Uncorrelated Sources Research Articles

An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias

Phase-synchronization is a manifestation of interaction between neuronal groups measurable from LFP, EEG or MEG signals, however, volume conduction can cause the coherence and the phase locking value to spuriously increase. It has been shown that the imaginary component of the coherency (ImC) cannot be spuriously increased by volume-conduction of independent sources. Recently, it was proposed that the phase lag index (PLI), which estimates to what extent the phase leads and lags between signals from two sensors are nonequiprobable, improves on the ImC. Compared to ImC, PLI has the advantage of being less influenced by phase delays. However, sensitivity to volume-conduction and noise, and capacity to detect changes in phase-synchronization, is hindered by the discontinuity of the PLI, as small perturbations turn phase lags into leads and vice versa. To solve this problem, we introduce a related index, namely the weighted phase lag index (WPLI). Differently from PLI, in WPLI the contribution of the observed phase leads and lags is weighted by the magnitude of the imaginary component of the cross-spectrum. We demonstrate two advantages of the WPLI over the PLI, in terms of reduced sensitivity to additional, uncorrelated noise sources and increased statistical power to detect changes in phase-synchronization. Another factor that can affect phase-synchronization indices is sample-size bias. We show that, when directly estimated, both PLI and the magnitude of the ImC have typically positively biased estimators. To solve this problem, we develop an unbiased estimator of the squared PLI, and a debiased estimator of the squared WPLI.

TOWARDS BRAIN-INSPIRED COMPUTING

We present introductory considerations and analysis toward computing applications based on the recently introduced deterministic logic scheme with random spike (pulse) trains [Phys. Lett. A373 (2009) 2338–2342]. Also, in considering the questions, "why random?" and "why pulses?", we show that the random pulse based scheme provides the advantages of realizing multivalued deterministic logic. Pulse trains are realized by an element called orthogonator. We discuss two different types of orthogonators, parallel (intersection-based) and serial (demultiplexer-based) orthogonators. The last one can be slower but it makes sequential logic design straightforward. We propose generating a multidimensional logic hyperspace [Phys. Lett. A373 (2009) 1928–1934] by using the zero-crossing events of uncorrelated Gaussian electrical noises available in the chips. The spike trains in the hyperspace are non-overlapping, and are referred to as neuro-bits. To demonstrate this idea, we generate three-dimensional hyperspace bases using the zero-crossing events of two uncorrelated Gaussian noise sources. In such a scenario, the detection of different hyperspace basis elements may have vastly differing delays. We show that it is possible to provide an identical speed for the detection of all the hyperspace bases elements using correlated noise sources, and demonstrate this for the two neuro-bits situation. The key impact of this paper is to demonstrate that a logic design approach using such neuro-bits can yield a fast, low power and environmental variation tolerant means of designing computer circuitry. It also enables the realization of multivalued logic, and also significantly increasing the complexity of computer circuits by allowing several neuro-bits to be transmitted on a single wire.

Single Antenna Power Measurements Based Direction Finding

In this paper, the problem of estimating direction-of-arrival (DOA) of multiple uncorrelated sources from single antenna power measurements is addressed. Utilizing the fact that the antenna pattern is bandlimited and can be modeled as a finite sum of complex exponentials, we first show that the problem can be transformed into a frequency estimation problem. Then, we explain how the annihilating filter method can be used to solve for the DOA in the noiseless case. In the presence of noise, we propose to use Cadzow denoising that is formulated as an iterative algorithm derived from exploiting the matrix rank and linear structure properties. Furthermore, we have also derived the Cramér-Rao Bound (CRB) and reviewed several alternative approaches that can be used as a comparison to the proposed approach. From the simulation and experimental results, we demonstrate that the proposed approach significantly outperforms other approaches. It is also evident from the Monte Carlo analysis that the proposed approach converges to the CRB.

General representation theorem for perturbed media and application to Green's function retrieval for scattering problems

SUMMARY Green's function reconstruction relies on representation theorems. For acoustic waves, it has been shown theoretically and observationally that a representation theorem of the correlation-type leads to the retrieval of the Green's function by cross-correlating fluctuations recorded at two locations and excited by uncorrelated sources. We extend the theory to any system that satisfies a linear partial differential equation and define an ‘interferometric operation’ that is more general than cross-correlation for the reconstruction. We analyse Green's function reconstruction for perturbed media and establish a representation theorem specifically for field perturbations. That representation is then applied to the general treatment of scattering problems, enabling interpretation of the contributions to Green's function reconstruction in terms of direct and scattered waves. Perhaps surprising, Green's functions that account for scattered waves cannot be reconstructed from scattered waves alone. For acoustic waves, retrieval of scattered waves also requires cross-correlating direct and scattered waves at receiver locations. The addition of cross-correlated scattered waves with themselves is necessary to cancel the spurious events that contaminate the retrieval of scattered waves from the cross-correlation of direct with scattered waves. We illustrate these concepts with numerical examples for the case of an open scattering medium. The same reasoning holds for the retrieval of any type of perturbations and can be applied to perturbation problems such as electromagnetic waves in conductive media and elastic waves in heterogeneous media.

Modeling and shaping specular and diffuse reflection sound fields in enclosures.

Steady‐state sound fields in enclosures, with specular and diffuse reflection boundaries, are modeled with an energy‐intensity boundary element method using uncorrelated broadband directional sources. The specular reflection case is solved using an iterative relaxation method extended from a 3‐D diffuse reflection solution. When chosen properly, only a few directivity harmonics are required. Starting with a diffuse calculation, higher harmonicsare estimated by post‐processing, and the original diffuse influence matrix is refined accordingly and converges in a few relaxation steps. The method is higher‐order accurate, computationally efficient, and similar to the diffuse case in that it includes strict enforcement of energy conservation. The simulations give accurate results compared to exact modal solutions. Sample calculations are presented to show that the mean‐square pressure spatial variation can be tailored using a combination of diffuse and specular surfaces for the design of acoustic spaces.

Developing a matched‐filter kernel for localization of complex sources in a dispersive ocean waveguide with array invariance.

The array invariant method was previously developed by Lee and Makris [J. Acoust. Soc. Am. (2006)] for instantaneously localizing both transient and continuous broadband acoustic sources after conventional plane‐wave beamforming and matched filtering array measurements in an ocean waveguide. The approach has been demonstrated with experimental data for a source transmitting linear frequency modulated pulses and theoretically for multiple uncorrelated broadband noise sources. Spectral analyzes of field‐recorded data acquired during the ocean acoustic waveguide remote sensing Gulf of Maine 2006 Experiment show that acoustic signatures from many random sources, such as marine mammal vocalizations, are complex and exhibit irregular patterns that vary over time. Furthermore, the signals embedded in noise may also contain interfering sources correlated with the signal over some time duration. Here, we extend the array invariant method for range and bearing estimation of such complex sources. A robust matched filter kernel based on the acoustic properties of field‐recorded whale vocalizations is developed to maximize the signal‐to‐noise ratio. Examples that simulate the beamformed and matched filtered array measurements of complex whale vocalizations embedded in noise in a random ocean waveguide are provided to demonstrate that range and bearing estimation using array invariance shows good agreement with true whale location.

Application of a Versatile "Real-Space" Validation Methodology to a Fire Model

This paper applies a pragmatic approach to validation of a fire-dynamics model involving computational fluid dynamics, combustion, participating-media radiation, and heat transfer. The validation problem involves experimental and predicted steady-state temperatures of a calorimeter in a wind-driven hydrocarbon pool fire. Significant aleatory and epistemic sources of uncertainty in the experiments and simulations exist and are transformed to a common basis of interval uncertainty for aggregation and comparison purposes. The validation comparison of experimental and simulation results, and corresponding criteria and procedures for model substantiation or refutation, take place in real space as opposed to space where various transform measures of discrepancy between experiment and simulation results are calculated and assessed. The versatile model validation approach handles difficulties associated with representing and aggregating aleatory and epistemic uncertainties (discrete and continuous) from multiple correlated and uncorrelated source types, including 1) experimental variability from multiple repeat experiments, 2) uncertainty of experimental inputs, 3) experimental output measurement uncertainties, 4) uncertainties that arise in data processing and inference from raw simulation and experiment outputs, 5) parameter and model-form uncertainties intrinsic to the model, and 6) numerical solution uncertainty from model discretization effects.

Unitary cyclic ESPRIT-like direction finding

Two unitary formulations of cyclic direction-of-arrival (DOA) algorithms, which are appropriate for both cyclic ESPRIT algorithm and conjugate cyclic ESPRIT algorithm, are proposed. Firstly, two approaches achieve a substantial reduction of the computational complexity via real-valued decomposition. Secondly, unitary method I cannot separate highly correlated or coherent signals, but unitary method II can separate them. Finally, these unitary methods allow to select desired signals and to ignore interferences for uncorrelated source scenarios, but only unitary method II has signal selective property in multipath propagation. Compared with cyclic ESPRIT algorithm, simulation results show the effectiveness of the proposed methods.

Time-resolved phonon-sideband spectroscopy

Phonon-assisted recombination in bulk CdS is analyzed by means of time-resolved photoluminescence spectroscopy. The experimental results demonstrate that both excitons and electron–hole plasma contribute to the phonon-sideband emission, depending on the excitation conditions. This observation is supported by a microscopic theory of interacting electrons, phonons, and photons that generalizes previous investigations by including both correlated and uncorrelated luminescence sources.

Relation Between the Mobility, $\hbox{1}/f$ Noise, and Channel Direction in MOSFETs Fabricated on (100) and (110) Silicon-Oriented Wafers

A study of the impact of the channel direction over the effective mobility and the 1/f noise in MOSFETs fabricated on (100) and (110) silicon-oriented wafers finding its outcome in the fabrication of future nonplanar device structures has been done. We found that, apart from a slight enhancement of the effective mobility maximum for the p-MOSFETs with a channel along the 100 direction, the channel direction had no effect on the noise level and performances of the transistors when they are fabricated on (100) silicon-oriented wafers. This suggests that a slight but effective enhancement of the already existing CMOS technology is possible by fabricating the MOSFETs with a channel along the 100 direction. Regarding the (110) silicon-oriented wafers, the modification of the channel direction resulted in a change of effective mobility, with the enhancement being maximum for a p-channel along the 110 direction and an n-channel along the 100 direction. Whereas this came with a noise level apparently unchanged for the p-MOSFETs, a perceptible change has been noticed for the n-MOSFETs, with the devices with a channel along the 100 direction showing the highest noise level. Finally, for the Si(110) n-MOSFETs, the earlier limitation of the effective mobility coming from the surface roughness scattering led to a negative transconductance; for the first time, it was clearly shown experimentally that two different uncorrelated noise sources generate the 1/f noise, with one becoming predominant over the other. The first noise source, attributed to the fluctuation of the insulator charge inducing fluctuations in both flatband voltage and mobility, initially contributes by itself to the total 1/f noise, then decreases and lets the second noise source, i.e., the fundamental mobility fluctuations, come out. This strongly suggests that, in the MOSFET, both noise sources, the fluctuation of the insulator charge and the fundamental mobility fluctuations subsist together, with one covering up the other according to the physical characteristics of the device and to the bias conditions.

DOA Estimation of Quasi-Stationary Signals With Less Sensors Than Sources and Unknown Spatial Noise Covariance: A Khatri–Rao Subspace Approach

In real-world applications such as those for speech and audio, there are signals that are nonstationary but can be modeled as being stationary within local time frames. Such signals are generally called quasi-stationary or locally stationary signals. This paper considers the problem of direction-of-arrival (DOA) estimation of quasi-stationary signals. Specifically, in our problem formulation we assume: i) sensor array of uniform linear structure; ii) mutually uncorrelated wide-sense quasi-stationary source signals; and iii) wide-sense stationary noise process with unknown, possibly nonwhite, spatial covariance. Under the assumptions above and by judiciously examining the structures of local second-order statistics (SOSs), we develop a Khatri-Rao (KR) subspace approach that has two notable advantages. First, through an identifiability analysis, it is proven that this KR subspace approach can operate even when the number of sensors is about half of the number of sources. The idea behind is to make use of a ¿virtual¿ array structure provided inherently in the local SOS model, of which the degree of freedom is about twice of that of the physical array. Second, the KR formulation naturally provides a simple yet effective way of eliminating the unknown spatial noise covariance from the signal SOSs. Extensive simulation results are provided to demonstrate the effectiveness of the KR subspace approach under various situations.

Retrieving the impulse response of the Earth due to random electromagnetic forcing

A derivation is presented of Green's function in an arbitrary, heterogeneous conductive medium subject to random, ambient, uncorrelated noise sources. The approach for extracting Green's function is based on the correlation of time series of magnetic field components at two independent locations. As in the related case for the electric field, where the volume distribution of noise sources must be spatially correlated with the heterogeneous conductivity distribution, Green's function for magnetic field requires noise sources to be spatially correlated with the volume distribution of magnetic permeability. For applications of electromagnetic imaging of Earth's deep subsurface, the effect of magnetic permeability variations in the subsurface is often assumed to be negligible when compared to the effect of conductivity variations. Hence, the expressions derived here may be useful for passive electromagnetic subsurface imaging, in apparent contrast to their electric field counterparts. Numerical validation exercises are described which validate this theory for Green's function estimation in the low-frequency limit.

Spatial coherence from ducks

It is not generally appreciated that radiation from uncorrelated random sources—for example, radiation generated by spontaneous emission of light by atoms—can produce a well-behaved, spatially coherent field over large regions. An illustration of this fact is the diffraction image of a star in the focal plane of a telescope. On a good observing night, the image will consist of a bright central spot surrounded by dark rings that represent regions in the focal plane where destructive interference cancels the light. This is a manifestation of strong correlation—a high degree of spatial coherence—between light fluctuations in the aperture of the telescope. The phenomenon illustrates the so-called van Cittert-Zernike theorem of optical coherence theory. 1 1. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics, Cambridge U. Press, Cambridge, UK (1995), sec. 4.4.4. , 2 2. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light, Cambridge U. Press, Cambridge, UK (2007), sec. 3.2. In this letter we provide an example of the generation of spatial coherence. Thirteen Rouen ducks jump into a still one-acre pond, disturbing the surface at randomly distributed positions and times. The water surface exhibits an irregular, rather incoherent spatial pattern, as seen in panel a of the figure. 3 3. The pictures are from a 28-second video clip, available at http://www.youtube.com/watch?v=4o48J4streE. With increasing distance and time, the pattern evolves into a more regular one, as captured in panels b, c, and d, which clearly indicate the generation of spatial coherence in the far field from randomly distributed sources. Generation of spatially coherent water waves from randomly distributed wave disturbances produced by 13 ducks jumping into a pool at time 00:47:12. The frame times are indicated.PPT|High resolutionREFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics, Cambridge U. Press, Cambridge, UK (1995), sec. 4.4.4. Google ScholarCrossref2. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light, Cambridge U. Press, Cambridge, UK (2007), sec. 3.2. Google Scholar3. The pictures are from a 28-second video clip, available at http://www.youtube.com/watch?v=4o48J4streE. Google Scholar© 2010 American Institute of Physics.

Modeling specular reflection in enclosures with energy-intensity boundary elements and an iterative relaxation method.

Steady-state sound fields in enclosures with specular reflection boundaries are modeled by an energy-intensity boundary element method using uncorrelated broadband directional sources. The specular reflection case is solved using an iterative relaxation method extended from a three dimensional (3-D) diffuse reflection solution. When chosen properly, few directivity harmonics are required. Starting with a diffuse calculation, higher harmonics are estimated by post-processing, and the original diffuse influence matrix is refined accordingly and converges in few relaxation steps. The method is higher-order accurate and similar to the diffuse case in that it includes strict enforcement of energy conservation. The method is computationally efficient, making it useful for the design of acoustic spaces. This new 3-D energy-intensity boundary element method utilizes an absorption scaling theory, allowing for direct solution of the element power distribution that describes the primary spatial variation caused by the effects of specular reflection, the absorption dependence on incidence angle, and the non-uniform spatial distribution of absorption and input power in the enclosure. Sample results show that differences between diffuse and specular solutions are often fairly small. The iterative relaxation method, with a limited number of specular harmonics, appears to provide a reasonable approach in practice. [Sponsored by NSF.]

Excess attenuation for sound propagation over an urban canyon

Because quiet areas in dense urban environments are important to well-being, the prediction of sound propagation to shielded urban areas is an ongoing research focus. Sound levels in shielded areas, such as canyons between rows of buildings, are strongly influenced by distant sources. Therefore, propagation factors such as metrology, screening, and intermediate canyons as occur between a source canyon and a receiver canyon must be addressed in an engineering propagation model. Though current models address many important propagation factors, engineering treatment of a closed urban canyon, subject to multiple internal reflections, remains difficult. A numerical investigation of sound propagation across the open tops of intermediate urban canyons has been performed, using the parabolic equation and equivalent sources methods. Results have been collected for various canyon geometries, and the influences of multiple canyons, canyon/rooftop absorption, variable rooftop height, wind gradient, and correlated versus uncorrelated source models have been investigated. Resulting wideband excess attenuation values ranged from -1 dB to -4 dB per canyon, and were fairly constant with frequency in many useful cases. By characterizing the excess attenuation of canyons intermediate to the source and receiver, the influence of these intermediate canyons could be addressed simply, without the overhead of a detailed numerical calculation. (c) 2010 Elsevier Ltd. All rights reserved.

Retrieving electric resistivity data from self‐potential measurements by cross‐correlation

We show that the two‐point cross‐correlation of self‐potential field recordings is equal to the electric resistivity between the two points. This holds under the condition that spatially and temporally uncorrelated noise sources exist throughout the volume. These sources should have a known amplitude spectrum and their correlated strengths should be proportional to the dissipative medium property function. Natural fluctuations, such as thermal noise, may occur that satisfy the necessary conditions. When these fluctuations are random deviations from a state of thermal equilibrium, the fluctuation‐dissipation theorem can be used to describe these sources. Other types of sources may exist, such as the ones creating the self‐potential field through coupling with fluctuations in pressure, temperature and chemical potential gradients.

Vector intensity reconstructions in a volume surrounding a rigid spherical microphone array

A technique is described to image the vector intensity in the near field of a spherical array of microphones flush mounted in a rigid sphere. The spatially measured pressure is decomposed into Fourier harmonics in order to reconstruct the volumetric vector intensity outside the sphere. The theory for this reconstruction is developed in this paper. The resulting intensity images are very successful at locating and quantifying unknown exterior acoustic sources, ideal for application in noise control problems in interior spaces such as automobiles and airplanes. Arrays of varying numbers of microphones and radii are considered and compared and errors are computed for both theory and experiment. It is demonstrated that this is an ill-posed problem below a cutoff frequency depending on array design, requiring Tikhonov regularization below cutoff. There is no low frequency limit on operation, although the signal-to-noise ratio is the determining factor for high-spatial resolution at low frequencies. It is shown that the upper frequency limit is set by the number of microphones in the array and is independent of noise. The accuracy of the approach is assessed by considering the exact solution for the scattering of a point source by a rigid sphere. Several field experiments are presented to demonstrate the utility of the technique. In these experiments, the partial field decomposition technique is used and holograms of multiple exterior sources are separated and their individual volumetric intensity fields imaged. In this manner, the intensity fields of two uncorrelated tube sources in an anechoic chamber are isolated from one another and separated intensity maps are obtained from over a broad frequency range. In a practical application, the vector intensity field in the interior of an automobile cabin is mapped at the fundamental of the engine vibration using the rigid sphere positioned at the driver's head. The source regions contributing to the interior cabin noise are identified.

Predicting Method for Transformation of Infragravity Waves with Interferometric Green's Functions

The propagation of infragravity waves in intermediate water depths near and in a port is investigated with field observations. A Green function method which is used for seismic interferometry is applied to estimate wave profiles of infragravity waves. The equations used in the method include Boussinesq equations with external forcing terms by fluctuating components of short gravity waves, atmospheric pressure and surface wind stresses. It is shown that when external forces are uncorrelated noise source, Green functions between two points can be retrieved by taking cross-correlation of records. The wave profiles of infragravity waves are estimated with the Green function and compared with the measured data. The agreement between them shows fairly good.

Source Localization and Sensing: A Nonparametric Iterative Adaptive Approach Based on Weighted Least Squares

Array processing is widely used in sensing applications for estimating the locations and waveforms of the sources in a given field. In the absence of a large number of snapshots, which is the case in numerous practical applications, such as underwater array processing, it becomes challenging to estimate the source parameters accurately. This paper presents a nonparametric and hyperparameter, free-weighted, least squares-based iterative adaptive approach for amplitude and phase estimation (IAA-APES) in array processing. IAA-APES can work well with few snapshots (even one), uncorrelated, partially correlated, and coherent sources, and arbitrary array geometries. IAA-APES is extended to give sparse results via a model-order selection tool, the Bayesian information criterion (BIC). Moreover, it is shown that further improvements in resolution and accuracy can be achieved by applying the parametric relaxation-based cyclic approach (RELAX) to refine the IAA-APES&BIC estimates if desired. IAA-APES can also be applied to active sensing applications, including single-input single-output (SISO) radar/sonar range-Doppler imaging and multi-input single-output (MISO) channel estimation for communications. Simulation results are presented to evaluate the performance of IAA-APES for all of these applications, and IAA-APES is shown to outperform a number of existing approaches.

Emergence of deterministic Green’s functions from noise generated by finite random sources

Two-point correlation functions of sufficiently diffuse wave fields generated by uncorrelated random sources are known to approximate deterministic Green's functions between the two points. This property is utilized increasingly for passive imaging and remote sensing of the environment. Here we show that the relation between the Green's functions and the noise cross-correlation function holds under much less restrictive conditions than previously thought. It can even hold when ambient noise sources have correlation ranges large compared to the wavelength. Admissible correlation ranges are limited from above by the size of the Fresnel zone at wave propagation between the points where noise cross correlation is evaluated.