search is conducted by measuring the angular power spectrum and performing a needlet wavelet analysis in two independent energy ranges. Both analyses are complementary since the angular power spectrum achieves a better performance in identifying large-scale patterns while the needlet wavelet analysis, considering the parameters used in this work, presents a higher efficiency in detecting smaller-scale anisotropies, potentially providing directional information on any observed anisotropies. No deviation from isotropy is observed on any angular scale in the energy range between 4 and 8 EeV. Above 8 EeV, an indication for a dipole moment is captured, while no other deviation from isotropy is observed for moments beyond the dipole one. The corresponding p-values obtained after accounting for searches blindly performed at several angular scales, are 1.3 × 10 -5 in the case of the angular power spectrum, and 2.5 × 10 -3 in the case of the needlet analysis. While these results are consistent with previous reports making use of the same data set, they provide extensions of the previous works through the thorough scans of the angular scales.
79 ASTRONOMY AND ASTROPHYSICS↗
S-Preconditioner for Multi-fold Data Reduction with Guaranteed User-Controlled Accuracy
The growing gap between the massive amounts of data generated by petascale scientific simulation codes and the capability of system hardware and software to effectively analyze this data necessitates data reduction. Yet, the increasing data complexity challenges most, if not all, of the existing data compression methods. In fact, lossless compression techniques offer no more than 10% reduction on scientific data that we have experience with, which is widely regarded as effectively incompressible. To bridge this gap, in this paper, we advocate a transformative strategy that enables fast, accurate, and multi-fold reduction of double-precision floating-point scientific data. The intuition behind our method is inspired by an effective use of preconditioners for linear algebra solvers optimized for a particular class of computational dwarfs (e.g., dense or sparse matrices). Focusing on a commonly used multi-resolution wavelet compression technique as the underlying solver for data reduction we propose the S-preconditioner, which transforms scientific data into a form with high global regularity to ensure a significant decrease in the number of wavelet coefficients stored for a segment of data. Combined with the subsequent EQ-calibrator, our resultant method (called S-Preconditioned EQ-Calibrated Wavelets (SPEQC-WAVELETS)), robustly achieved a 4- to 5- fold data reduction while guaranteeing user-defined accuracy of reconstructed data to be within 1% point-by-point relative error, lower than 0:01 Normalized RMSE, and higher than 0:99 Pearson Correlation. In this paper, we show the results we obtained by testing our method on six petascale simulation codes including fusion, combustion, climate, astrophysics, and subsurface groundwater in addition to 13 publicly available scientific datasets. We also demonstrate that application-driven data mining tasks performed on decompressed variables or their derived quantities produce results of comparable quality with the ones for the original data.
Jin, Ye↗
TU-CD-BRA-01: A Novel 3D Registration Method for Multiparametric Radiological Images
Purpose: Multiparametric and multimodality radiological imaging methods, such as, magnetic resonance imaging(MRI), computed tomography(CT), and positron emission tomography(PET), provide multiple types of tissue contrast and anatomical information for clinical diagnosis. However, these radiological modalities are acquired using very different technical parameters, e.g.,field of view(FOV), matrix size, and scan planes, which, can lead to challenges in registering the different data sets. Therefore, we developed a hybrid registration method based on 3D wavelet transformation and 3D interpolations that performs 3D resampling and rotation of the target radiological images without loss of information Methods: T1-weighted, T2-weighted, diffusion-weighted-imaging(DWI), dynamic-contrast-enhanced(DCE) MRI and PET/CT were used in the registration algorithm from breast and prostate data at 3T MRI and multimodality(PET/CT) cases. The hybrid registration scheme consists of several steps to reslice and match each modality using a combination of 3D wavelets, interpolations, and affine registration steps. First, orthogonal reslicing is performed to equalize FOV, matrix sizes and the number of slices using wavelet transformation. Second, angular resampling of the target data is performed to match the reference data. Finally, using optimized angles from resampling, 3D registration is performed using similarity transformation(scaling and translation) between the reference and resliced target volume is performed. After registration, the mean-square-error(MSE) and Dice Similarity(DS) between the reference and registered target volumes were calculated. Results: The 3D registration method registered synthetic and clinical data with significant improvement(p<0.05) of overlap between anatomical structures. After transforming and deforming the synthetic data, the MSE and Dice similarity were 0.12 and 0.99. The average improvement of the MSE in breast was 62%(0.27 to 0.10) and prostate was 63%(0.13 to 0.04;p<0.05). The Dice similarity was in breast 8%(0.91 to 0.99) and for prostate was 89%(0.01 to 0.90;p<0.05) Conclusion: Our 3D wavelet hybrid registration approach registered diverse breast and prostate data of different radiological images(MR/PET/CT) with a high accuracy.
60 APPLIED LIFE SCIENCES↗
The use of multiwavelets for uncertainty estimation in seismic surface wave dispersion.
This report describes a new single-station analysis method to estimate the dispersion and uncer- tainty of seismic surface waves using the multiwavelet transform. Typically, when estimating the dispersion of a surface wave using only a single seismic station, the seismogram is decomposed into a series of narrow-band realizations using a bank of narrow-band filters. By then enveloping and normalizing the filtered seismograms and identifying the maximum power as a function of frequency, the group velocity can be estimated if the source-receiver distance is known. However, using the filter bank method, there is no robust way to estimate uncertainty. In this report, I in- troduce a new method of estimating the group velocity that includes an estimate of uncertainty. The method is similar to the conventional filter bank method, but uses a class of functions, called Slepian wavelets, to compute a series of wavelet transforms of the data. Each wavelet transform is mathematically similar to a filter bank, however, the time-frequency tradeoff is optimized. By taking multiple wavelet transforms, I form a population of dispersion estimates from which stan- dard statistical methods can be used to estimate uncertainty. I demonstrate the utility of this new method by applying it to synthetic data as well as ambient-noise surface-wave cross-correlelograms recorded by the University of Nevada Seismic Network.
58 GEOSCIENCES↗