Denoising using local ICA and kernel-PCA

We present a denoising algorithm for enhancing noisy signals based on local independent component analysis (ICA). This is done by applying ICA to the signal in localized delayed coordinates. The components resembling the signals can be detected by various criteria depending on the nature of the signal. Estimators of kurtosis or the variance of the autocorrelation have been considered. The algorithm proposed can favorably be applied to the problem of denoising multidimensional data like images or fMRI data sets. In comparison to denoising algorithms using wavelets, Wiener filters and kernel PCA the local PCA and ICA algorithms perform considerably better. We provide applications of the algorithm to images and the analysis of protein NMR spectra.