HYCA: A New Technique for Hyperspectral Compressive Sensing

Hyperspectral imaging relies on sophisticated acquisition and data processing systems able to acquire, process, store, and transmit hundreds or thousands of image bands from a given area of interest. In this paper, we exploit the high correlation existing among the components of the hyperspectral data sets to introduce a new compressive sensing methodology, termed hyperspectral coded aperture (HYCA), which largely reduces the number of measurements necessary to correctly reconstruct the original data. HYCA relies on two central properties of most hyperspectral images, usually termed data cubes: 1) the spectral vectors live on a low-dimensional subspace; and 2) the spectral bands present high correlation in both the spatial and the spectral domain. The former property allows to represent the data vectors using a small number of coordinates. In this paper, we particularly exploit the high spatial correlation mentioned in the latter property, which implies that each coordinate is piecewise smooth and thus compressible using local differences. The measurement matrix computes a small number of random projections for every spectral vector, which is connected with coded aperture schemes. The reconstruction of the data cube is obtained by solving a convex optimization problem containing a data term linked to the measurement matrix and a total variation regularizer. The solution of this optimization problem is obtained by an instance of the alternating direction method of multipliers that decomposes very hard problems into a cyclic sequence of simpler problems. In order to address the need to set up the parameters involved in the HYCA algorithm, we also develop a constrained version of HYCA (C-HYCA), in which all the parameters can be automatically estimated, which is an important aspect for practical application of the algorithm. A series of experiments with simulated and real data shows the effectiveness of HYCA and C-HYCA, indicating their potential in real-world applications.