Strohmeier Daniel, Bekhti Yousra, Haueisen Jens, Gramfort Alexandre
IEEE Trans Med Imaging. 2016 Oct;35(10):2218-2228. doi: 10.1109/TMI.2016.2553445. Epub 2016 Apr 13.
Source imaging based on magnetoencephalography (MEG) and electroencephalography (EEG) allows for the non-invasive analysis of brain activity with high temporal and good spatial resolution. As the bioelectromagnetic inverse problem is ill-posed, constraints are required. For the analysis of evoked brain activity, spatial sparsity of the neuronal activation is a common assumption. It is often taken into account using convex constraints based on the l-norm. The resulting source estimates are however biased in amplitude and often suboptimal in terms of source selection due to high correlations in the forward model. In this work, we demonstrate that an inverse solver based on a block-separable penalty with a Frobenius norm per block and a l-quasinorm over blocks addresses both of these issues. For solving the resulting non-convex optimization problem, we propose the iterative reweighted Mixed Norm Estimate (irMxNE), an optimization scheme based on iterative reweighted convex surrogate optimization problems, which are solved efficiently using a block coordinate descent scheme and an active set strategy. We compare the proposed sparse imaging method to the dSPM and the RAP-MUSIC approach based on two MEG data sets. We provide empirical evidence based on simulations and analysis of MEG data that the proposed method improves on the standard Mixed Norm Estimate (MxNE) in terms of amplitude bias, support recovery, and stability.
基于脑磁图（MEG）和脑电图（EEG）的源成像能够以高时间分辨率和良好空间分辨率对大脑活动进行无创分析。由于生物电磁逆问题是不适定的，因此需要施加约束。对于诱发脑活动的分析，神经元激活的空间稀疏性是一个常见假设。通常使用基于 l - 范数的凸约束来考虑这一假设。然而，由于正向模型中的高相关性，所得的源估计在幅度上存在偏差，并且在源选择方面往往不是最优的。在这项工作中，我们证明基于每个块具有弗罗贝尼乌斯范数和块上的 l - 拟范数的块可分惩罚的逆求解器解决了这两个问题。为了解决由此产生的非凸优化问题，我们提出了迭代重加权混合范数估计（irMxNE），这是一种基于迭代重加权凸替代优化问题的优化方案，可使用块坐标下降方案和活动集策略有效地求解。我们基于两个MEG数据集将所提出的稀疏成像方法与dSPM和RAP - MUSIC方法进行比较。我们基于模拟和MEG数据分析提供了经验证据，表明所提出的方法在幅度偏差、支持恢复和稳定性方面优于标准混合范数估计（MxNE）。
