Colored Coded-Apertures for Spectral Image Unmixing

Hyperspectral remote sensing technology provides detailed spectral information from every pixel in an image. Due to the low spatial resolution of hyperspectral image sensors, and the presence of multiple materials in a scene, each pixel can contain more than one spectral signature. Therefore, endmember extraction is used to determine the pure spectral signature of the mixed materials and its corresponding abundance map in a remotely sensed hyperspectral scene. Advanced endmember extraction algorithms have been proposed to solve this linear problem called spectral unmixing. However, such techniques require the acquisition of the complete hyperspectral data cube to perform the unmixing procedure. Researchers show that using colored coded-apertures improve the quality of reconstruction in compressive spectral imaging (CSI) systems under compressive sensing theory (CS). This work aims at developing a compressive supervised spectral unmixing scheme to estimate the endmembers and the abundance map from compressive measurements. The compressive measurements are acquired by using colored coded-apertures in a compressive spectral imaging system. Then a numerical procedure estimates the sparse vector representation in a 3D dictionary by solving a constrained sparse optimization problem. The 3D dictionary is formed by a 2-D wavelet basis and a known endmembers spectral library, where the Wavelet basis is used to exploit the spatial information. The colored coded-apertures are designed such that the sensing matrix satisfies the restricted isometry property with high probability. Simulations show that the proposed scheme attains comparable results to the full data cube unmixing technique, but using fewer measurements.