Single Snapshot System for Compressive Covariance Matrix Estimation for Hyperspectral Imaging via Lenslet Array

Compressive Covariance Sampling (CCS) is a strategy used to recover the covariance matrix (CM) directly from compressive measurements. Several works have proven the advantages of CSS in Compressive Spectral Imaging (CSI) but most of these algorithms require multiple random projections of the scene to obtain good reconstructions. However, several low-resolution copies of the scene can be captured in a single snapshot through a lenslet array. For this reason, this paper proposes a sensing protocol and a single snapshot CCS optical architecture using a lenslet array based on the Dual Dispersive Aperture Spectral Imager(DD-CASSI) that allows the recovery of the covariance matrix with a single snapshot. In this architecture uses the lenslet array allows to obtain different projections of the image in a shot due to the special coded aperture. In order to validate the proposed approach, simulations evaluated the quality of the recovered CM and the performance recovering the spectral signatures against traditional methods. Results show that the image reconstructions using CM have PSNR values about 30 dB, and reconstructed spectrum has a spectral angle mapper (SAM) error less than 15 degrees compared to the original spectral signatures.