Multivariate Analysis for the Processing of Signals

Traitement de signaux par analyse multivariée

Crescent Diagnostics, UCD-NOVA, Belfield, Dublin 4 - Ireland
e-mail: rene@jrenwickbeattie.com

^⋆ Corresponding author

Abstract

Real-world experiments are becoming increasingly more complex, needing techniques capable of tracking this complexity. Signal based measurements are often used to capture this complexity, where a signal is a record of a sample’s response to a parameter (e.g. time, displacement, voltage, wavelength) that is varied over a range of values. In signals the responses at each value of the varied parameter are related to each other, depending on the composition or state sample being measured. Since signals contain multiple information points, they have rich information content but are generally complex to comprehend. Multivariate Analysis (MA) has profoundly transformed their analysis by allowing gross simplification of the tangled web of variation. In addition MA has also provided the advantage of being much more robust to the influence of noise than univariate methods of analysis. In recent years, there has been a growing awareness that the nature of the multivariate methods allows exploitation of its benefits for purposes other than data analysis, such as pre-processing of signals with the aim of eliminating irrelevant variations prior to analysis of the signal of interest. It has been shown that exploiting multivariate data reduction in an appropriate way can allow high fidelity denoising (removal of irreproducible non-signals), consistent and reproducible noise-insensitive correction of baseline distortions (removal of reproducible non-signals), accurate elimination of interfering signals (removal of reproducible but unwanted signals) and the standardisation of signal amplitude fluctuations. At present, the field is relatively small but the possibilities for much wider application are considerable. Where signal properties are suitable for MA (such as the signal being stationary along the x-axis), these signal based corrections have the potential to be highly reproducible, and highly adaptable and are applicable in situations where the data is noisy or where the variations in the signals can be complex. As science seeks to probe datasets in less and less tightly controlled situations the ability to provide high-fidelity corrections in a very flexible manner is becoming more critical and multivariate based signal processing has the potential to provide many solutions.

Résumé

L’analyse multivariée, dont l’analyse en composantes principales (ACP), a transformé, dans des contextes concrets, l’étude de mesures complexes, formées de signaux chargés d’informations. Si la réduction de dimension permet de simplifier grossièrement un enchevêtrement de variations multidimensionnelles, elle est également plus robuste aux perturbations que les méthodes d’analyse univariées. Plus récemment, il est apparu que les propriétés des méthodes multivariées les rendaient propices à d’autres usages que statistiques, comme le traitement des signaux pour l’élimination des variations/fluctuations non pertinentes pour une analyse ultérieure. Il a été montré que l’exploitation spécifique de la réduction de dimension permet un débruitage précis (suppression de “non-signaux/perturbation” non reproductibles), la soustraction fiable et consistante de la ligne de base (suppression de “non-signaux/perturbation” reproductibles), l’élimination d’interférences (suppression de “signaux” reproductibles et inutiles), ainsi que la standardisation des fluctuations d’amplitude des signaux.

Si ce champ d’investigation est encore restreint, les possibilités de diffusion de ses applications sont considérables. En effet, ces améliorations, intrinsèquement liées aux signaux eux-mêmes, sont hautement reproductibles entre les répétitions, possèdent une grande capacité d’adaptation et d’application à des situations de bruit, ou de variations complexes dans les signaux. Alors que les disciplines scientifiques sondent des volumes de données toujours plus volumineux, dans des situations de moins en moins étroitement contrôlées, la capacité à apporter des corrections/améliorations précises/hautes résolutions, de manière flexible, devient de plus en plus critique. Aussi les traitements de signaux multivariés offrent un éventail de solutions potentiellement très large.