MUSIC-type Methods Research Articles

Sparse cortical source localization using spatio-temporal atoms.

This paper addresses the problem of sparse localization of cortical sources from scalp EEG recordings. Localization algorithms use propagation model under spatial and/or temporal constraints, but their performance highly depends on the data signal-to-noise ratio (SNR). In this work we propose a dictionary based sparse localization method which uses a data driven spatio-temporal dictionary to reconstruct the measurements using Single Best Replacement (SBR) and Continuation Single Best Replacement (CSBR) algorithms. We tested and compared our methods with the well-known MUSIC and RAP-MUSIC algorithms on simulated realistic data. Tests were carried out for different noise levels. The results show that our method has a strong advantage over MUSIC-type methods in case of synchronized sources.

Multiple signal classification method for detecting point-like scatterers embedded in an inhomogeneous background medium

The multiple signal classification (MUSIC) type method has been widely used to detect point-like scatterers embedded in a homogeneous background medium. This paper extends the MUSIC-type method to the detection of point-like scatterers that are embedded in an inhomogeneous background. Although the background Green's function at each test point is not directly available in inhomogeneous background scenario, this paper proposes an approach, based on the finite element method, to simultaneously obtain the Green's function at all test points. Numerical simulations illustrate the efficacy of the proposed theory and algorithm presented in this paper, and some interesting observations, which are absent in homogeneous background scenario, are highlighted and discussed.

Performance analysis of velocity–pressure smoothing for direction‐of‐arrival estimation of coherent signals

AbstractIn this paper, we consider the problem of direction‐of‐arrival (DOA) estimation of coherent signals by using a number of identically oriented acoustic vector‐sensors, wherein source decorrelation can be achieved by velocity–pressure smoothing. We examine the effect of velocity–pressure smoothing on the performance of MUSIC‐type methods in terms of the overall root mean‐square errors (RMSE) of DOA estimates. The closed‐form expression for the overall RMSE is derived and analyzed. We also compare velocity–pressure smoothing with the conventional spatial smoothing technique. Simulation results are given to confirm the analyses. Copyright © 2009 John Wiley & Sons, Ltd.

An Asymptotic Factorization Method for Inverse Electromagnetic Scattering in Layered Media

We consider the inverse problem to reconstruct the number and the positions of a collection of finitely many small perfectly conducting scatterers buried within the lower halfspace of an unbounded two-layered background medium from near field measurements of time harmonic electromagnetic fields. For this purpose we first study the direct scattering problem and derive an asymptotic expansion of the scattered field, as the size of the scatterers tends to zero. Integral equation methods and a factorization of the corresponding near field measurement operator are applied to prove this expansion. In the second part of this work we use the asymptotic expansion to justify a noniterative reconstruction algorithm, which is a combination of factorization methods and MUSIC-type methods. We illustrate the feasibility of this method by a numerical example.

Identification of small inhomogeneities: Asymptotic factorization

We consider the boundary value problem of calculating the electrostatic potential for a homogeneous conductor containing finitely many small insulating inclusions. We give a new proof of the asymptotic expansion of the electrostatic potential in terms of the background potential, the location of the inhomogeneities and their geometry, as the size of the inhomogeneities tends to zero. Such asymptotic expansions have already been used to design direct (i.e. noniterative) reconstruction algorithms for the determination of the location of the small inclusions from electrostatic measurements on the boundary, e.g. MUSIC-type methods. Our derivation of the asymptotic formulas is based on integral equation methods. It demonstrates the strong relation between factorization methods and MUSIC-type methods for the solution of this inverse problem.

Rational invariant subspace approximations with applications

Subspace methods such as MUSIC, minimum norm, and ESPRIT have gained considerable attention due to their superior performance in sinusoidal and direction-of-arrival (DOA) estimation, but they are also known to be of high computational cost. In this paper, new fast algorithms for approximating signal and noise subspaces and that do not require exact eigendecomposition are presented. These algorithms approximate the required subspace using rational and power-like methods applied to the direct data or the sample covariance matrix. Several ESPRIT- as well as MUSIC-type methods are developed based on these approximations. A substantial computational saving can be gained comparing with those associated with the eigendecomposition-based methods. These methods are demonstrated to have performance comparable to that of MUSIC yet will require fewer computations to obtain the signal subspace matrix.

DOA and frequency estimation using fast subspace algorithms

Eigendecomposition-based methods such as MUSIC, minimum norm, and ESPRIT estimators are popular for their high resolution property in sinusoidal and direction of arrival (DOA) estimation but they are also known to be of high computational demand. In this paper, new fast and robust algorithms for DOA frequency estimation are presented. These algorithms approximate the required signal and noise subspace using rational and power-like methods applied to the sample covariance matrix and have been shown to be applicable to ESPRIT-type as well as MUSIC-type methods. It is also shown that a substantial computational saving would be gained compared to those associated with the eigendecomposition-based methods. Simulations results show that these approximated estimators have comparable performance at low signal-to-noise ratio (SNR) to their standard counterparts and are robust against overestimating the number of impinging signals.

Array processing using joint diagonalization

A new approach to array processing (i.e., direction-finding, signal separation and reconstruction, and calibration) is considered. The main advantages of the advocated approach is that the multidimensional search associated with maximum likelihood-based estimators or the single-dimensional search associated with MUSIC-type methods are eliminated. While the proposed method is based on the Analytical Constant Modulus Algorithm that was recently proposed by Van der Veen and Paulraj, it is not limited to constant modulus signals or any other specific type of signals. The sensor array elements are assumed to have the same, up to a multiplicative constant, angle-dependent, unknown gain pattern. We show that under this assumption it is possible to estimate the array response matrix and then use the result for direction finding, if the nominal array manifold is known, at least approximately. It is also possible to use the estimated array response matrix in order to separate and reconstruct the signals, or calibrate the array shape or response. We provide performance analysis of the algorithm and compare the results with computer simulations. We also examine the sensitivity of algorithm to the model assumptions. The method can be applied in the presence of specular multipath (using spatial smoothing) but it is not suitable for signal separation in the presence of severe diffuse multipath.