Hyperspectral imagery provides significant information about the spectral characteristics of objects and materials present
in a scene. It enables object and feature detection, classification, or identification based on the acquired spectral characteristics.
However, it 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 which demands enormous computational
resources in terms of storage, computationm, and I/O throughputs. Specialized optical architectures have been developed
for the compressed acquisition of spectral images using a reduced set of coded measurements contrary to traditional architectures
that need a complete set of measurements of the data cube for image acquisition, dealing with the storage and
acquisition limitations. Despite this improvement, if any processing is desired, the image has to be reconstructed by an
inverse algorithm in order to be processed, which is also an expensive task. In this paper, a sparsity-based algorithm for
target detection in compressed spectral images is presented. Specifically, the target detection model adapts a sparsity-based
target detector to work in a compressive domain, modifying the sparse representation basis in the compressive sensing
problem by means of over-complete training dictionaries and a wavelet basis representation. Simulations show that the
presented method can achieve even better detection results than the state of the art methods.