  This paper discusses the reconstruction of partially sampled spectrum-images
to accelerate the acquisition in scanning transmission electron microscopy
(STEM). The problem of image reconstruction has been widely considered in the
literature for many imaging modalities, but only a few attempts handled 3D data
such as spectral images acquired by STEM electron energy loss spectroscopy
(EELS). Besides, among the methods proposed in the microscopy literature, some
are fast but inaccurate while others provide accurate reconstruction but at the
price of a high computation burden. Thus none of the proposed reconstruction
methods fulfills our expectations in terms of accuracy and computation
complexity. In this paper, we propose a fast and accurate reconstruction method
suited for atomic-scale EELS. This method is compared to popular solutions such
as beta process factor analysis (BPFA) which is used for the first time on
STEM-EELS images. Experiments based on real as synthetic data will be
conducted.
