Separation of water artifacts in 2D NOESY protein spectra using congruent matrix pencils

Multidimensional proton nuclear magnetic resonance spectra of biomolecules dissolved in aqueous solutions are usually contaminated by an intense water artifact. We discuss the application of a generalized eigenvalue decomposition (GEVD) method using a matrix pencil to solve the blind source separation (BSS) problem of removing the intense solvent peak and related artifacts. The method explores correlation matrices of the signals and their filtered versions in the frequency domain and implements a two-step algebraic procedure to solve the GEVD. Two-dimensional nuclear Overhauser enhancement spectroscopy (2D NOESY) of dissolved proteins is studied. Results are compared to those obtained with the SOBI [Belouchrani et al., IEEE Trans. Signal Process. 45(2) (1997) 434–444] algorithm which jointly diagonalizes several time-delayed correlation matrices and to those of the fastICA [Hyvärinen and Oja, Neural Comput. 9 (1996) 1483–1492] algorithm which exploits higher order statistical dependencies of random variables.