Scanning transmission electron microscopy (STEM) offers the ability to acquire several single- and multi-channels signals generated simultaneously for each probe position: cathodoluminescence (CL), electron energy loss spectroscopy (EELS) and high-angle annular dark-field imaging (HAADF). However, in some cases, sensitive samples (e.g., biological samples or molecular structures) may suffer from irradiation damages during acquisition. As a consequence, it is often necessary to reduce probe current or dwell time, which could significantly lower the signal-to-noise ratio. Another approach consists in acquiring only a subset of pixels randomly chosen in a given region of interest. This particular experimental set-up has been implemented on the STEM VG HB501 (LPS, Orsay, France), with the beam following a predetermined random path. The reconstruction of HAADF images is then straightforward with well known algorithms. However, when reconstructing the associated spectrum image, the high number of energy bands makes the problem computationally expensive.