GPU implementation of fully constrained linear spectral unmixing for remotely sensed hyperspectral data exploitation

Spectral unmixing is an important task for remotely sensed hyperspectral data exploitation. The spectral signatures collected in natural environments are invariably a mixture of the pure signatures of the various materials found within the spatial extent of the ground instantaneous field view of the imaging instrument. Spectral unmixing aims at inferring such pure spectral signatures, called endmembers, and the material fractions, called fractional abundances, at each pixel of the scene. A standard technique for spectral mixture analysis is linear spectral unmixing, which assumes that the collected spectra at the spectrometer can be expressed in the form of a linear combination of endmembers weighted by their corresponding abundances, expected to obey two constraints, i.e. all abundances should be non-negative, and the sum of abundances for a given pixel should be unity. Several techniques have been developed in the literature for unconstrained, partially constrained and fully constrained linear spectral unmixing, which can be computationally expensive (in particular, for complex highdimensional scenes with a high number of endmembers). In this paper, we develop new parallel implementations of unconstrained, partially constrained and fully constrained linear spectral unmixing algorithms. The implementations have been developed in programmable graphics processing units (GPUs), an exciting development in the field of commodity computing that fits very well the requirements of on-board data processing scenarios, in which low-weight and low-power integrated components are mandatory to reduce mission payload. Our experiments, conducted with a hyperspectral scene collected over the World Trade Center area in New York City, indicate that the proposed implementations provide relevant speedups over the corresponding serial versions in latest-generation Tesla C1060 GPU architectures.