Nonlinear hyperspectral unmixing with robust nonnegative matrix factorization

Abstract--This paper introduces a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures. This new model not only generalizes the commonly used linear mixing model, but also allows for possible nonlinear effects to be easily handled, relying on mild assumptions regarding these nonlinearities. The standard nonnegativity and sum-to-one constraints inherent to spectral unmixing are coupled with a group-sparse constraint imposed on the nonlinearity component. The data fidelity term is expressed as a β -divergence, a continuous family of dissimilarity measures that takes the squared Euclidean distance and the generalized Kullback-Leibler divergence as special cases. The penalized objective is minimized with a block-coordinate descent that involves majorization-minimization updates. Simulation results obtained on synthetic and real data show that the proposed strategy competes with state-of-the-art linear and nonlinear unmixing methods. Spectral unmixing (SU) is an issue of prime interest when analyzing hyperspectral data since it provides a comprehensive and meaningful description of the collected measurements in various application fields including remote sensing [1], planetology [2], food monitoring [3] or spectro-microscopy [4]. Most of the hyperspectral unmixing algorithms proposed in the signal & image processing and geoscience literatures rely on the commonly admitted linear mixing model (LMM),Y MA . Indeed, LMM provides a good approximation of the physical process underlying the observations and has resulted in interesting results for most applications. However, for several specific applications, LMM may be inaccurate and other nonlinear models need to be advocated [7]. For instance, in remotely sensed images composed of vegetation (e.g., trees), interactions of photons with multiple components of the scene lead to nonlinear effects that can be taken into account N. Dobigeon is with University of Toulouse, IRIT/INP-ENSEEIHT, 2 rue Camichel, BP 7122, 31071 Toulouse cedex 7, France.