Multilayer and Multi-Image Resolution

There are some important issues linked to the bilinear nature of multi-image analysis. First, the fact of obtaining a single matrix for all images ensures spectral consistency of the resolution-that is, the same constituent will always be associated with the same pure spectrum in all analyzed images. Second, the stretched matrix of concentrahon profiles respects the natural difference of shape of the distribution maps among images. 

the subindex i refers to each individual constituent, and an sCi value is calculated for each constituent in each of the layers. CiS and CS are the signal contribution of the ith component and the global signal within a layer image, respectively. 

The signal contribution plot helps to understand the reasons for the spectral inconsistency linked to the individual image analysis, coming from the large difference in representativity of the image constituents in the different layers. Thus, three compounds have a very minor signal in the deepest layers and, as a consequence, the resolved spectra obtained from the individual analyses of these layers are of poor quality and differ significantly from the spectra obtained from the top 

Another example of the gain in resolution quality from the complementary information among different images is seen in the analysis of a series of pills with different percentages of excipient and active principle ingredient (API) of 0, 20, 40, 60 and 80% [65]. The different proportions of compounds in the pills ensure a good recovery of the pure spectra, and also of the distribution maps of all compounds, even when one of them is present in only a small proportion. It should 

A positive consequence of multi-image analysis is the recovery of quantitative information. At this point, it should be taken into account that quantitation from images measured in reflection is never as accurate and precise as from images measured in transmission. The more representative the surface scarmed is from the rest of the sample, then the more reliable the quantitative information will be. When referring to quantitative information, it is possible to differentiate between within-image and between-image quantitation. 

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