Surface-source modeling and estimation using biomagnetic measurements

We propose a number of electric source models that are spatially distributed on an unknown surface for biomagnetism. These can be useful to model, e.g., patches of electrical activity on the cortex. We use a realistic head (or another organ) model and discuss the special case of a spherical head model with radial sensors resulting in more efficient computations of the estimates for magnetoencephalography. We derive forward solutions, maximum likelihood (ML) estimates, and Cramér-Rao bound (CRB) expressions for the unknown source parameters. A model selection method is applied to decide on the most appropriate model. We also present numerical examples to compare the performances and computational costs of the different models and illustrate when it is possible to distinguish between surface and focal sources or line sources. Finally, we apply our methods to real biomagnetic data of phantom human torso and demonstrate the applicability of them.     

Performance analysis of reduced-rank beamformers for estimating dipole source signals using EEG/MEG

We study the performance of various beamformers for estimating a current dipole source at a known location using electroencephalography (EEG) and magnetoencephalography (MEG). We present our beamformers in the form of the generalized sidelobe canceler (GSC). Under this structure, the beamformer can be solved by finding a filter that achieves the minimum mean-squared error (MMSE) between the mainbeam response and filtered observed signal. We express the MMSE as a function of the filter's rank and use it as a criterion to evaluate the performance of the beamformers. We do not make any assumptions on the rank of the interference-plus-noise covariance matrix. Instead, we treat it as low-rank and derive a general expression for the MMSE. We present numerical examples to compare the MSE performance of beamformers commonly studied in the literature: principal components (PCs), cross-spectral metrics (CSMs), and eigencanceler (EIG) beamformers. Our results show that good estimates of the dipole source signals can be achieved using reduced-rank beamformers even for low signal-to-noise ratio (SNR) values.     

Model selection in spatio-temporal electromagnetic source analysis

Several methods [model selection procedures (MSPs)] to determine the number of sources in electroencephalogram (EEG) and magnetoencphalogram (MEG) data have previously been investigated in an instantaneous analysis. In this paper, these MSPs are extended to a spatio-temporal analysis if possible. It is seen that the residual variance (RV) tends to overestimate the number of sources. The Akaike information criterion (AIC) and the Wald test on amplitudes (WA) and the Wald test on locations (WL) have the highest probabilities of selecting the correct number of sources. The WA has the advantage that it offers the opportunity to test which source is active at which time sample.     

Statistical analysis of two nonlinear least-squares estimators of sine-wave parameters in the colored-noise case

This paper establishes the large-sample accuracy properties of two nonlinear least-squares estimators (NLSE) of sine-wave parameters: the basic NLSE, which ignores the possible correlation of the noise, and the optimal NLSE, which, besides the sine-wave parameters, also estimates the noise correlation (appropriately parametrized). It is shown that these two NLS estimators have thesame accuracy in large samples. This result provides complete justification for preferring the computationally less expensive basic NLSE over the optimal NLSE. Both estimators are shown to achieve the Cramér-Rao Bound (CRB) as the sample size increases. A simple explicit expression for the CRB matrix is provided, which should be useful in studying the performance of sine-wave parameter estimators designed to work in the colored-noise case.The work of A. Nehorai was supported by the Air Force Office of Scientific Research, under Grant No. AFOSR-88-0080.     

Adaptive null-forming scheme in digital hearing aids

We propose an effective adaptive null-forming scheme for two nearby microphones in endfire orientation that are used in digital hearing aids and in many other hearing devices. This adaptive null-forming scheme is mainly based on an adaptive combination of two fixed polar patterns that act to make the null of the combined polar pattern of the system output always be toward the direction of the noise. The adaptive combination of these two fixed polar patterns is accomplished by simply updating an adaptive gain following the output of the first polar pattern unit. The value of this gain is updated by minimizing the power of the system output, and related adaptive algorithms to update this gain are also given. We have implemented this proposed system on the basis of a programmable DSP chip and performed various tests. Theoretical analyses and testing results demonstrated the effectiveness of the proposed system and the accuracy of its implementation     

Analysis of a polarized seismic wave model

We present a model for polarized seismic waves where the data are collected by three-component geophone receivers. The model is based on two parameters describing the polarization properties of the waveforms. These parameters are the ellipticity and the orientation angle of the polarization ellipse. The model describes longitudinal waveforms (P-waves) as well as elliptically polarized waves. For the latter waves the direction-of-propagation of the waveform is in the plane spanned by the ellipse's major and minor axes; Rayleigh waves are treated as a special case. We analyze the identifiability of the models and derive the Cramer-Rao and mean-square-angular-error (MSAE) bounds involving one or two three-component geophones     

A Sequential Detector for Biochemical Release in Realistic Environments

We develop a sequential detector for the release of a biochemical substance, with potential applications in environmental security. The proposed detector provides online detection of the appearance of a biochemical source in realistic complex environments. To obtain optimal performance, we use an integrated approach combining statistical analysis of measurements given by an array of biochemical sensors with a physical model of the dispersion, amenable to arbitrary geometries and wind turbulence. We first focus on formulating a detector that is applicable in the presence of unknown source parameters (e.g., release time, intensity, and location). We then derive a bound on the expected delay before a false detection in order to select the threshold of the test. For a fixed false-alarm rate, we obtain the detection probability of a release as a function of its location and initial concentration. Numerical examples illustrate the applicability of our methods to real-world scenarios of an urban area and indoor ventilation duct.     

Acoustic vector-sensor array processing

A method is presented for localizing acoustic sources using an array of sensors, the output of each being a vector consisting of the acoustic pressure and acoustic particle velocity. The authors derive a compact expression for the Cramer-Rao bound (CRB) on the estimation errors of the source direction-of-arrival (DOA) parameters in the multi-source multi-vector-sensor model. An explicit expression is found for the mean-square angular error (MSAE) bound for source localization with a single vector sensor. The authors present two simple algorithms for estimating the source DOA with this sensor, along with their statistical performance analyses