Institut Mines-Telecom, Telecom ParisTech, CNRS LTCI, Paris, France.
Neuroimage. 2013 Apr 15;70:410-22. doi: 10.1016/j.neuroimage.2012.12.051. Epub 2013 Jan 4.
Magnetoencephalography (MEG) and electroencephalography (EEG) allow functional brain imaging with high temporal resolution. While solving the inverse problem independently at every time point can give an image of the active brain at every millisecond, such a procedure does not capitalize on the temporal dynamics of the signal. Linear inverse methods (minimum-norm, dSPM, sLORETA, beamformers) typically assume that the signal is stationary: regularization parameter and data covariance are independent of time and the time varying signal-to-noise ratio (SNR). Other recently proposed non-linear inverse solvers promoting focal activations estimate the sources in both space and time while also assuming stationary sources during a time interval. However such a hypothesis holds only for short time intervals. To overcome this limitation, we propose time-frequency mixed-norm estimates (TF-MxNE), which use time-frequency analysis to regularize the ill-posed inverse problem. This method makes use of structured sparse priors defined in the time-frequency domain, offering more accurate estimates by capturing the non-stationary and transient nature of brain signals. State-of-the-art convex optimization procedures based on proximal operators are employed, allowing the derivation of a fast estimation algorithm. The accuracy of the TF-MxNE is compared with recently proposed inverse solvers with help of simulations and by analyzing publicly available MEG datasets.
脑磁图 (MEG) 和脑电图 (EEG) 允许以高时间分辨率进行功能性大脑成像。虽然在每个时间点独立求解逆问题可以给出每毫秒活跃大脑的图像，但这种方法并没有利用信号的时间动态。线性逆方法（最小范数、dSPM、sLORETA、波束形成器）通常假设信号是静止的：正则化参数和数据协方差与时间无关，并且时变信噪比 (SNR) 也与时间无关。其他最近提出的促进焦点激活的非线性逆求解器在估计空间和时间中的源时，同时也假设在一段时间内源是静止的。然而，这种假设仅适用于短时间间隔。为了克服这一限制，我们提出了时频混合范数估计 (TF-MxNE)，它利用时频分析来正则化病态逆问题。该方法利用在时频域中定义的结构化稀疏先验，通过捕获脑信号的非平稳和瞬态特性，提供更准确的估计。使用基于近端算子的最先进凸优化程序来实现，允许快速推导出估计算法。借助模拟和分析公开可用的 MEG 数据集，将 TF-MxNE 的准确性与最近提出的逆求解器进行了比较。
