Spatial and Spectral Exploration

The rows related to the purest pixels will provide good approximations of the pure spectra sought, whereas the columns linked to the purest spectral channels will allow for building approximate distribution maps of the pure constituents. 

SIMPLISMA is one of the main methodologies used for this purpose and, as stated before, can be used to identify either the purest pixels or the purest spectral channels in an image [18]. If the focus is on finding the purest pixels, a purity index, pi, will be calculated per each pixel spectrum as  

Pixel area Pixel area Pixel area (1,1) (1,2) (1,3) 

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]. 

There are many algorithms that work using different mathematical criteria to look for the most dissimilar variables in a data set [110]. As an example, SIM-PLISMA is one of the pioneering methodologies used for this purpose and, as 

The pixels selected (a-d) are located in zones associated with the four constituents described and, therefore, their spectra will be very close, when not identical, to the real pure spectra sought. However, spectral channels 1-3 produce reasonable distribution maps for the drop, interphase, and additive constituents, and channel 4 fails in giving a good map for the off-drop phase. Channel 4, although being the most representative for the off-drop phase, has signal contributions from the rest of components and, therefore, produces an unacceptable map for this component. 

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 

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