This paper is concerned with variational and Bayesian approaches to neuro-electromagnetic inverse problems (EEG and MEG). The strong indeterminacy of these problems is tackled by introducing sparsity inducing regularization/priors in a transformed domain, namely a spatial wavelet domain. Sparsity in the wavelet domain allows to reach ''data compression'' in the cortical sources domain. Spatial wavelets defined on the mesh graph of the triangulated cortical surface are used, in combination with sparse regression techniques, namely LASSO regression or sparse Bayesian learning, to provide localized and compressed estimates for brain activity from sensor data. Numerical results on simulated and real MEG data are provided, which outline the performances of the proposed approach in terms of localization.

翻译：本文研究神经电磁逆问题（脑电图与脑磁图）的变分与贝叶斯方法。通过在变换域（即空间小波域）引入稀疏性诱导的正则化/先验，解决了这些问题的强烈不确定性。小波域中的稀疏性可在皮层源域实现"数据压缩"。我们采用定义在三角化皮层表面网格图上的空间小波，结合稀疏回归技术（即LASSO回归或稀疏贝叶斯学习），从传感器数据中提供局域化且压缩的脑活动估计。模拟与真实脑磁图数据的数值结果展示了所提方法在定位方面的性能表现。