Anisotropic Noise Research Articles

Source distribution of ocean microseisms and implications for time-dependent noise tomography

A qualitative analysis of ocean microseism source distribution observed in North America during fall and winter months was carried out. I review the theory of the origin of ocean microseisms and show that it can be used in conjunction with wave-wave interaction maps to quantify the source distribution anisotropy. It is demonstrated that microseisms generation in the North Atlantic and in the North Pacific Oceans are inherently different. North Atlantic microseisms are generated predominantly in the deep ocean, while North Pacific microseisms are dominated by coastal reflections. In spite of these differences both result from repeated ocean wave patterns that give rise to an anisotropic noise pattern, which cannot be randomized by time averaging. Considering time-varying ambient noise imaging, which aims to resolve a fraction of a percent changes in the crust over short distances, the source anisotropy would introduce a relatively significant error that needs to be accounted for.

Analysis of SNR for acoustic vector sensor linear array in volume and surface-generated noise fields

Acoustic vector sensor consists of pressure and particle velocity sensors, which measure the three-dimensional acoustic particle velocity, as well as the pressure at one location at the same time. By preserving the amplitude and phase information of the pressure and particle velocity, they possess a number of advantages over traditional scalar sensors. Signal-to-noise ratio (SNR) gain (which is often called array gain) is one of such advantages and is always interested by all of us. But it is not unchangeable if the spatial correlation of the noise field varies. Much more important, it is difficult to be given if the noise becomes complex. In this paper, spatial correlation of the vector field of isotropic volume-noise and surface-generated noise has been introduced briefly. Based on the results, the combined SNR output of a vector linear array is investigated and the maximum gain is given in the specified noise. Computer simulation shows that the output of one array in the same noise is not the same in different gestures. And then we find the best gesture through SNR calculation and obtain the biggest gain, which has important meaning to guide how to deploy an array in practice. We also should use the array with respect to the characteristics of the real ambient noise, especially in anisotropic noise field.

Bearing estimation using compressive sensing.

The performance of compressive sensing for determining bearing angle on a horizontal array is presented. The sampling requirements for infinite signal-to-noise ratio (SNR) is shown first. Detection capabilities are determined using a suboptimal array which is degraded both in length and number of elements. Using a detection threshold based on additive noise, the number of samples needed per tonal is shown as a function of SNR. The effects of anisotropic noise and array element location uncertainty in an oceanic waveguide are discussed. [Work supported by the Office of Naval Research.]

Retrieval of deterministic ray travel times from noise cross-correlations.

Two-point correlation functions of diffuse wave fields are known to approximate the deterministic Green’s functions that describe wave propagation between the two points. The deterministic ray travel times retrieved from cross-correlations of ambient noise recorded on vertical line arrays of hydrophones serve as the input data for passive acoustic thermometry and tomography of the water column. Accuracy of the sound-speed and water temperature inversions is largely controlled by the accuracy of the ray travel time measurement. Achieving oceanographically relevant results requires the relative error of the passive travel time measurements to be less than 0.1%. Often, the absolute error of the travel time measurement needs to be small compared to the acoustic wave period. In this paper, stationary-point analysis of an asymptotic, high-frequency integral representation of the noise cross-correlation function is used to determine ways for accurate retrieval of ray travel times. Limitations on the accuracy of the travel time retrieval due to noise anisotropy, medium non-stationarity, source and receiver motion, and finite noise averaging times are discussed. [Work supported by ONR.]

Orientation-Dependent Entanglement Lifetime in a Squeezed Atomic Clock

We study experimentally the application of a class of entangled states, squeezed spin states, to the improvement of atomic-clock precision. In the presence of anisotropic noise, the entanglement lifetime is strongly dependent on squeezing orientation. We measure the Allan deviation spectrum of a clock operated with a phase-squeezed input state. For averaging times up to 50s the squeezed clock achieves a given precision 2.8(3)times faster than a clock operating at the standard quantum limit.

Noise-induced switching near a depth two heteroclinic network and an application to Boussinesq convection

We investigate the robust heteroclinic dynamics arising in a system of ordinary differential equations in R(4) with symmetry [Formula in text]. This system arises from the normal form reduction of a 1: squate root of 2 mode interaction for Boussinesq convection. We investigate the structure of a particular robust heteroclinic attractor with "depth two connections" from equilibria to subcycles as well as connections between equilibria. The "subcycle" is not asymptotically stable, due to nearby trajectories undertaking an "excursion," but it is a Milnor attractor, meaning that a positive measure set of nearby initial conditions converges to the subcycle. We investigate the dynamics in the presence of noise and find a number of interesting properties. We confirm that typical trajectories wind around the subcycle with very occasional excursions near a depth two connection. The frequency of excursions depends on noise intensity in a subtle manner; in particular, for anisotropic noise, the depth two connection may be visited much more often than for isotropic noise, and more generally the long term statistics of the system depends not only on the noise strength but also on the anisotropy of the noise. Similar properties are confirmed in simulations of Boussinesq convection for parameters giving an attractor with depth two connections.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 1. Velocity and acceleration distributions

The effect of fluid velocity fluctuations on the dynamics of the particles in a turbulent gas–solid suspension is analysed in the low-Reynolds-number and high Stokes number limits, where the particle relaxation time is long compared with the correlation time for the fluid velocity fluctuations, and the drag force on the particles due to the fluid can be expressed by the modified Stokes law. The direct numerical simulation procedure is used for solving the Navier–Stokes equations for the fluid, the particles are modelled as hard spheres which undergo elastic collisions and a one-way coupling algorithm is used where the force exerted by the fluid on the particles is incorporated, but not the reverse force exerted by the particles on the fluid. The particle mean and root-mean-square (RMS) fluctuating velocities, as well as the probability distribution function for the particle velocity fluctuations and the distribution of acceleration of the particles in the central region of the Couette (where the velocity profile is linear and the RMS velocities are nearly constant), are examined. It is found that the distribution of particle velocities is very different from a Gaussian, especially in the spanwise and wall-normal directions. However, the distribution of the acceleration fluctuation on the particles is found to be close to a Gaussian, though the distribution is highly anisotropic and there is a correlation between the fluctuations in the flow and gradient directions. The non-Gaussian nature of the particle velocity fluctuations is found to be due to inter-particle collisions induced by the large particle velocity fluctuations in the flow direction. It is also found that the acceleration distribution on the particles is in very good agreement with the distribution that is calculated from the velocity fluctuations in the fluid, using the Stokes drag law, indicating that there is very little correlation between the fluid velocity fluctuations and the particle velocity fluctuations in the presence of one-way coupling. All of these results indicate that the effect of the turbulent fluid velocity fluctuations can be accurately represented by an anisotropic Gaussian white noise.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 2. The fluctuating-force model

A fluctuating-force model is developed for representing the effect of the turbulent fluid velocity fluctuations on the particle phase in a turbulent gas–solid suspension in the limit of high Stokes number, where the particle relaxation time is large compared with the correlation time for the fluid velocity fluctuations. In the model, a fluctuating force is incorporated in the equation of motion for the particles, and the force distribution is assumed to be an anisotropic Gaussian white noise. It is shown that this is equivalent to incorporating a diffusion term in the Boltzmann equation for the particle velocity distribution functions. The variance of the force distribution, or equivalently the diffusion coefficient in the Boltzmann equation, is related to the time correlation functions for the fluid velocity fluctuations. The fluctuating-force model is applied to the specific case of a Couette flow of a turbulent particle–gas suspension, for which both the fluid and particle velocity distributions were evaluated using direct numerical simulations by Goswami & Kumaran (2010). It is found that the fluctuating-force simulation is able to quantitatively predict the concentration, mean velocity profiles and the mean square velocities, both at relatively low volume fractions, where the viscous relaxation time is small compared with the time between collisions, and at higher volume fractions, where the time between collisions is small compared with the viscous relaxation time. The simulations are also able to predict the velocity distributions in the centre of the Couette, even in cases in which the velocity distribution is very different from a Gaussian distribution.

Estimation of Optimal Fiducial Target Registration Error in the Presence of Heteroscedastic Noise

We study the effect of point dependent (heteroscedastic) and identically distributed anisotropic fiducial localization noise on fiducial target registration error (TRE). We derive an analytic expression, based on the concept of mechanism spatial stiffness, for predicting TRE. The accuracy of the predicted TRE is compared to simulated values where the optimal registration transformation is computed using the heteroscedastic errors in variables algorithm. The predicted values are shown to be contained by the 95% confidence intervals of the root mean square TRE obtained from the simulations.

Constitutive equations for weakly entangled linear polymers

To interpret the viscoelastic behaviour of entangled linear polymers in terms of dynamics of a single macromolecule, we have been developing the approach, which allows one to study systematically deviations from the Rouse dynamics, when adding non-Markovian and anisotropic noise. It was shown earlier, that the introduction of specific form of non-Markovian dynamics leads to emerging of an intermediate length, which has the meaning of a tube radius and/or the length of a macromolecule between adjacent entanglements. The additional introduction of local anisotropy of mobility of particles allows one to get the results of the conventional reptation-tube model for both mobility and relaxation times of macromolecular coil and, beyond it, to estimate a transition point between weakly (the length of macromolecules M < 10 M e , no reptation) and strongly (the length of macromolecules M > 10 M e , reptation) entangled polymer systems. The adequate mesoscopic equation allows us to develop theory of different relaxation phenomena, in particular, a theory of viscoelasticity and to formulate constitutive equations for linear polymers, which, due to the difference of mechanisms of relaxation, appear to be different for the two types of entangled systems.

SU-FF-J-167: MRI-To-CT Deformable Registration for Treatment Planning of Breast Irradiation

Purpose: Breast MRI provides enhanced tissue differentiation and physiological information that greatly improves the delineation of targets for breast cancerradiotherapy.MRI needs to be registered with CT as the CT provides the electron density information for dose calculation and alignment in IGRT. We are developing a technique to deformably register MRI to CT, allowing for the transfer of the MRI‐defined structures to the CT for dose calculation, and the dose distribution from CT to MRI for outcome analysis. Method and Materials: An MRI data series was acquired, using a breast coil on a large bore 3T scanner (Verio, Siemens), with prone patient position using multiple sequences including T1, T1 fat saturation (FS), T2, T2FS, and T1FS with contrast. A CT was taken shortly after MRI acquisition. The multi‐form MRIs were rigidly registered to the CT. Anisotropic (edge preserving) noise filtering is applied to the images. A deformable image registration program developed using ITK then registers the MRIs individually to the CT using B‐Spline with Mattes mutual information as a metric and LBFGSB as the optimizer. MRI‐defined structures were overlaid on the CT for treatment planning, and the dose distribution transferred from CT to MRIs for analysis of radiation response based on multi‐form MRIs, using the deformation field obtained. Results: Multi‐form MRIs for prone breast were successfully registered to CT as gauged by high mutual information. Registration amongst the MRI modalities showed negligible deformation between them. T1FS registered best with the CT. Consequently its deformation field was used to deform the other MRIs. This improved the agreement between these MRIs and the CT over their individual registration. The deformation field was used for dose overlay on multi‐form MRIs.Conclusion: The deformable image registration tool developed successfully registers multi‐form MRIs to CT for treatment planning of prone breast radiotherapy.

Likelihood analysis of CMB temperature and polarization power spectra

Microwave background temperature and polarization observations are a powerful way to constrain cosmological parameters if the likelihood function can be calculated accurately. The temperature and polarization fields are correlated, partial-sky coverage correlates power spectrum estimators at different $l$, and the likelihood function for a theory spectrum given a set of observed estimators is non-Gaussian. An accurate analysis must model all these properties. Most existing likelihood approximations are good enough for a temperature-only analysis, however they cannot reliably handle temperature-polarization correlations. We give a new general approximation applicable for correlated Gaussian fields observed on part of the sky. The approximation models the non-Gaussian form exactly in the ideal full-sky limit and is fast to evaluate using a precomputed covariance matrix and set of power spectrum estimators. We show with simulations that it is good enough to obtain correct results at $l\ensuremath{\gtrsim}30$ where an exact calculation becomes impossible. We also show that some Gaussian approximations give reliable parameter constraints even though they do not capture the shape of the likelihood function at each $l$ accurately. Finally we test the approximations on simulations with realistically anisotropic noise and asymmetric foreground mask.

Unsupervised Whisker Tracking in Unrestrained Behaving Animals

Understanding how whisker-based tactile information is represented in the nervous system requires quantification of sensory input and observation of neural activity during whisking and whisker touch. Chronic electrophysiological methods have long been available to study neural responses in awake and behaving animals; however, methods to quantify the sensory input on whiskers have not yet been developed. Here we describe an unsupervised algorithm to track whisker movements in high-speed video recordings and to quantify the statistics of the tactile information on whiskers in freely behaving animals during haptic object exploration. The algorithm does not require human identification of whiskers, nor does it assume the shape, location, orientation, length of whiskers, or direction of the whisker movements. The algorithm performs well on temporary loss of whisker visibility and under low-light/low-contrast conditions even with inherent anisotropic noise and non-Gaussian variability in the signal. Using this algorithm, we define the speed [protraction (P), 1,081 +/- 322; retraction (R), 1,564 +/- 549 degrees /s], duration (P, 34 +/- 10; R, 24 +/- 8 ms), amplitude (P = R, 40 +/- 13 degrees ), and frequency (19 +/- 7 Hz) of active whisking in freely behaving mice. We furthermore quantify whisker deflection induced changes in whisking kinematics and calculate the statistics (i.e., speed, amplitude and duration) of whisker touch and finally show that whisker deprivation does not alter whisking kinematics during haptic exploration.

Anisotropic Noise Samples

We present a practical approach to generate stochastic anisotropic samples with Poisson-disk characteristic over a two-dimensional domain. In contrast to isotropic samples, we understand anisotropic samples as non-overlapping ellipses whose size and density match a given anisotropic metric. Anisotropic noise samples are useful for many visualization and graphics applications. The spot samples can be used as input for texture generation, e.g., line integral convolution (LIC), but can also be used directly for visualization. The definition of the spot samples using a metric tensor makes them especially suitable for the visualization of tensor fields that can be translated into a metric. Our work combines ideas from sampling theory and mesh generation. To generate these samples with the desired properties we construct a first set of non-overlapping ellipses whose distribution closely matches the underlying metric. This set of samples is used as input for a generalized anisotropic Lloyd relaxation to distribute noise samples more evenly. Instead of computing the Voronoi tessellation explicitly, we introduce a discrete approach which combines the Voronoi cell and centroid computation in one step. Our method supports automatic packing of the elliptical samples, resulting in textures similar to those generated by anisotropic reaction-diffusion methods. We use Fourier analysis tools for quality measurement of uniformly distributed samples. The resulting samples have nice sampling properties, for example, they satisfy a blue noise property where low frequencies in the power spectrum are reduced to a minimum.

Point-Based Rigid-Body Registration Using an Unscented Kalman Filter

We present and validate a novel registration algorithm mapping two data sets, generated from a rigid object, in the presence of Gaussian noise. The proposed method is based on the Unscented Kalman Filter (UKF) algorithm that is generally employed for analyzing nonlinear systems corrupted by additive Gaussian noise. First, we employ our proposed registration algorithm to fit two randomly generated data sets in the presence of isotropic Gaussian noise, when the corresponding points between the two data sets are assumed to be known. Then, we extend the registration method to the case where the data (with known correspondences) is stimulated by anisotropic Gaussian noise. The new registration method not only reliably converges to the correct registration solution, but it also estimates the variance, as a confidence measure, for each of the estimated registration transformation parameters. Furthermore, we employ the proposed registration algorithm for rigid-body, point-based registration where corresponding points between two registering data sets are unknown. The algorithm is tested on point data sets which are garnered from a pelvic cadaver and a scaphoid bone phantom by means of computed tomography (CT) and tracked free-hand ultrasound imaging. The collected 3-D points in the ultrasound frame are registered to the 3-D meshes in the CT frame by using the proposed and the standard Iterative Closest Points (ICP) registration algorithms. Experimental results demonstrate that our proposed method significantly outperforms the ICP registration algorithm in the presence of additive Gaussian noise. It is also shown that the proposed registration algorithm is more robust than the ICP registration algorithm in terms of outliers in data sets and initial misalignment between the two data sets.

Predictive Measures of Directional Benefit Part 2: Verification of Different Approaches to Estimating Directional Benefit

In this investigation, the relation between various directivity measures and subject performance with directional microphone hearing aids was determined. Test devices included first- and second-order directional microphones. Recordings of sentences and noise (Hearing in Noise Test, HINT) were made through each test device in simple, complex, and anisotropic background noise conditions. Twenty-six subjects, with normal hearing, were administered the HINT test recordings and directional benefit was computed. These measures were correlated to theoretical, free-field, and Knowles Electronic Manikin for Acoustic Research (KEMAR) directivity index (DI) values, as well as front-to-back ratios (FBR), in situ signal-to-noise ratios (SNR), and a newly proposed Db SNR, wherein a predictive value of the SNR improvement is calculated as a function of the noise source incidence. The different predictive scores showed high correlation to the measured directional benefit scores in the complex (diffuse-like) background noise condition (r = 0.89 to 0.97, p < 0.05) but not across all background noise conditions (r = 0.45 to 0.97, p < 0.05). The Db SNR approach and the in situ SNR measures provided excellent prediction of subject performance in all background noise conditions (0.85 to 0.97, p < 0.05). None of the predictive measures could account for the effects of reverberation on the speech signal (r = 0.35 to 0.40, p < 0.05). For environments that included a discrete number of noise sources, the in situ SNR and Db SNR estimates were most predictive of subject performance. No predictive approach was indicative of the directional benefit achieved when the speech was also subjected to reverberation (temporal distortion). This finding has implications for real-world estimates of directional benefit.

Method and apparatus for high-frequency passive sonar performance prediction

A system and method for predicting passive, high-frequency sonar array performance at any underwater location, implemented as a software package running on a computer. An operator selects an arbitrary geographical location, specifies a sonar array and defines a target. The necessary bathymetry, and associated oceanographic, environmental and meteorological data are automatically acquired or generated, along with appropriate models for ocean surface and bottom reflectivity, and vertical noise directionality. A Comprehensive Acoustic System Simulation (CASS) software module performs appropriate ray tracing, which is used to produce Cross-Spectral Density (CSD) matrices for the target and the anisotropic ambient noise. These are used to generate graphic and numeric representations of the array's performance at the selected location. A time of year may also be specified and the appropriate anisotropic noise field for conditions expected at that location at that time of year will be generated. Shipping realizations may be incorporated.

Primordial Non‐Gaussianity and Analytical Formula for Minkowski Functionals of the Cosmic Microwave Background and Large‐Scale Structure

We derive analytical formulae for the Minkowski functionals of the cosmic microwave background (CMB) and large-scale structure (LSS) from primordial non-Gaussianity. These formulae enable us to estimate a nonlinear coupling parameter, fNL, directly from the CMB and LSS data without relying on numerical simulations of non-Gaussian primordial fluctuations. One can use these formulae to estimate statistical errors on fNL from Gaussian realizations, which are much faster to generate than non-Gaussian ones, fully taking into account the cosmic/sampling variance, beam smearing, survey mask, etc. We show that the CMB data from the Wilkinson Microwave Anisotropy Probe should be sensitive to |fNL| ≃ 40 at the 68% confidence level. The Planck data should be sensitive to |fNL| ≃ 20. As for the LSS data, the late-time non-Gaussianity arising from gravitational instability and galaxy biasing makes it more challenging to detect primordial non-Gaussianity at low redshifts. The late-time effects obscure the primordial signals at small spatial scales. High-redshift galaxy surveys at z > 2 covering ~10 Gpc3 volume would be required for the LSS data to detect |fNL| ≃ 100. Minkowski functionals are nicely complementary to the bispectrum because the Minkowski functionals are defined in real space and the bispectrum is defined in Fourier space. This property makes the Minkowski functionals a useful tool in the presence of real-world issues such as anisotropic noise, foreground, and survey masks. Our formalism can be easily extended to scale-dependent fNL.

Adaptive beamformer trade-off study of an expendable array for biologic vocalizations

Adaptive beamformers exploit the ambient noise anisotropy to increase the array gain against this background, enhance target detection, and increase the resolution of the beam response. A prototype expendable array was developed and tested for high-frequency passive detection and localization of marine mammals. This latest array consists of vertical poly(vinylidene fluoride) (PVDF) wire elements arranged in a horizontal 6×6 grid with the corner elements removed for a total of 32 lines. The length of the wires forms a vertical beam response that allows exploitation of the ambient noise directionality in elevation while the horizontal aperture provides full coverage in azimuth. The performance and computational demand of selected adaptive and conventional beamformers are compared in a trade-off study to determine their possible use in this expendable system. This trade-off study accounts for the demand of computational resources in addition to the predicted system performance as adjuncts to ocean observatories. [This effort is partly supported by JHU/APL and the Office of Naval Research (ONR).]

Quantitative and topographical evaluation of ankle articular cartilage using high resolution MRI

The objectives of this study were to quantitatively evaluate the articular cartilage layers of the ankle and describe the cartilage topographical distribution across the joint surfaces using high resolution MRI and image segmentation. An anisotropic diffusion noise reduction algorithm and a directional gradient vector flow (dGVF) snake segmentation algorithm were applied to cartilage sensitive MR images. Eight cadaveric ankles were studied. Six repeated data sets were acquired in five of the ankles. Quantitative parameters were calculated for each cartilage layer; coefficients of variation (CV) were calculated from the six repeated data sets; and 3D thickness distribution maps were generated. The noise reduction algorithm produced marked image enhancement. Mean cartilage thickness ranged from 0.91 +/- 0.08 mm in the fibula to 1.34 +/- 0.14 mm in the talus. Mean cartilage volume was 3.32 +/- 0.55 ml, 1.72 +/- 0.25 ml, and 0.35 +/- 0.06 ml for the talus, tibia, and fibula, respectively. Mean CV ranged 2.82%-5.04% for quantitative parameters in the talus and tibia. The reported noise reduction and segmentation technique allow precise extraction of ankle cartilage and 3D reconstructions show that the thickest cartilage occurs over the talar shoulders, where osteochondritits dissecans (OCD) lesions commonly occur.