A spectral image is a 3-dimensional spatio-spectral set with a large amount of spectral information for each spatial location of a scene. Compressive Spectral Imaging techniques (CSI) permit to capture the 3D scene in 2-dimensional coded projections. The Coded Aperture Snapshot Spectral Imager (CASSI) is an optical architecture to sense a spectral image in a single projection by applying CSI. CSI increases the sensing speed and reduces the amount of collected data compared to traditional methods. The 3D scene is then recovered by solving an ℓ ₁ -based optimization problem. However, this problem assumes that the scene is sparse in some known orthonormal basis. In contrast, a technique called Matrix Completion (MC) allows the recovery of a scene without such prior knowledge. The MC reconstruction algorithms rely on a low-rank structure of the scene. Moreover, the quality of the estimated scene from …