Biomagnetic Imaging Laboratory, Department of Radiology and Biomedical Imaging, University of California San Francisco San Francisco, CA, USA ; Joint Graduate Group in Bioengineering, University of California San Francisco/University of California Berkeley San Francisco, CA, USA.
Front Neurosci. 2012 Dec 26;6:186. doi: 10.3389/fnins.2012.00186. eCollection 2012.
Uncovering brain activity from magnetoencephalography (MEG) data requires solving an ill-posed inverse problem, greatly confounded by noise, interference, and correlated sources. Sparse reconstruction algorithms, such as Champagne, show great promise in that they provide focal brain activations robust to these confounds. In this paper, we address the technical considerations of statistically thresholding brain images obtained from sparse reconstruction algorithms. The source power distribution of sparse algorithms makes this class of algorithms ill-suited to "conventional" techniques. We propose two non-parametric resampling methods hypothesized to be compatible with sparse algorithms. The first adapts the maximal statistic procedure to sparse reconstruction results and the second departs from the maximal statistic, putting forth a less stringent procedure that protects against spurious peaks. Simulated MEG data and three real data sets are utilized to demonstrate the efficacy of the proposed methods. Two sparse algorithms, Champagne and generalized minimum-current estimation (G-MCE), are compared to two non-sparse algorithms, a variant of minimum-norm estimation, sLORETA, and an adaptive beamformer. The results, in general, demonstrate that the already sparse images obtained from Champagne and G-MCE are further thresholded by both proposed statistical thresholding procedures. While non-sparse algorithms are thresholded by the maximal statistic procedure, they are not made sparse. The work presented here is one of the first attempts to address the problem of statistically thresholding sparse reconstructions, and aims to improve upon this already advantageous and powerful class of algorithm.
从脑磁图 (MEG) 数据中揭示大脑活动需要解决一个病态反问题，这个问题极大地受到噪声、干扰和相关源的影响。稀疏重建算法，如 Champagne，在这方面表现出很大的潜力，因为它们提供了对这些混杂因素具有鲁棒性的焦点大脑激活。在本文中，我们解决了从稀疏重建算法获得的脑图像进行统计阈值处理的技术考虑因素。稀疏算法的源功率分布使得这类算法不适合“传统”技术。我们提出了两种非参数重采样方法，假设它们与稀疏算法兼容。第一种方法将最大统计量程序应用于稀疏重建结果，第二种方法则背离最大统计量程序，提出一种不太严格的程序，以防止虚假峰值。模拟 MEG 数据和三个真实数据集被用于演示所提出方法的有效性。将两种稀疏算法（Champagne 和广义最小电流估计（G-MCE））与两种非稀疏算法（最小范数估计的变体 sLORETA 和自适应波束形成器）进行比较。结果总体上表明，已经从 Champagne 和 G-MCE 获得的稀疏图像可以通过两种提出的统计阈值处理程序进一步进行阈值处理。虽然非稀疏算法可以通过最大统计量程序进行阈值处理，但它们不会变得稀疏。本文的工作是首次尝试解决统计稀疏重建阈值处理问题的工作之一，旨在改进这一已经具有优势和强大的算法类别。
