  Terahertz (THz) technology has been a great candidate for applications,
including pharmaceutic analysis, chemical identification, and remote sensing
and imaging due to its non-invasive and non-destructive properties. Among those
applications, penetrating-type hyperspectral THz signals, which provide crucial
material information, normally involve a noisy, complex mixture system.
Additionally, the measured THz signals could be ill-conditioned due to the
overlap of the material absorption peak in the measured bands. To address those
issues, we consider penetrating-type signal mixtures and aim to develop a blind
hyperspectral unmixing (HU) method without requiring any information from a
prebuilt database. The proposed HYperspectral Penetrating-type Ellipsoidal
ReconstructION (HYPERION) algorithm is unsupervised, not relying on collecting
extensive data or sophisticated model training. Instead, it is developed based
on elegant ellipsoidal geometry under a very mild requirement on data purity,
whose excellent efficacy is experimentally demonstrated.
