Multiple Signal Classification Method Research Articles

Multiple dipole modeling and localization from spatio-temporal MEG data.

An array of biomagnetometers may be used to measure the spatio-temporal neuromagnetic field or magnetoencephalogram (MEG) produced by neural activity in the brain. A popular model for the neural activity produced in response to a given sensory stimulus is a set of current dipoles, where each dipole represents the primary current associated with the combined activation of a large number of neurons located in a small volume of the brain. An important problem in the interpretation of MEG data from evoked response experiments is the localization of these neural current dipoles. We present here a linear algebraic framework for three common spatio-temporal dipole models: i) unconstrained dipoles, ii) dipoles with a fixed location, and iii) dipoles with a fixed orientation and location. In all cases, we assume that the location, orientation, and magnitude of the dipoles are unknown. With a common model, we show how the parameter estimation problem may be decomposed into the estimation of the time invariant parameters using nonlinear least-squares minimization, followed by linear estimation of the associated time varying parameters. A subspace formulation is presented and used to derive a suboptimal least-squares subspace scanning method. The resulting algorithm is a special case of the well-known MUltiple SIgnal Classification (MUSIC) method, in which the solution (multiple dipole locations) is found by scanning potential locations using a simple one dipole model. Principal components analysis (PCA) dipole fitting has also been used to individually fit single dipoles in a multiple dipole problem. Analysis is presented here to show why PCA dipole fitting will fail in general, whereas the subspace method presented here will generally succeed. Numerically efficient means of calculating the cost functions are presented, and problems of model order selection and missing moments are discussed. Results from a simulation and a somatosensory experiment are presented.

Deterministic frequency‐wavenumber methods and direct measurements of rupture propagation during earthquakes using a dense array: Theory and methods

We present an approach for measuring the spatial extent, duration, directions and speeds of rupture propagation during an earthquake using array signal processing techniques. Unlike most previous approaches, no assumptions are made regarding the directions and speeds of propagation. The solution we obtain is unique, and its accuracy, precision and resolution can be estimated. We use preprocessing and coprocessing techniques that improve the accuracy/precision of existing frequency‐wavenumber methods. Subarray spatial averaging modifies frequency‐wavenumber techniques so that they are sensitive to multiple deterministic (transient) as well as stochastic (stationary) signals. This technique is also advantageous because it ensemble averages the cross spectral matrix and reduces the variance of the frequency‐wavenumber spectrum. Seismogram alignment is a preprocessing procedure that accounts for nonplanar wavefronts due to lateral velocity variations beneath an array. This procedure also allows us to study signals of interest using much shorter time windows than has previously been possible. The use of short time windows is important for reducing uncertainty in estimates of arrival times of seismic phases. We tested subarray spatial averaging and seismogram alignment with a variety of frequency‐wavenumber techniques and found that the multiple signal classification (MUSIC) method gave the best resolution of multiple signals. We also note that standard theoretical estimates of uncertainties in peak locations of frequency‐wavenumber spectra are much smaller than those typically observed using seismic arrays and we present a different formula that more accurately describes observed uncertainties. Using synthetic P and S body‐wave seismograms from extended earthquake sources we show that the above array signal processing techniques can be combined with ray theory to obtain accurate estimates of the locations and rupture times of an earthquake's high‐frequency seismic sources. We show how to estimate uncertainties in source locations and rupture times due to limitations of the data, uncertainties in source parameters, and uncertainties in velocity structure. We find that the size of the uncertainties can be very sensitive to a fault's geometry relative to an array and we suggest criteria for optimizing an array's location. We show that high‐frequency source locations and their associated rupture times can be used to estimate an earthquake's spatial extent, duration, directions and speeds of rupture propagation.

Statistical analysis of MUSIC and subspace rotation estimates of sinusoidal frequencies

Consideration is given to the analysis of the large-sample second-order properties of multiple signal classification (MUSIC) and subspace rotation (SUR) methods, such as ESPRIT, for sinusoidal frequency estimation. Explicit expressions for the covariance elements of the estimation errors associated with either method are derived. These expressions of covariances are then used to analyze and compare the statistical performances of the MUSIC and SUR estimation (SURE) methods. Both MUSIC and SURE are based on the eigendecomposition of a sample data covariance matrix. The expressions for the estimation error variances derived are used to study the dependence of MUSIC and SURE performances on the dimension of the data covariance matrix used. >

Music analysis applied to NMR

Here, we would like to present an alternative for this transform, the multiple signal identification and classification method (MUSIC). This is a spectral estimator, like FFT, that has proven to be very useful in molecular dynamics studies (3, 4), and other applications. For certain cases this method has advantages over the FFT

Short time molecular dynamics simulations: Stressed polyethylene results

AbstractThe multiple signal classification method (MUSIC) for frequency estimation is used to compute the spectrum (intensity versus frequency) for stressed polyethylene in a crystal from the time‐dependent structure factor. In this article we demonstrate that MUSIC can accurately determine the frequencies for our model from very short time trajectories and can compute the frequency shifts for various stress perturbations. A preliminary study of the dynamical effects of stress on the fracture of a PE chain showed that at low stress the chain had an irregular period of the end‐to‐end distance (reaction coordinate) oscillation and at higher stress a periodic extension and contraction.

Calculation of ab initio frequencies from short time classical trajectories

The multiple signal classification method (MUSIC) for frequency estimation is used to compute harmonic and transition frequencies for a three-mode model of water using classical trajectories. Only very-short-time correlation functions (approximately one-half to one vibrational period) are needed to compute the frequencies generated directly from quantum chemistry methods.

Dispersion curves from short-time molecular dynamics simulations. 1. Diatomic chain results

The multiple signal classification method (MUSIC) for frequency estimation is used to compute the frequency dispersion curves of a diatomic chain from the time-dependent structure factor. In this paper, the authors demonstrate that MUSIC can accurately determine the frequencies from very short time trajectories. MUSIC is also used to show how the frequencies can vary in time, i.e., along a trajectory. The method is ideally suited for analyzing molecular dynamics simulations of large systems.

Calculation of semiclassical transition frequencies from short-time classical trajectories

The multiple signal classification method (MUSIC) for frequency estimation is used to compute semiclassical transition frequencies for the Hénon-Heiles potential and a three-mode model of H 2O. Only very short-time correlation functions are needed to compute transition frequencies, and classically chaotic dissociative trajectories can be used in some cases. The method is shown to lead to very significant reduction of necessary trajectory integration times.

A vector space approach to direction finding in a coherent multipath environment

The superresolution methods of spatial spectrum estimation heretofore reported are known to break down when arriving signals from different directions are coherent. It is shown here that this deficiency can be overcome by replacing the direction-of-arrival (DOA) search vector ordinarily used with a linear combination of such vectors. Particular attention is here given to extending the multiple signal classification (MUSIC) method to cover such cases. A procedure for determining the proper linear combination is presented so that determination of the separate coherent signal arrival angles involves a multidimensional search in angle only. Such a search is demonstrated for coherent two-ray and three-ray multipath environments.