Denoising Using Local ICA and a Generalized Eigendecomposition with Time-Delayed Signals

We present denoising algorithms based on either local independent component analysis (ICA) and a minimum description length (MDL) estimator or a generalized eigenvalue decomposition (GEVD) using a matrix pencil of time-delayed signals. Both methods are applied to signals embedded in delayed coordinates in a high-dim feature space Ω and denoising is achieved by projecting onto a lower dimensional signal subspace. We discuss the algorithms and provide applications to the analysis of 2D NOESY protein NMR spectra.

[1]  Aapo Hyvärinen,et al.  A Fast Fixed-Point Algorithm for Independent Component Analysis , 1997, Neural Computation.

[2]  Phillip A. Regalia,et al.  On the behavior of information theoretic criteria for model order selection , 2001, IEEE Trans. Signal Process..

[3]  Fabian J. Theis,et al.  AUTOMATIC DENOISING USING LOCAL INDEPENDENT COMPONENT ANALYSIS , 2004 .

[4]  Fabian J. Theis,et al.  Blind Source Separation of Water Artefacts in NMR Spectra using a Matrix Pencil , 2003 .

[5]  Rute Almeida,et al.  dAMUSE - A new tool for denoising and BSS , 2005 .

[6]  K. Lehnertz,et al.  Nonlinear denoising of transient signals with application to event-related potentials , 2000, physics/0001069.

[7]  Anil K. Jain,et al.  Algorithms for Clustering Data , 1988 .

[8]  Simon Haykin,et al.  Image Denoising by Sparse Code Shrinkage , 2001 .

[9]  Fabian J Theis,et al.  On the use of independent component analysis to remove water artefacts of 2D NMR protein spectra , 2003 .

[10]  Nuno Ferreira,et al.  On-line source separation of temporally correlated signals , 2002, 2002 11th European Signal Processing Conference.

[11]  Simon Haykin,et al.  Intelligent Signal Processing , 2001 .

[12]  Ana Maria Tomé.  AN ITERATIVE EIGENDECOMPOSITION APPROACH TO BLIND SOURCE SEPARATION , 2001 .

[13]  V. Moskvina,et al.  Approximate Projectors in Singular Spectrum Analysis , 2002, SIAM J. Matrix Anal. Appl..

[14]  A.M. Tome.  Blind source separation using a matrix pencil , 2000, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium.