Improved reconstruction for compressive hyperspectral imaging using spatial-spectral non-local means regularization

Compressive sensing has emerged as a novel sensing theory that can override the Shannon-Nyquist limit, having powerful implications in reducing the dimensionality of hyperspectral imaging acquisition demands. In order to recover the hyperspectral datacube from limited optically compressed measurements, we present a new reconstruction algorithm that exploits the space and spectral correlations through non-local means regularization. Based on a simple compressive sensing hyperspectral architecture that uses a digital micromirror device and a spectrometer, the reconstruction process is solved with the help of split Bregman optimization techniques, including penalty functions defined according to the spatial and spectral properties of the scene and noise sources.