<p>Spectral imaging aims to capture and process a 3-dimensional spectral image with a large amount of spectral information for each spatial location. Compressive spectral imaging techniques (CSI) increases the sensing speed and reduces the amount of collected data compared to traditional spectral imaging methods. The coded aperture snapshot spectral imager (CASSI) is an optical architecture to sense a spectral image in a single 2D coded projection by applying CSI. Typically, the 3D scene is recovered by solving an L1-based optimization problem that assumes the scene is sparse in some known orthonormal basis. In contrast, the matrix completion technique (MC) allows to recover the scene without such prior knowledge. The MC reconstruction algorithms rely on a low-rank structure of the scene. Moreover, the CASSI system uses coded aperture patterns that determine the quality of the estimated scene. Therefore, this paper proposes the design of an optimal coded aperture set for the MC methodology. The designed set is attained by maximizing the distance between the translucent elements in the coded aperture. Visualization of the recovered spectral signals and simulations over different databases show average improvement when the designed coded set is used between 1-3 dBs compared to the complementary coded aperture set, and between 3-9 dBs compared to the conventional random coded aperture set.</p>
Recovering spectral images from compressive measurements using designed coded apertures and Matrix Completion Theory