Sequential deconvolution — Unmixing of blurred hyperspectral data

We consider hyperspectral unmixing problems where the observed images are blurred during the acquisition process, e.g. in micro / spectroscopy. Geometrical spectral unmixing consists in extracting the pure materials contained in the image as the vertices of the minimum-volume simplex (MVS) enclosing the data. In [1], we showed that the blur caused a contraction of the MVS, which implies that a deconvolution step is necessary to correctly unmix the image. In this paper, we study two sequential procedures consisting in deblurring and unmixing the blurred hyperspectral image. Despite its computational appeal, we will show that an unmixing / deconvolution strategy is outperformed by a deconvolution / unmixing approach.