We present a single disperser spectral imager that exploits recent theoretical work in the area of compressed sensing to achieve snapshot spectral imaging. An experimental prototype is used to capture the spatiospectral information of a scene that consists of two balls illuminated by different light sources. An iterative algorithm is used to reconstruct the data cube. The average spectral resolution is 3.6 nm per spectral channel. The accuracy of the instrument is demonstrated by comparison of the spectra acquired with the proposed system with the spectra acquired by a nonimaging reference spectrometer.

This paper describes a single-shot spectral imaging approach based on the concept of compressive sensing. The primary features of the system design are two dispersive elements, arranged in opposition and surrounding a binary-valued aperture code. In contrast to thin-film approaches to spectral filtering, this structure results in easily-controllable, spatially-varying, spectral filter functions with narrow features. Measurement of the input scene through these filters is equivalent to projective measurement in the spectral domain, and hence can be treated with the compressive sensing frameworks recently developed by a number of groups. We present a reconstruction framework and demonstrate its application to experimental data.

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Observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where the number of unknowns may potentially be larger than the number of observations and f* admits sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

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