Spectral reconstruction

Modern pure component spectral reconstruction from multi-component spectroscopic data has its origins in a 1973 paper by Lawton and Sylvester [75] in which a known two component system was studied, and the pure component spectra were determined. The term curve resolution became intimately associated with pure component spectral reconstruction in the chemometrics literature [76]. 

The first two vectors are taken and the 2x2 problem associated with Eq. (15) was solved. The resulting MIR spectral reconstructions are very good (Figure 4. 6), even though six vectors of information were discarded prior to reconstruction. 

The homogeneous rhodium catalyzed hydroformylation of isoprene was the first application of SA to spectral reconstruction of a real catalytic system [92]. The MIR... 

Figure 4.10 Spectral reconstruction progression of Rli4 (a-CO)9(p-CO)3 during entropy minimization process by simulated annealing optimization ...

In order to confirm above possibilities, we have obtained time-dependent spectra by spectral reconstruction procedure [9] (Fig. 5). From the time dependent spectra, spectral shift... 

There is reasonably good agreement between the measurements made by spectral reconstruction and the linear wavelength method. This supports the validity of this method which takes considerably less instrument time (see above). 

Sehat, N., Kramer, J.K.G., Mossoba, M.M., Yurawecz, M.P., Roach, J.A.G., Eulitz, K., Morehouse, K.M., Ku, Y. 1998. Identification of conjugated linoleic acid isomers in cheese by gas chromatography, silver ion high performance liquid chromatography and mass spectral reconstructed ion profiles. Comparison of chromatographic elution sequences. Lipids 33, 963-971. 

We have used the spectral reconstruction method to obtain a time-resolved fluorescence spectrum [13] When the fluorescence up-conversion method is used, the relative intensity between each wavelength becomes uncertain because the angle of the nonlinear crystal has to be tuned at each wavelength of observation. However, the intensity of the fluorescence /(A, (), at a given time t and wavelength A, can be obtained from the normalized fitted decay series D(t, A) and intensity of the steady-state fluorescence /0(A) ... 

From 1982 through 1985, few NIR analyses of dosage forms were published. Since 1986, there have been many articles. The first was a 1986 paper by Ciurczak and Maldacker [33] using NIR for tablet formulation blends, examining the use of spectral subtraction, spectral reconstruction, and discriminant analysis. Blends were prepared where actives—aspirin (ASA), butalbital (BUT), and caffeine (CAF)—were omitted from the formulation or varied over a range from 90 to 110% of label strength. 

Identification of constituents by spectral reconstruction was performed with commercially available software, based on work by Honigs [34], later expanded upon by Honigs, Heiftje, and Hirschfeld [35]. Using a series of mixtures of known concentrations, the spectrum of the drug was reconstructed, providing identification of actives in the blend. 

Table 6.12 displays the Fade-reconstructed data for the normal glandular prostate at partial signal lengths Np = 600 and Np = 700. The spectral reconstructed parameters are listed with six decimals. However, the input concentrations are given with one or maximum two decimals to be consistent with the data from Ref. [54]. 

Some additional calculations were performed for comparison sake, using as a criterion the RMS error of spectral reconstruction. In particular, each spectrum was compressed to the degree which allows it reconstruction with the RMS = 0.0127. This value corresponds to the mean value of RMS observed for the data compressed by PCA. or in the joint basis accounting for the 99% of data variance. DWT with RMS criterion (where RMS = 0.0127) leads to 66.8 wavelet coefficients. For illustrative purpose the original spectrum and the spectrum reconstructed with RMS = 0.0127 are presented in Fig. 6. 

The first set, denoted as Rl, is required for spectra matching, whereas the second set, denoted as R2, is necessary for spectral reconstruction. A new, unknown signal has to be decomposed using filter F, and represented by the set of wavelet coefficients in the compressed basis. Matching procedure is... 

Time-resolved emission spectra Although there have been several attempts to simplify the characterisation of the SR process, the determination of time-resolved emission spectra (TRES) is certainly the most general and most precise way to quantitatively describe the solvent response. The time-resolved emission spectra are usually determined by spectral reconstruction [96, 97, 106]. The time-resolved emission spectrum at a given time t is calculated from the wavelength dependent time-resolved decays by relative normalization to the steady-state spectrum [107]. By fitting the TRES at different times t by the empirical log-normal function, the emission maximum frequencies i (t) (or 2(t) see Fig. 6.26) and the total Stokes-shift Ac (or A2) are usually derived [106]. Since c(t) contains both information about the polarity (Ac) and the viscosity of the reported environment, the spectral shift c(t) may be normalized to the total shift Ac. The resulting correlation functions C(t) (Eq. (7)) describe the time course of the solvent response and allow for comparison of the SR-kinetic and, thus, of relative micro-viscosities, reported from environments of different polarities [96, 97, 106, 108, 109, 116, 117, 122]... 

Sehat, N., J.K.G. Kramer, M.M. Mossoba, M.P Yurawecz, J.A.G. Roach, K. Euhtz, K.M. Morehouse, and Y. Ku. Conjugated Linoleic Acid Isomers in Cheese by Gas Chromatography, Silver Ion High Performance Liquid Chromatography and Mass Spectral Reconstructed Ion Profdes. Comparison of Chromatographic Elution Sequences, Iwids A 963-971 (1998). 

Chromatography, Silver Ion High Performance Liquid Chromatography and Mass Spectral Reconstructed Ion Profiles. Comparison of Chromatographic Elution Sequences. 963-71 (1998). 

The equality of transformations of the mixed time—frequency data and the completely Fourier transformed data is a consequence of Parseval s theorem (5.4) and has been previously discussed [10,11]. It can also be understood by taking into account that the spectral reconstruction is achieved by relating two direct dimensions via an indirect dimension, which in turn is discarded. Whether two frequency domains are correlated via a common time domain or a common frequency domain is therefore equivalent. It is also equivalent to Noda s model of relating two IR wavenumber dimensions via a common perturbation stemming from either time or sample space. From the matrix representation, it can be seen that Noda s synchronous matrix O, Eqs. (5.6) and (5.17) corresponds to the covariance map according to Eq. (5.16), if the data matrices yielding O are composed of... 

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