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