Principal component analysis of large layer density in Compton scattering measurements

A multivariate approach based on Principal Component Analysis (PCA) was used to analyze the energy distribution of n Monte Carlo simulated Compton scattered photon spectra describing the electron density of large layers. Three to five layers with different density distribution were used to test the algorithm; each layer was obtained by collecting 25 Compton spectra coming from sensitive volumes (SVs) where the complementary conditions of high and low density were realized (respectively full and void SV). The density variation inside a single layer is described by a two principal components (PCs) linear model that depicts the electron density of each SV: the layer density distribution appears to be correctly described even in the presence of very low signal-to-noise Compton spectra. Density profiles for layers at different depths were comparatively analyzed in order to show that, at least within one mean-free-path distance, it is possible to describe the layer density distribution by the PCA without any correction for the beam attenuation