Coded aperture optimization in compressive spectral imaging

This thesis establishes the Coded Aperture Snapshot Spectral Imaging (CASSI) RIP constants in terms of the statistical properties of the coded aperture entries such that the concentration of the eigenvalues of the sub-matrices associate to the CASSI sensing matrix is maximized. More specifically, the optimal ℓ1-coded apertures are designed when their entries are drawn from: (a) Boolean random variables, (b) binary random variables, (c) random signed and unsigned gray scale values.;ℓ1-coded apertures can also be designed for specific applications such as compressive spectral selectivity. Spectral imaging selectivity is sought in diverse applications since relevant information often lies within a subset of spectral bands. Capturing and reconstructing all the spectral bands in the observed image cube, to then throw away a large portion of this data is inefficient. First, the ℓ1-selective coded aperture optimization problem, in this case, is shown to be analogous to the optimization of a constrained multichannel filter bank. The optimal ℓ1-selective coded apertures allow the decomposition of the CASSI measurement into several periodic subsets, each having information from only a few selected spectral bands. This first design approach, however, limits the selective spectral profiles to be periodic patterns. Further, the minimum number of shots is restricted to the periodicity of the spectral pattern. In most practical applications, however, the spectral profiles of interest are not periodic and the number of shots is additionally restricted by the application at hand. A second optimization approach for coded aperture spectral selectivity is then developed, where the ℓ1-selective coded aperture design is generalized to a more general and more effective mathematical framework for multi-shot CASSI, allowing the reconstruction of arbitrary subset of bands, periodic or aperiodic, while minimizing the required number of shots. The new approach aims at the optimization of ℓ1-selective coded aperture sets such that a group of compressive spectral measurements is constructed, each with information from a specific subset of bands. A matrix representation of CASSI is introduced permitting the optimization of spectrally selective coded aperture sets. Further, each ℓ1-selective coded aperture set forms a matrix such that rank minimization is used to reduce the number of CASSI shots needed. Conditions for the code apertures are identified such that a Restricted Isometry Property in the CASSI compressive measurements is satisfied with higher probability.;This thesis extends further the compressive capabilities of CASSI by replacing the traditional blocking-unblocking ℓ1-coded apertures by a set of ℓ1-colored coded apertures. The features of the ℓ 1-colored coded apertures are optical filters whose spatial and spectral structure can be properly designed such that the number of projections are minimized and the quality of reconstructed images is maximized. The optimal design of the ℓ1-colored coded apertures aims to better satisfy a new Restricted Isometry Property (RIP) in CASSI. The optimal designs are compared with designs based on random selection of the coded aperture colors and with the traditional blocking-unblocking coded apertures. Extensive simulations show the improvement in PSNR of the reconstructed images when the optimal colored coded apertures designs are used in CASSI.;Finally, this dissertation develops a higher order precision model for the optical sensing in CASSI that includes a more accurate discretization of the underlying signals, leading to image reconstructions less dependent on calibration. Further, the higher order model results in improved image quality reconstruction of the underlying scene than that achieved by the traditional model. The proposed higher precision computational model is also more suitable for reconfigurable multi-frame CASSI systems where multiple coded apertures are used sequentially to capture the hyperspectral scene. Several simulations and experimental measurements demonstrate the benefits of the new discretization model. (Abstract shortened by UMI.).