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Spectral Artifacts (spectral + artifact)
Selected AbstractsTikhonov regularization in standardized and general form for multivariate calibration with application towards removing unwanted spectral artifactsJOURNAL OF CHEMOMETRICS, Issue 1-2 2006Forrest Stout Abstract Tikhonov regularization (TR) is an approach to form a multivariate calibration model for y,=,Xb. It includes a regulation operator matrix L that is usually set to the identity matrix I and in this situation, TR is said to operate in standard form and is the same as ridge regression (RR). Alternatively, TR can function in general form with L,,,I where L is used to remove unwanted spectral artifacts. To simplify the computations for TR in general form, a standardization process can be used on X and y to transform the problem into TR in standard form and a RR algorithm can now be used. The calculated regression vector in standardized space must be back-transformed to the general form which can now be applied to spectra that have not been standardized. The calibration model building methods of principal component regression (PCR), partial least squares (PLS) and others can also be implemented with the standardized X and y. Regardless of the calibration method, armed with y, X and L, a regression vector is sought that can correct for irrelevant spectral variation in predicting y. In this study, L is set to various derivative operators to obtain smoothed TR, PCR and PLS regression vectors in order to generate models robust to noise and/or temperature effects. Results of this smoothing process are examined for spectral data without excessive noise or other artifacts, spectral data with additional noise added and spectral data exhibiting temperature-induced peak shifts. When the noise level is small, derivative operator smoothing was found to slightly degrade the root mean square error of validation (RMSEV) as well as the prediction variance indicator represented by the regression vector 2-norm thereby deteriorating the model harmony (bias/variance tradeoff). The effective rank (ER) (parsimony) was found to decrease with smoothing and in doing so; a harmony/parsimony tradeoff is formed. For the temperature-affected data and some of the noisy data, derivative operator smoothing decreases the RMSEV, but at a cost of greater values for . The ER was found to increase and hence, the parsimony degraded. A simulated data set from a previous study that used TR in general form was reexamined. In the present study, the standardization process is used with L set to the spectral noise structure to eliminate undesirable spectral regions (wavelength selection) and TR, PCR and PLS are evaluated. There was a significant decrease in bias at a sacrifice to variance with wavelength selection and the parsimony essentially remains the same. This paper includes discussion on the utility of using TR to remove other undesired spectral patterns resulting from chemical, environmental and/or instrumental influences. The discussion also incorporates using TR as a method for calibration transfer. Copyright © 2006 John Wiley & Sons, Ltd. [source] Desensitizing models using covariance matrix transforms or counter-balanced distortionsJOURNAL OF CHEMOMETRICS, Issue 4 2005Rocco DiFoggio Abstract This paper presents a generalization of the Lagrange multiplier equation for a regression subject to constraints. It introduces two methods for desensitizing models to anticipated spectral artifacts such as baseline variations, wavelength shift, or trace contaminants. For models derived from a covariance matrix such as multiple linear regression (MLR) and principal components regression (PCR) models, the first method shows how a covariance matrix can be desensitized to an artifact spectrum, v, by adding ,2v,,,v to it. For models not derived from a covariance matrix, such as partial least squares (PLS) or neural network (NN) models, the second method shows how distorted copies of the original spectra can be prepared in a counter-balanced manner to achieve desensitization. Unlike earlier methods that added random distortions to spectra, these new methods never introduce any accidental correlations between the added distortions and the Y -block. The degree of desensitization is controlled by a parameter, ,, for each artifact from zero (no desensitization) to infinity (complete desensitization, which is the Lagrange multiplier limit). Unlike Lagrange multipliers, these methods permit partial desensitization so we can individually vary the degree of desensitization to each artifact, which is important when desensitization to one artifact inhibits desensitization to another. Copyright © 2005 John Wiley & Sons, Ltd. [source] Fast multidimensional localized parallel NMR spectroscopy for the analysis of samplesMAGNETIC RESONANCE IN CHEMISTRY, Issue 10 2010Marino Vega-Vazquez Abstract A parallel localized spectroscopy (PALSY) method is presented to speed up the acquisition of multidimensional NMR (nD) spectra. The sample is virtually divided into a discrete number of nonoverlapping slices that relax independently during consecutive scans of the experiment, affording a substantial reduction in the interscan relaxation delay and the total experiment time. PALSY was tested for the acquisition of three experiments 2D COSY, 2D DQF-COSY and 2D TQF-COSY in parallel, affording a time-saving factor of 3,4. Some unique advantages are that the achievable resolution in any dimension is not compromised in any way: it uses conventional NMR data processing, it is not prone to generate spectral artifacts, and once calibrated, it can be used routinely with these and other combinations of NMR spectra. Copyright © 2010 John Wiley & Sons, Ltd. [source] | ||||||||||