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1D Current Source Density (CSD) Estimation in Inverse Theory: A Unified Framework for Higher-Order Spectral Regularization of Quadrature and Expansion-Type CSD Methods

机译:逆理论中的一维电流源密度(CSD)估计:正交和扩展型CSD方法的高阶谱正则化的统一框架

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Estimation of current source density (CSD) from the low-frequency part of extracellular electric potential recordings is an unstable linear inverse problem. To make the estimation possible in an experimental setting where recordings are contaminated with noise, it is necessary to stabilize the inversion. Here we present a unified framework for zero- and higher-order singular-value-decomposition (SVD)—based spectral regularization of 1D (linear) CSD estimation from local field potentials. The framework is based on two general approaches commonly employed for solving inverse problems: quadrature and basis function expansion. We first show that both inverse CSD (iCSD) and kernel CSD (kCSD) fall into the category of basis function expansion methods. We then use these general categories to introduce two new estimation methods, quadrature CSD (qCSD), based on discretizing the CSD integral equation with a chosen quadrature rule, and representer CSD (rCSD), an even-determined basis function expansion method that uses the problem’s data kernels (representers) as basis functions. To determine the best candidate methods to use in the analysis of experimental data, we compared the different methods on simulations under three regularization schemes (Tikhonov, tSVD, and dSVD), three regularization parameter selection methods (NCP, L-curve, and GCV), and seven different a priori spatial smoothness constraints on the CSD distribution. This resulted in a comparison of 531 estimation schemes. We evaluated the estimation schemes according to their source reconstruction accuracy by testing them using different simulated noise levels, lateral source diameters, and CSD depth profiles. We found that ranking schemes according to the average error over all tested conditions results in a reproducible ranking, where the top schemes are found to perform well in the majority of tested conditions. However, there is no single best estimation scheme that outperforms all others- under all tested conditions. The unified framework we propose expands the set of available estimation methods, provides increased flexibility for 1D CSD estimation in noisy experimental conditions, and allows for a meaningful comparison between estimation schemes.
机译:从细胞外电势记录的低频部分估计电流源密度(CSD)是一个不稳定的线性反问题。为了在录音被噪声污染的实验环境中进行估算,必须稳定反演。在这里,我们为零阶和高阶奇异值分解(SVD)提供了一个统一的框架,该框架基于局部场电势对一维(线性)CSD估计的频谱正则化。该框架基于解决反问题常用的两种通用方法:正交和基函数扩展。我们首先显示逆CSD(iCSD)和内核CSD(kCSD)都属于基函数扩展方法。然后,我们使用这些一般类别介绍两种新的估算方法:基于使用选定正交规则离散化CSD积分方程的正交CSD(qCSD),以及使用C的偶数确定基函数扩展方法表示CSD(rCSD)。问题的数据核(代表)作为基础函数。为了确定用于分析实验数据的最佳候选方法,我们在三种正则化方案(Tikhonov,tSVD和dSVD),三种正则化参数选择方法(NCP,L曲线和GCV)下比较了不同的模拟方法。 ,以及CSD分布上的七个不同的先验空间平滑度约束。结果比较了531种估计方案。我们通过使用不同的模拟噪声水平,横向声源直径和CSD深度剖面对其进行测试,根据声源重建精度对估计方案进行了评估。我们发现,根据所有测试条件下的平均误差对方案进行排序可以得出可重复的排名,其中顶级方案在大多数测试条件下均表现良好。但是,在所有测试条件下,没有一个最佳的估计方案能胜过其他所有方案。我们提出的统一框架扩展了可用的估计方法集,在嘈杂的实验条件下为一维CSD估计提供了更大的灵活性,并允许在估计方案之间进行有意义的比较。

著录项

  • 来源
    《Neural computation》 |2016年第7期|1305-1355|共51页
  • 作者

    Pascal Kropf; Amir Shmuel;

  • 作者单位

    McConnell Brain Imaging Center, Montreal Neurological Institute, Department of Neurology and Neurosurgery, McGill University, Montreal, QC, H3A 2B4, Canada pascal.kropf@mail.mcgill.ca;

  • 收录信息 美国《科学引文索引》(SCI);美国《化学文摘》(CA);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
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