Gutiérrez David, Nehorai Arye, Dogandzić Aleksandar
Department of Computer Systems Engineering and Automation, Institute of Research in Applied Mathematics and Systems, National Autonomous University of Mexico, Mexico City 01000, Mexico.
IEEE Trans Biomed Eng. 2006 May;53(5):840-4. doi: 10.1109/TBME.2005.863942.
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.
我们研究了各种波束形成器在使用脑电图（EEG）和脑磁图（MEG）估计已知位置的电流偶极子源时的性能。我们以广义旁瓣对消器（GSC）的形式展示我们的波束形成器。在这种结构下，波束形成器可以通过找到一个滤波器来求解，该滤波器能使主波束响应与滤波后的观测信号之间的均方误差（MMSE）最小。我们将MMSE表示为滤波器秩的函数，并将其用作评估波束形成器性能的标准。我们不对干扰加噪声协方差矩阵的秩做任何假设。相反，我们将其视为低秩，并推导MMSE的一般表达式。我们给出数值示例，以比较文献中常用的波束形成器的均方误差（MSE）性能：主成分（PC）、互谱度量（CSM）和特征对消器（EIG）波束形成器。我们的结果表明，即使对于低信噪比（SNR）值，使用降秩波束形成器也能实现对偶极子源信号的良好估计。
