Image chemometric

The quahty of an analytical result also depends on the vaUdity of the sample utilized and the method chosen for data analysis. There are articles describiag Sampling and automated sample preparation (see Automated instrumentation) as well as articles emphasizing data treatment (see Chemometrics Computer technology), data iaterpretation (see Databases Imaging technology), and the communication of data within the laboratory or process system (see Expert systems Laboratory information managet nt systems). 

Multiway and particularly three-way analysis of data has become an important subject in chemometrics. This is the result of the development of hyphenated detection methods (such as in combined chromatography-spectrometry) and yields three-way data structures the ways of which are defined by samples, retention times and wavelengths. In multivariate process analysis, three-way data are obtained from various batches, quality measures and times of observation [55]. In image analysis, the three modes are formed by the horizontal and vertical coordinates of the pixels within a frame and the successive frames that have been recorded. In this rapidly developing field one already finds an extensive body of literature and only a brief outline can be given here. For a more comprehensive reading and a discussion of practical applications we refer to the reviews by Geladi [56], Smilde [57] and Henrion [58]. 

Sections on matrix algebra, analytic geometry, experimental design, instrument and system calibration, noise, derivatives and their use in data analysis, linearity and nonlinearity are described. Collaborative laboratory studies, using ANOVA, testing for systematic error, ranking tests for collaborative studies, and efficient comparison of two analytical methods are included. Discussion on topics such as the limitations in analytical accuracy and brief introductions to the statistics of spectral searches and the chemometrics of imaging spectroscopy are included. 

The multivariate tools typically used for the NIR-CI analysis of pharmaceutical products fall into two main categories pattern recognition techniques and factor-based chemometric analysis methods. Pattern recognition algorithms such as spectral correlation or Euclidian distance calculations basically determine the similarity of a sample spectrum to a reference spectrum. These tools are especially useful for images where the individual pixels yield relatively unmixed spectra. These techniques can be used to quickly define spatial distributions of known materials based on external reference spectra. Alternatively, they can be used with internal references, to locate and classify regions with similar spectral response. 

CHEMICAL IMAGING AND CHEMOMETRICS USEFUL TOOLS FOR PROCESS ANALYTICAL TECHNOLOGY... 

The data cube combines spectral and spatial information and therefore includes the requisite statistics for spectral classifications. However, new chemometric strategies have to be applied to interpret chemical imaging results. 

Multivariate Image Analysis Strong and Weak Multiway Methods Strong and weak -way methods analyze 3D and 2D matrices, respectively. Hyperspectral data cube structure is described using chemometric vocabulary [17]. A two-way matrix, such as a classical NIR spectroscopy data set, has two modes object (matrix lines) and V variables (matrix columns). Hyperspectral data cubes possess two object modes and one variable mode and can be written as an OOV data array because of their two spatial directions. 

Classical chemometric methods, that is, the classification and regression presented in Section 4.3.1, are also applied to hyperspectral images.However,XxYx X matrices have to be unfolded into (1 ) 1 matrices before processing. In other words, the three-way OOV array is unfolded into a classical two-way OV matrix. 

Juan, A. D.,Tauler, R., Dyson, R., Marcolli, C., Rault, M., and Maeder, M. (2004), Spectroscopic imaging and chemometrics A powerful combination for global and local sample analysis, TrAC Trends Anal. Chem., 23,70-79. 

Yves Roggo, F. Hoffmann-La Roche, Ltd., Basel, Switzerland, Process Analytical Technology Chemical Imaging and Chemometrics Useful Tools for Process Analytical Technology... 

Chemometric Methods for Biomedical Raman Spectroscopy and Imaging... 

Fig. 8.3. A Acquired high SNR data and simulated noisy spectra (peak-to-peak noise = 0.001, 0.01, 0.1, and 0.4 a.u.), showing the degradation in data quality. Spectra are offset for clarity. B Spectra after noise reduction demonstrate the dramatic gains possible by chemometric methods. C Noise reduction was implemented to classify breast tissue and application of noise rejection allowed the same quality of classification (accuracy) to be recovered at higher noise levels. D In another example, image fidelity (here the nitrile stretching vibrational mode at 2227 cm-1) is much enhanced as a result of spectral noise rejection A and C are reproduced from Reddy and Bhargava, Submitted [165], D is reproduced from [43]...

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