Denoising using local projective subspace methods

Abstract

In this paper we present previous termdenoisingnext term algorithms for enhancing noisy signals based on previous termLocalnext term ICA (LICA), Delayed AMUSE (dAMUSE) and Kernel PCA (KPCA). The algorithm LICA relies on applying ICA locally to clusters of signals embedded in a high-dimensional feature space of delayed coordinates. The components resembling the signals can be detected by various criteria like estimators of kurtosis or the variance of autocorrelations depending on the statistical nature of the signal. The algorithm proposed can be applied favorably to the problem of previous termdenoisingnext term multi-dimensional data. Another projective subspace previous termdenoisingnext term method using delayed coordinates has been proposed recently with the algorithm dAMUSE. It combines the solution of blind source separation problems with previous termdenoisingnext term efforts in an elegant way and proofs to be very efficient and fast. Finally, KPCA represents a non-linear projective subspace method that is well suited for previous termdenoisingnext term also. Besides illustrative applications to toy examples and images, we provide an application of all algorithms considered to the analysis of protein NMR spectra.