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A blind compressive sensing algorithm is proposed to reconstruct hyperspectral images from spectrally-compressed measurements. The wavelength-dependent data are coded and then superposed, mapping the three-dimensional hyperspectral datacube to a two-dimensional image. The inversion algorithm learns a dictionary in situ from the measurements via globallocal shrinkage priors. By using RGB images as side information of the compressive sensing system, the proposed approach is extended to learn a coupled dictionary from the joint dataset of the compressed measurements and the corresponding RGB images, to improve reconstruction quality. A prototype camera is built using a liquid-crystal-on-silicon modulator. Experimental reconstructions of hyperspectral datacubes from both simulated and real compressed measurements demonstrate the efficacy of the proposed inversion algorithm, the feasibility of the camera and the benefit of side information.Index Terms-Compressive sensing, hyperspectral image, side information, Bayesian shrinkage, dictionary learning, blind compressive sensing, computational photography, coded aperture snapshot spectral imaging (CASSI), spatial light modulation.

The primary role of a red blood cell (RBC) is delivering oxygen throughout our body. Abnormalities of this basic function lead to anemia and are caused by numerous diseases such as malaria and sickle cell anemia. As prompt and inexpensive tests for blood screening are in demand, we have developed a faster and reliable way to measure morphological parameters associated with the structure of red blood cells and the size distribution of the cells in a whole blood smear. Modeling the RBC shape under Born approximation, we are able to determine parameters of clinical relevance, such as the diameter, thickness and dimple size. From a measured quantitative phase image of a blood smear, we can determine the average and standard deviation of the red blood cell volume simultaneously, i.e., without analyzing each cell individually. This approach may open the door for a new generation of label-free, high-throughput blood testing.

We report experimental evidence of correlation-induced spectral changes in biological tissues. The overall spectral shift in our transmission measurements is to the red and the mean wavelength of the original spectrum is up 10% larger. These results indicate that the spectral changes due to elastic scattering are significant and likely to hinder all spectroscopic measurements based on the inelastic (i.e., emission and absorption) interaction between light and tissues. Thus, simultaneous morphology and spectral measurements are required for accurate measurements spectroscopic information.

Stochastic fields do not generally possess a Fourier transform. This makes the second-order statistics calculation very difficult, as it requires solving a fourth-order stochastic wave equation. This problem was alleviated by Wolf who introduced the coherent mode decomposition and, as a result, space-frequency statistics propagation of wide-sense stationary fields. In this paper we show that if, in addition to wide-sense stationarity, the fields are also wide-sense statistically homogeneous, then monochromatic plane waves can be used as an eigenfunction basis for the cross spectral density. Furthermore, the eigenvalue associated with a plane wave, exp[i(k · r-ωt)], is given by the spatiotemporal power spectrum evaluated at the frequency (k, ω). We show that the second-order statistics of these fields is fully described by the spatiotemporal power spectrum, a real, positive function. Thus, the second-order statistics can be efficiently propagated in the wavevector-frequency representation using a new framework of deterministic signals associated with random fields. Analogous to the complex analytic signal representation of a field, the deterministic signal is a mathematical construct meant to simplify calculations. Specifically, the deterministic signal associated with a random field is defined such that it has the identical autocorrelation as the actual random field. Calculations for propagating spatial and temporal correlations are simplified greatly because one only needs to solve a deterministic wave equation of second order. We illustrate the power of the wavevector-frequency representation with calculations of spatial coherence in the far zone of an incoherent source, as well as coherence effects induced by biological tissues.