Coded aperture snapshot spectral imaging systems (CASSI) sense the three-dimensional spatio-spectral information of a scene using a single two-dimensional focal plane array snapshot. The compressive CASSI measurements are often modeled as the summation of coded and shifted versions of the spectral voxels of the underlying scene. This coarse approximation of the analog CASSI sensing phenomena is then compensated by calibration preprocessing prior to signal reconstruction. This paper 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 multiframe CASSI systems where multiple coded apertures are used sequentially to capture the hyperspectral scene. Several simulations and experimental measurements demonstrate the benefits of the discretization model.
Compressive spectral imaging (CSI) captures multispectral imagery using fewer measurements than those required by traditional Shannon-Nyquist theory-based sensing procedures. CSI systems acquire coded and dispersed random projections of the scene rather than direct measurements of the voxels. To date, the coding procedure in CSI has been realized through the use of block-unblock coded apertures (CAs), commonly implemented as chrome-on-quartz photomasks. These apertures block or permit us to pass the entire spectrum from the scene at given spatial locations, thus modulating the spatial characteristics of the scene. This paper extends the framework of CSI by replacing the traditional block-unblock photomasks by patterned optical filter arrays, referred to as colored coded apertures (CCAs). These, in turn, allow the source to be modulated not only spatially but spectrally as well, entailing more powerful coding strategies. The proposed CCAs are synthesized through linear combinations of low-pass, high-pass, and bandpass filters, paired with binary pattern ensembles realized by a digital micromirror device. The optical forward model of the proposed CSI architecture is presented along with a proof-of-concept implementation, which achieves noticeable improvements in the quality of the reconstruction.
We consider a compressive hyperspectral imaging reconstruction problem, where three-dimensional spatio-spectral information about a scene is sensed by a coded aperture snapshot spectral imager (CASSI). The CASSI imaging process can be modeled as suppressing three-dimensional coded and shifted voxels and projecting these onto a two-dimensional plane, such that the number of acquired measurements is greatly reduced. On the other hand, because the measurements are highly compressive, the reconstruction process becomes challenging. We previously proposed a compressive imaging reconstruction algorithm that is applied to two-dimensional images based on the approximate message passing (AMP) framework. AMP is an iterative algorithm that can be used in signal and image reconstruction by performing denoising at each iteration. We employed an adaptive Wiener filter as the image denoiser, and called our algorithm "AMP-Wiener." In this paper, we extend AMP-Wiener to three-dimensional hyperspectral image reconstruction, and call it "AMP-3D-Wiener." Applying the AMP framework to the CASSI system is challenging, because the matrix that models the CASSI system is highly sparse, and such a matrix is not suitable to AMP and makes it difficult for AMP to converge. Therefore, we modify the adaptive Wiener filter and employ a technique called damping to solve for the divergence issue of AMP. Our approach is applied in nature, and the numerical experiments show that AMP-3D-Wiener outperforms existing widely-used algorithms such as gradient projection for sparse reconstruction (GPSR) and two-step iterative shrinkage/thresholding (TwIST) given a similar amount of runtime. Moreover, in contrast to GPSR and TwIST, AMP-3D-Wiener need not tune any parameters, which simplifies the reconstruction process.Comment: 13 pages, to appear in Journal of Selected Topics in Signal Processin
Compressive sensing is a powerful sensing and reconstruction framework for recovering high dimensional signals with only a handful of observations and for spectral imaging, compressive sensing offers a novel method of multispectral imaging. Specifically, the coded aperture snapshot spectral imager (CASSI) system has been demonstrated to produce multi-spectral data cubes color images from a single snapshot taken by a monochrome image sensor. In this paper, we expand the theoretical framework of CASSI to include the spectral sensitivity of the image sensor pixels to account for color and then investigate the impact on image quality using either a traditional color image sensor that spatially multiplexes red, green, and blue light filters or a novel Foveon image sensor which stacks red, green, and blue pixels on top of one another.
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