A Subspace Time-Domain Algorithm for Automated NMR Spectral Normalization

Abstract

Recently, two methods have been proposed for quantitatively comparing NMR spectra of control and treated samples, in order to examine the possible occurring variations in cell metabolism and/or structure in response to numerous physical, chemical, and biological agents. These methods are the maximum superposition normalization algorithm (MaSNAl) and the minimum rank normalization algorithm (MiRaNAl). In this paper a new subspace-based time-domain normalization algorithm, denoted by SuTdNAl (subspace time-domain normalization algorithm), is presented. By the determination of the intersection of the column spaces of two Hankel matrices, the common signal poles and further on the components having proportionally varying amplitudes are detected. The method has the advantage that it is computationally less intensive than the MaSNAl and the MiRaNAl. Furthermore, no approximate estimate of the normalization factor is required. The algorithm was tested by Monte Carlo simulations on a set of simulation signals. It was shown that the SuTdNAl has a statistical performance similar to that of the MiRaNAl, which itself is an improvement over the MaSNAl. Furthermore, two samples of known contents are compared with the MiRaNAl, the SuTdNAl, and an older method using a standard. Finally, the SuTdNAl is tested on a realistic simulation example derived from an in vitro measurement on cells.