Nonlinear Regularized Wiener Filtering With Kernels: Application in Denoising MEG Data Corrupted by ECG

Magnetoencephalographic and electroencephalographic recordings are often contaminated by artifacts such as eye movements, blinks, and cardiac or muscle activity. These artifacts, whose amplitude may exceed that of brain signals, may severely interfere with the detection and analysis of events of interest. In this paper, we consider a nonlinear approach for cardiac artifacts removal from magnetoencephalographic data, based on Wiener filtering. In recent works, nonlinear Wiener filtering based on reproducing kernel Hilbert spaces and the kernel trick has been proposed. However, the filter parameters are determined by the resolution of a linear system which may be ill conditioned. To deal with this problem, we introduce three kernel methods that provide powerful tools for solving ill-conditioned problems, namely, kernel principal component analysis, kernel partial least squares, and kernel ridge regression. A common feature of these methods is that they regularize the solution by assuming an appropriate prior on the class of possible solutions. We avoid the use of QRS-synchronous averaging techniques, which may induce distortions in brain signals if artifacts are not well detected. Moreover, our approach shows the nonlinear relation between magnetoencephalographic and electrocardiographic signals