Non-linear Wiener filter in reproducing kernel Hilbert space

Wiener filters are used widely for inverse problems. From an observed signal, a Wiener filter provides the best restored signal with respect to the square error averaged over the original signal and the noise among linear operators. We introduce the non-linear Wiener filter, which is a kernel-based extension of the Wiener filter. When the kernel method is applied to the Wiener filter directly, the dimensions of the space where the calculation has to be done is very large since noise samples have to be used. We provide a realistic solution using the first order approximation. Moreover, we provide the experimental results to demonstrate the advantages of this method