Gorodnitsky I F, George J S, Rao B D
Electrical Engineering Department, University of California at San Diego, La Jolla 92093-0407, USA.
Electroencephalogr Clin Neurophysiol. 1995 Oct;95(4):231-51. doi: 10.1016/0013-4694(95)00107-a.
The paper describes a new algorithm for tomographic source reconstruction in neural electromagnetic inverse problems. Termed FOCUSS (FOCal Underdetermined System Solution), this algorithm combines the desired features of the two major approaches to electromagnetic inverse procedures. Like multiple current dipole modeling methods, FOCUSS produces high resolution solutions appropriate for the highly localized sources often encountered in electromagnetic imaging. Like linear estimation methods, FOCUSS allows current sources to assume arbitrary shapes and it preserves the generality and ease of application characteristic of this group of methods. It stands apart from standard signal processing techniques because, as an initialization-dependent algorithm, it accommodates the non-unique set of feasible solutions that arise from the neuroelectric source constraints. FOCUSS is based on recursive, weighted norm minimization. The consequence of the repeated weighting procedure is, in effect, to concentrate the solution in the minimal active regions that are essential for accurately reproducing the measurements. The FOCUSS algorithm is introduced and its properties are illustrated in the context of a number of simulations, first using exact measurements in 2- and 3-D problems, and then in the presence of noise and modeling errors. The results suggest that FOCUSS is a powerful algorithm with considerable utility for tomographic current estimation.
本文描述了一种用于神经电磁逆问题中断层源重建的新算法。该算法称为FOCUSS（聚焦欠定系统解法），它结合了电磁逆过程中两种主要方法的理想特性。与多电流偶极子建模方法一样，FOCUSS能产生适用于电磁成像中经常遇到的高度局域化源的高分辨率解。与线性估计方法一样，FOCUSS允许电流源具有任意形状，并且保留了这类方法的通用性和易于应用的特点。它与标准信号处理技术不同，因为作为一种依赖初始化的算法，它能处理由神经电源约束产生的非唯一可行解集。FOCUSS基于递归加权范数最小化。重复加权过程的结果实际上是将解集中在对精确再现测量至关重要的最小活动区域。本文介绍了FOCUSS算法，并在一些模拟中展示了其特性，首先在二维和三维问题中使用精确测量，然后在存在噪声和建模误差的情况下进行模拟。结果表明，FOCUSS是一种强大的算法，在断层电流估计方面具有相当大的实用性。
