Regularized kernel-based Wiener filtering. Application to magnetoencephalographic signals denoising

We take a new approach in nonlinear Wiener filtering. This approach is based on the theory of reproducing kernel Hilbert spaces (RKHS). By means of the well-known "kernel trick", the arithmetic operations are carried out in the initial space. We show that the solution is given by solving a linear system which may be ill-conditioned. To find a solution for such a problem, we resorted to a kernel principal component analysis (KPCA) method to perform dimensionality reduction in RKHS. A new reduced-rank Wiener filter based on KPCA is thus elaborated. It is applied on magnetoencephalographic (MEG) data for cardiac artifacts extraction.