FSIW-EFA

The information obtained in the FSIW-EFA exploratory analysis is used in the resolution step. The total number of compounds in the three-way data set has been found to be equal to three (active, excipient, and unknown). The iterative optimization process starts with a matrix ST containing the initial estimates found by... 

Figure 2.9 FSIW-EFA modus operand (monolayer Raman emulsion image), (a) Construction of pixel windows ...

As with its parent algorithm, the local character of the PCA analyses performed by FSIW-EFA is particularly suitable in the detection of very minor compounds in the image (impurities) that could pass unnoticed in a global PCA analysis. This aspect has been particularly useful for the analysis of impurities in images of pharmaceutical formulations. For this type of sample, FSIW-EFA has also provided relevant information on piU heterogeneity [65]. 

FSIW-EFA can also be used in multilayer images, taking into account the 3-D neighborhood of the voxels to build the small windows to be PCA-scanned [70]. 

An exploratory analysis performed by FSIW-EFA provides an estimate of the number of components in each pixel. For resolution purposes, only those pixels in the partial local rank map will be potentially constrained, because these are the pixels for which a robust estimation of the number of missing components can be obtained. However, the FSIW-EFA information is not sufficient to identify which components are absent from the constrained pixels. For identification purposes, the local rank information should be combined with reference spectral information, the ideal reference being the pure spectra of the constituents, although in most images not all of these are known. For the image components with no pure spectrum available, the reference taken is an approximation of this pure spectrum. These approximate pure spectra can be obtained by pure variable selection methods, or they may be the result of a simpler MCR-ALS analysis where only non-negativity constraints have been applied. 

Although these pills were supposed to be formed by two constituents, a FSIW-EFA analysis detected the presence of a third compound (impurity) in some cases [65]. According to the theoretical composition of the piU and to the local rank analysis, information on the presence/absence of constituents in the different images could be introduced in the multi-image resolution process. From the pure spectra resolved and the distribution maps in Figure 2.17, the positive influence of the pill with the largest amount of impurity was noticeable when this compound was modeled in pills where it was present in very few pixels only. 

Fixed-size image window-evolving factor analysis (FSIW-EFA) is an evolution of the local rank algorithm fixed size moving window-EFA [111], particularly designed for the study of the local pixel complexity in images [112]. To do so, two main ideas are taken into account the need to divide the image into small areas to get local information and the need to preserve the 2D or 3D spatial... 

Figure 2.9 FSIW-EFA modus operand (monolayer Raman emulsion image), (a) Construction of pixel windows (b) singular value plots of local PCA analyses (c) complete local rank map and (d) partial local rank map.

FSIW-EFA can also be used in multilayer images, taking into account the 3D neighborhood of the voxels to build the small windows to be PCA scanned [112]. In this context, a number of local rank maps equal to the number of layers in the image are obtained. It is important to note that the information in the local rank map of a particular layer has been obtained taking into consideration the pixels of that layer and those in the neighboring layers in the depth direction. 

Qualitative exploratory analysis for example principal component analysis (PCA), fixed size image window-evolving factor analysis (FSIW-EFA). 

FSIW-EFA fixed size image window-evolving factor analysis—Surface screening for number of components GC-MS gas chromatography-mass spectrometiy... 

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