Band-Target Entropy Minimization. A Robust Algorithm for Pure Component Spectral Recovery. Application to Complex Randomized Mixtures of Six Components

Abstract

A newly developed self-modeling curve resolution method, band-target entropy minimization (BTEM), is described. This method starts with the data decomposition of a set of spectroscopic mixture data using singular value decomposition. It is followed by the transformation of the orthonormal basis vectors/loading vectors into individual pure component spectra one at a time. The transformation is based in part on some seminal ideas borrowed from information entropy theory with the desire to maximize the simplicity of the recovered pure component spectrum. Thus, the proper estimate is obtained via minimization of the proposed information entropy function or via minimization of derivative and area of the spectral estimate. Nonnegativity constraints are also imposed on the recovered pure component spectral estimate and its corresponding concentrations. As its name suggests, in this method, one targets a spectral feature readily observed in loading vectors to retain, and then combinations of the loading vectors are searched to achieve the global minimum value of an appropriate objective function. The major advantage of this method is its one spectrum at a time approach and its capability of recovering minor components having low spectroscopic signals. To illustrate the application of BTEM, spectral resolution was performed on FT-IR measurements of very highly overlapping mixture spectra containing six organic species with a two-component background interference (air). BTEM estimates were also compared with the estimates obtained using other self-modeling curve resolution techniques, i.e., SIMPLISMA, IPCA, OPA-ALS, and SIMPLISMA-ALS.

Monte Carlo Algorithm for Least Dependent Non-Negative Mixture Decomposition

“…In addition, the pure spectra of mixture constituents were measured in separate experiments. Thus, this mixture problem offered a test case complicated by experimental features typical to analytical practice, such as non-linearities, instrumental noise, the presence of spectrometer background and impurities (residual water and CO 2 in this case [24]). …”

“…The estimated components were then compared to the pure sources, computing the normalized inner products between them [7,24]. The results are given in Table 1 which also contains the respective values obtained by two MCR methods -SIMPLISMA [21] and BTEM [24].…”

“…The estimated components were then compared to the pure sources, computing the normalized inner products between them [7,24]. The results are given in Table 1 which also contains the respective values obtained by two MCR methods -SIMPLISMA [21] and BTEM [24]. SNICA was applied to this data set with a 3 step annealing schedule taking T 1 = 6 We used the implementation by P. Tichavsky available at http://www.utia.cas.cz/user data/scientific/SI dept/Tichavsky.html.…”

“…On this data set, the estimates produced by SNICA are more accurate than those obtained by SIMPLISMA and BTEM without ALS and compare favorably with the results obtained by MILCA and ALSversions of these algorithms. Notice that in order to produce accurate estimates SIMPLISMA needs ALS postprocessing corrections [28,24] (see also Fig. 3b).…”

“…[27]. While the above are general purpose BSS methods, there exist more specialized chemometrics (MCR) algorithms designed to use non-negativity (see, e.g., [12,13,14,15,16,24,28]). In many of them, some variant of principle component analysis is used to first prewhiten the data, i.e.…”