Source localization using recursively applied and projected (RAP)MUSIC

A new method for source localization is described that is based on a modification of the well-known MUSIC algorithm. In classical MUSIC, the array manifold vector is projected onto an estimate of the signal subspace. Errors in the estimate of the signal subspace can make localization of multiple sources difficult. Recursively applied and projected (RAP) MUSIC uses each successively located source to form an intermediate array gain matrix and projects both the array manifold and the signal subspace estimate into its orthogonal complement. The MUSIC projection to find the next source is then performed in this reduced subspace. Special assumptions about the array manifold structure, such as Vandermonde or shift invariance, are not required. Using the metric of principal angles, we describe a general form of the RAP-MUSIC algorithm for the case of diversely polarized sources. Through a uniform linear array simulation with two highly correlated sources, we demonstrate the improved Monte Carlo error performance of RAP-MUSIC relative to MUSIC and two other sequential subspace methods: S and IES-MUSIC. We then demonstrate the more general utility of this algorithm for multidimensional array manifolds in a magnetoencephalography (MEG) source localization simulation     

多维延时相关MUSIC方法:一种求解脑电逆问题的新方法

将经典的多信号分类算法(MUSIC)用于研究脑电逆问题时存在两个问题:对有色噪音敏感和不能识别相干源.近年人们提出了利用延时相关、高阶累积量或假设已知噪音协方差来缓解有色噪音对算法的影响.对于相干源,则有人提出了递归的多维MUSIC方法.本文在这些工作的基础上建立了一种基于延时相关阵的、叠代的多维MUSIC算法.仿真数据及实际脑电应用研究表明,该方法能在压制有色噪音的同时识别多个相干源,因而具有明显的意义.     

Applicability of MUSIC-Type Imaging in Two-Dimensional Electromagnetic Inverse Problems

The behavior of the multiple signal classification (MUSIC) algorithm is investigated when used to locate small dielectric cylinders of specific characteristics in noise-free and noisy scenarios using the TE incidence. We have made three observations regarding the performance of MUSIC in the two-dimensional TE scenario, which reveal the significance of the choice of signal subspace while employing MUSIC and the shortcoming of traditional MUSIC when used to detect degenerate cylinders (which might be so due to the material or geometry of the cylinders). The detailed analysis of the sources induced on a cylinder and their linear dependency on each other gives a distinct insight into the use of MUSIC algorithm to locate it. A non-iterative retrieval algorithm is provided that is based on the least squares method, which retrieves the electric and magnetic polarization tensors of the small cylinders. The algorithm proposed here is mathematically a simple and direct representation of the physical principles and is applicable to degenerate cylinders as well.     

A note on “A fast high-resolution method for bearing estimation in shallow ocean”

In the referenced paper [by Jin, Huang, Zhang, and Hou, Multidimensional Systems and Signal Processing, 20(4): 397–406, 2009], a rank-reduction based direction finding algorithm called Rayleigh MUSIC (R-MUSIC) is proposed to deal with the multimode nature of the acoustic propagation in the shallow ocean. However, when a linear array is utilized, R-MUSIC degrades severely for sources located in the vicinity of the array broadside. In this note, a measure is given to overcome this drawback.     

Multiple dipole modeling and localization from spatio-temporal MEGdata

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.     

Noise covariance incorporated MEG-MUSIC algorithm: a method formultiple-dipole estimation tolerant of the influence of background brainactivity

This paper proposes a method of localizing multiple current dipoles from spatio-temporal biomagnetic data. The method is based on the multiple signal classification (MUSIC) algorithm and is tolerant of the influence of background brain activity. In this method, the noise covariance matrix is estimated using a portion of the data that contains noise, but does not contain any signal information. Then, a modified noise subspace projector is formed using the generalized eigenvectors of the noise and measured-data covariance matrices. The MUSIC localizer is calculated using this noise subspace projector and the noise covariance matrix. The results from a computer simulation have verified the effectiveness of the method. The method was then applied to source estimation for auditory-evoked fields elicited by syllable speech sounds. The results strongly suggest the method's effectiveness in removing the influence of background activity     

Paired MEG data set source localization using recursively applied and projected (RAP) MUSIC

An important class of experiments in functional brain mapping involves collecting pairs of data corresponding to separate "Task" and "Control" conditions. The data are then analyzed to determine what activity occurs during the Task experiment but not in the Control. Here we describe a new method for processing paired magnetoencephalographic (MEG) data sets using our recursively applied and projected multiple signal classification (RAP-MUSIC) algorithm. In this method the signal subspace of the Task data is projected against the orthogonal complement of the Control data signal subspace to obtain a subspace which describes spatial activity unique to the Task. A RAP-MUSIC localization search is then performed on this projected data to localize the sources which are active in the Task but not in the Control data. In addition to dipolar sources, effective blocking of more complex sources, e.g., multiple synchronously activated dipoles or synchronously activated distributed source activity, is possible since these topographies are well-described by the Control data signal subspace. Unlike previously published methods, the proposed method is shown to be effective in situations where the time series associated with Control and Task activity possess significant cross correlation. The method also allows for straightforward determination of the estimated time series of the localized target sources. A multiepoch MEG simulation and a phantom experiment are presented to demonstrate the ability of this method to successfully identify sources and their time series in the Task data.     

加权伪噪声子空间投影的修正MUSIC算法

多重信号分类（multiple signal classification: MUSIC）方法通过计算搜索导向矢量与噪声或信号子空间的距离来估计波达方向,对采样协方差矩阵的依赖性较大。在小快拍或存在强弱临近信号条件下,采样协方差矩阵的估计值与真实值通常存在较大差异,导致估计的噪声或信号子空间发生畸变,严重恶化了MUSIC方法的波达角估计性能。针对该问题,本文提出采用加权伪噪声子空间投影的改进方法（称为wpnMUSIC）。该方法在修正数据相关矩阵的基础上估计与搜索导向矢量对应的伪噪声子空间并利用其在伪噪声子空间的投影值对MUSIC空间谱进行加权处理,在保持子空间处理方法高分辨能力的同时改善了对小快拍和强弱信号的稳健性。理论分析和仿真实验表明本文方法对强弱临近目标的分辨能力优于MUSIC方法。      

Statistical maps for EEG dipolar source localization

We present a method that estimates three-dimensional statistical maps for electroencephalogram (EEG) source localization. The maps assess the likelihood that a point in the brain contains a dipolar source, under the hypothesis of one, two or three activated sources. This is achieved by examining all combinations of one to three dipoles on a coarse grid and attributing to each combination a score based on an F statistic. The probability density function of the statistic under the null hypothesis is estimated nonparametrically, using bootstrap resampling. A theoretical F distribution is then fitted to the empirical distribution in order to allow correction for multiple comparisons. The maps allow for the systematic exploration of the solution space for dipolar sources. They permit to test whether the data support a given solution. They do not rely on the assumption of uncorrelated source time courses. They can be compared to other statistical parametric maps such as those used in functional magnetic resonance imaging (fMRI). Results are presented for both simulated and real data. The maps were compared with LORETA and MUSIC results. For the real data consisting of an average of epileptic spikes, we observed good agreement between the EEG statistical maps, intracranial EEG recordings, and fMRI activations.     

Novel high-resolution DOA estimation using subspace projection method

The performance of multiple signal classification(MUSIC) algorithm with regard to solving closely spaced direction of arrivals(DOAs) depends strongly upon the signal-to-noise ratio(SNR) and snapshots.In order to solve this problem,a method by reconstructing the spatial spectrum function with both noise subspace and signal subspace is presented in this paper.The key idea is to apply the full information contained in covariance matrix and change the projection weights of steering vector on the noise and signal subspace by their revised eigenvalues,respectively.Comparing with the MUSIC algorithm,it does not increase any computational complexity either,and remarkably,it has the advantages of simultaneously reducing noise and keeping the high-resolution ability under low SNR and small sample sized scenarios.Simulation and experiment results are included to demonstrate the superior performance of the proposed algorithm.     

Oblique Projections for Direction-of-Arrival Estimation With Prior Knowledge

Estimation of directions-of-arrival (DOA) is an important problem in various applications and a priori knowledge on the source location is sometimes available. To exploit this information, standard methods are based on the orthogonal projection of the steering manifold onto the noise subspace associated with the a priori known DOA. In this paper, we derive and analyze the Cramer-Rao bound associated with this model and in particular we point out the limitations of this approach when the known and unknown DOA are closely spaced and the associated sources are uncorrelated (block-diagonal source covariance). To fill this need, we propose to integrate a priori known locations of several sources into the MUSIC algorithm based on oblique projection of the steering manifold. Finally, we show that the proposed approach is able to almost completely cancel the influence of the known DOA on the unknown ones for block-diagonal source covariance and for sufficient signal-to-noise ratio (SNR).     

Coded asynchronous CDMA and its efficient detection

In this paper, receiver design and performance analysis for coded asynchronous code-division multiple access (CDMA) systems is considered. The receiver front-end consists of the near-far resistant multiuser detector known as the projection receiver (PR). The PR performs multiple-access interference resolution and is followed by error-control decoding. The output of the projection receiver yields the appropriate metric (i.e., soft information) for decoding of the coded sequences. An expression for the metric is derived that allows the use of a standard sequence decoder (e.g., Viterbi algorithm, M-algorithm) for the error-control code. It is then shown that the metric computer has an elegant adaptive implementation based on an extension of the familiar recursive least squares (RLS) algorithm. The adaptive PR operates on a single sample per chip and achieves a performance virtually identical to the algebraic PR, but with significantly less complexity. The receiver performance is studied for CDMA systems with fixed and random spreading sequences, and theoretical performance degradations with regard to the single-user bound are derived. The near-far resistance of the PR is also proven, and demonstrated by simulation     

Signal processing applications of oblique projection operators

Oblique projection operators are used to project measurements onto a low-rank subspace along a direction that is oblique to the subspace. They may be used to enhance signals while nulling interferences. In the paper, the authors give several basic results for oblique projections, including formulas for constructing oblique projections with desired range and null space. They analyze the algebra and geometry of oblique projections in order to understand their properties. They then show how oblique projections can be used to separate signals from structured noise (such as impulse noise), damped or undamped interfering sinusoids (such as power line interference), and narrow-band noise. In some of the problems addressed, the oblique projection provides an alternative way to implement an already known solution. Expressing these solutions as oblique projections brings geometrical insight to the study of the solution. The geometry of oblique projections enables one to compute performance in terms of angles between signal and noise subspaces. As a special case of removing impulse noise, the authors can use oblique projections to interpolate missing data samples. In array processing, oblique projections can be used to simultaneously steer beams and nulls. In communications, oblique projections can be used to remove intersymbol interference     

电磁矢量传感器阵列信号波达角估计的模R投影MUSIC简

 为了充分利用电磁矢量传感器阵列数据中存在的多维结构,本文探讨了具有多维数据结构的电磁矢量传感器阵列多模张量模型的建立,以及模R信号子空间的定义,提出一种基于模R信号子空间投影的MUSIC算法.分析表明:由于模R投影方法可充分利用电磁矢量传感器阵列中的多维结构信息,从而可提高信号子空间的估计精度,进而可使MUSIC算法的性能得以改善.计算机的仿真研究验证了模R投影MUSIC算法明显优于传统MUSIC方法.     

Efficient localization of synchronous EEG source activities using a modified RAP-MUSIC algorithm

Synchronization across different brain regions is suggested to be a possible mechanism for functional integration. Noninvasive analysis of the synchronization among cortical areas is possible if the electrical sources can be estimated by solving the electroencephalography inverse problem. Among various inverse algorithms, spatio-temporal dipole fitting methods such as RAP-MUSIC and R-MUSIC have demonstrated superior ability in the localization of a restricted number of independent sources, and also have the ability to reliably reproduce temporal waveforms. However, these algorithms experience difficulty in reconstructing multiple correlated sources. Accurate reconstruction of correlated brain activities is critical in synchronization analysis. In this study, we modified the well-known inverse algorithm RAP-MUSIC to a multistage process which analyzes the correlation of candidate sources and searches for independent topographies (ITs) among precorrelated groups. Comparative studies were carried out on both simulated data and clinical seizure data. The results demonstrated superior performance with the modified algorithm compared to the original RAP-MUSIC in recovering synchronous sources and localizing the epileptiform activity. The modified RAP-MUSIC algorithm, thus, has potential in neurological applications involving significant synchronous brain activities.     

An iterative subspace-based multi-pitch estimation algorithm

In this paper, we present an iterative method for estimation of pitches from signals containing multiple sources using subspace techniques. The resulting estimator is termed Iterative Harmonic MUltiple SIgnal Classification (I-HMUSIC). Different modifications of I-HMUSIC are proposed that improve upon the classical MUSIC algorithm, including a computationally efficient method for noise subspace updating I-HMUSIC and its modifications are evaluated and compared with both the Cramér-Rao lower bound (CRLB) and non-iterative HMUSIC; good statistical performances have been obtained.     

二维多源测向的实时处理算法及实现

研究用二维MUSIC算法，解决阵列处理二维多源测向的快速实现问题。利用阵列流形具有的对称性，减少阵列流形和空间谱的计算量。在判定出信号源个数后，有选择地使用信号子空间或噪声子空间去计算空间谱，进一步减少计算量。采用2片ADI公司的高性能DSP芯片（ADSP21160），用并行处理方法实现了二维多源测向的实时处理。     

基于子空间旋转变换的低复杂度波达角估计算法

多重信号分选(MUltiple SIgnal Classification, MUSIC)算法是波达方向(Direction-Of-Arrival, DOA)估计的最重要算法之一,但庞大的计算量使其工程实用性大打折扣。为降低MUSIC的计算量,该文基于子空间旋转(Subspace Rotation Technique, SRT)变换思想提出了一种高效改进算法,即SRT-MUSIC算法。SRT-MUSIC利用秩亏特性对噪声子空间矩阵按行分块并以旋转变换得到降维噪声子空间,进而基于该降维噪声子空间与导向矢量的正交性构造空间谱估计信号DOA。理论分析表明：SRT-MUSIC能有效避免空间谱搜索中的冗余运算,从而成倍降低算法的计算量。对于大阵元、少信号情况,所提算法计算效率优势更为明显。仿真实验证明了SRT-MUSIC的有效性和高效性。     

A pencil-MUSIC algorithm for finding two-dimensional angles andpolarizations using crossed dipoles

The authors study the problem of finding two-dimensional (2-D) angles of wave arrival and wave polarizations using a uniform rectangular array of crossed dipoles. The method presented effectively exploits the redundancy in this array via 2-D moving-window smoothing to handle coherent sources and to achieve optimum noise sensitivity. The method combines the computational advantages of the MUSIC and matrix pencil approaches. The method is shown in simulation to be nearly optimum compared with the Cramer-Rao bound     

Unsupervised hyperspectral image analysis with projection pursuit

Principal components analysis (PCA) is effective at compressing information in multivariate data sets by computing orthogonal projections that maximize the amount of data variance. Unfortunately, information content in hyperspectral images does not always coincide with such projections. The authors propose an application of projection pursuit (PP), which seeks to find a set of projections that are "interesting," in the sense that they deviate from the Gaussian distribution assumption. Once these projections are obtained, they can be used for image compression, segmentation, or enhancement for visual analysis. To find these projections, a two-step iterative process is followed where they first search for a projection that maximizes a projection index based on the information divergence of the projection's estimated probability distribution from the Gaussian distribution and then reduce the rank by projecting the data onto the subspace orthogonal to the previous projections. To calculate each projection, they use a simplified approach to maximizing the projection index, which does not require an optimization algorithm. It searches for a solution by obtaining a set of candidate projections from the data and choosing the one with the highest projection index. The effectiveness of this method is demonstrated through simulated examples as well as data from the hyperspectral digital imagery collection experiment (HYDICE) and the spatially enhanced broadband array spectrograph system (SEBASS).