A New Technique for Hyperspectral Compressive Sensing Using Spectral Unmixing

In hyperspectral imaging, the instruments measure the light reflected by the Earth surface in hundreds or thousands of spectral bands, generating huge amounts of data that must be effectively processed. The real-time requirements of some applications demand large bandwidths between the sensor and the ground stations. In order to simplify the hardware and software requirements of the hyperspectral acquisition systems, we develop a compressive sensing (CS) based technique for hyperspectral image reconstruction. CS is applicable when the data is compressible (or sparse) in a given basis or frame. This is usually the case with hyperspectral images as a consequence of its high correlation. The hyperspectral images which are compressible can be recovered from a number of measurements much smaller than the size of the original data. This compressed version of the data can then be sent to a ground station that will recover the original image by running a reconstruction algorithm. Specifically, in this work we elaborate on a previously introduced hyperspectral coded aperture (HYCA) algorithm. The performance of HYCA relies on the tuning of a regularization parameter, which is a time consuming task. Herein, we introduce a constrained formulation of HYCA, termed constrained HYCA (C-HYCA), which does not depend on any regularization parameter. C-HYCA optimization is solved with the C-SALSA alternating direction method of multipliers. In a series of experiments with simulated and real data we show that C-HYCA performance is similar to that of HYCA obtained with the best regularization parameter setting.