Spectral image unmixing from optimal coded-aperture compressive measurements

Hyperspectral remote sensing often captures imagery where the spectral profiles of the spatial pixels are the result of the reflectance contribution of numerous materials. Spectral unmixing is then used to extract the collection of materials, or endmembers, contained in the measured spectra, and a set of corresponding fractions that indicate the abundance of each material present at each pixel. This work aims at developing a spectral unmixing algorithm directly from compressive measurements acquired using the coded-aperture snapshot spectral imaging (CASSI) system. The proposed method first uses the compressive measurements to find a sparse vector representation of each pixel in a 3-D dictionary formed by a 2-D wavelet basis and a known spectral library of endmembers. The sparse vector representation is estimated by solving a sparsity-constrained optimization problem using an algorithm based on the variable splitting augmented Lagrangian multipliers method. The performance of the proposed spectral unmixing method is improved by taking optimal CASSI compressive measurements obtained when optimal coded apertures are used in the optical system. The optimal coded apertures are designed such that the CASSI sensing matrix satisfies a Restricted Isometry Property (RIP) with high probability. Simulations with synthetic hyperspectral cubes illustrate the accuracy of the proposed unmixing method.