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TWO-DIMENSIONAL SIGNAL PROCESSING TECHNIQUES IN CHEMISTRY
3.1. GENERAL FEATURES OF TWO-DIMENSIONAL DATA
In recent years, numerous “hyphenated instrument” technologies have appeared on the market, such as high-performance liquid chromatography with diode array detection (HPLC-DAD), gas chromatography with mass spectroscopic detection (GC-MS), gas chromatography with infrared spectroscopic detection (GC-IR), high-performance liquid chromatography with mass spectroscopic detection (HPLC-MS), and capillary electrophoresis with diode array detection (CE-DAD). In general, the data produced by the hyphenated instruments are matrices where every row is an object (spectrum) and every column is a variable [the chromatogram at a given wavelength, wavenumber, or m/z (mass/charge) unit] as illustrated in Figure 3.1.
The data obtained by such hyphenated instrumentation in chemistry is generally called two-dimensional or two-way data and have the following features:
1. The two-dimensional data contain both information of chromatogram and spectra. When a sample is measured by the hyphenated instrument, the data collected can always be arranged as a matrix, say, X, where every row is an object (spectrum) and every column is a variable (the chromatogram at a given wavelength, wavenumber, or m/z unit). According to the Lambert-Beer law or similar rules, the matrix can be expressed by the product of two matrices as follows:
X = CSt = ck sk (3.1)
here A is the number of absorbing components coexisting in the system, while the ci and sk (k = 1,2,... , A) values are pure concentration profiles
Chemometrics: From Basics To Wavelet Transform, edited by Foo-tim Chau, Yi-zeng Liang, Junbin Gao, and Xue-guang Shao. Chemical Analysis Series, Vol. 164.
ISBN 0-471-20242-8. Copyright © 2004 John Wiley & Sons, Inc.
two-dimensional signal processing techniques in chemistry
Figure 3.1. Illustration of two-dimensional data from the hyphenated instrument.
and spectra, respectively. The data of Equation (3.1) are called bilinear two-way data.
2. The feature of the noise pattern of the two-dimensional data is quite different from that of the one-dimensional data. It should be noted that the two-dimensional (2D) data are contributed from a combination of chromatographic (e.g., LC, GC, HPLC) and a multichannel detectors (e.g., UV, IR, MS). Within a given time interval, a complete spectrum within a specific wavelength range is acquired. Consequently, random errors that occur during chromatographic development will influence the corresponding spectra. Apart from these unavoidable correlated fluctuations, the data will also be contaminated with spurious detector noise, which is sometime correlated between neighboring channels. Moreover, noise that is proportional to the size of the signal is more common than purely additive noise. As a result, the overall noise present in the real data collected from a ‘‘spectrochro-matograph’’ will be correlated and, more importantly, the noise should also be heteroscedastic. Thus, pretreatment of 2D data becomes more difficult.