Spatiotemporal blue noise coded aperture design for multi-shot compressive spectral imaging.

Multi-shot coded aperture snapshot spectral imaging (CASSI) systems capture the spectral information of a scene using a small set of coded focal plane array (FPA) compressive measurements. Compressed sensing (CS) reconstruction algorithms are then used to reconstruct the underlying spectral 3D data cube from an underdetermined system of linear equations. Multiple snapshots result in a less ill-posed inverse problem and improved reconstructions. The only varying components in CASSI are the coded apertures, whose structure is crucial inasmuch as they determine the minimum number of FPA measurements needed for correct image reconstruction and the corresponding attainable quality. Traditionally, the spatial structures of the coded aperture entries are selected at random, leading to suboptimal reconstruction solutions. This work presents an optimal structure design of a set of coded apertures by optimizing the concentration of measure of the multi-shot CASSI sensing matrix and its incoherence with respect to the sparse representation basis. First, the CASSI matrix system representation in terms of the ensemble of random projections is established. Then, the restricted isometry property (RIP) of the CASSI projections is determined as a function of the coded aperture entries. The optimal coded aperture structures are designed under the criterion of satisfying the RIP with high probability, coined spatiotemporal blue noise (BN) coded apertures. Furthermore, an algorithm that implements the BN ensembles is presented. Extensive simulations and a testbed implementation are developed to illustrate the improvements of the BN coded apertures over the traditionally used coded aperture structures, in terms of spectral image reconstruction PSNR and SSIM.