Fast Hyperspectral Unmixing in Presence of Nonlinearity or Mismodeling Effects

Abstract

This paper presents two novel hyperspectral mixture models and associated unmixing algorithms. The two models assume a linear mixing model corrupted by an additive term whose expression can be adapted to account for multiple scattering nonlinearities (NL), or mismodelling effects (ME). The NL model generalizes bilinear models by taking into account higher order interaction terms. The ME model accounts for different effects such as endmember variability or the presence of outliers. The abundance and residual parameters of these models are estimated by considering a convex formulation suitable for fast estimation algorithms. This formulation accounts for constraints such as the sum-to-one and non-negativity of the abundances, the non-negativity of the nonlinearity coefficients, the spectral smoothness of the ME terms and the spatial sparseness of the residuals. The resulting convex problem is solved using the alternating direction method of multipliers (ADMM) whose convergence is ensured theoretically. The proposed mixture models and their unmixing algorithms are validated on both synthetic and real images showing competitive results regarding the quality of the inference and the computational complexity when compared to the state-of-the-art algorithms.

Blind separation of sparse sources in the presence of outliers

“…They have been essentially used in the NMF framework with optimization methods [2,[12][13][14][15] or a Bayesian approach [16]. These methods strongly rely on the positivity of both 80 the sources and the mixing matrix, which is not necessarily a valid assumption in general settings.…”

Fast hyperspectral unmixing in presence of sparse multiple scattering nonlinearities

“…where mi,j = mi ⊙ mj, and the interaction terms are weighted by the coefficient √ 2 obtained by comparison with a homogeneous polynomial kernel of the 2nd degree (see [23] for more details regarding these coefficients and the construction of Q (K) ). In what follows, and for brevity, we drop the order index (K) for general statements (related to all interaction orders) and only include it when dealing with specific orders.…”

“…1 admit analytical solutions that are not presented here for brevity (see [23]). The computational complexity of Algo.…”

Unsupervised Nonlinear Hyperspectral Unmixing Based on Bilinear Mixture Models via Geometric Projection and Constrained Nonnegative Matrix Factorization

“…Their performances have been validated by the convincing field experiments in [33,34]. For more complex scenarios such as urban areas, higher-order scatterings have been taken into account [35][36][37]. Heylen et al [37] presented a multilinear mixing (MLM) model by introducing a probability parameter of light undergoing further interactions, and all orders of multiple scatterings can be included.…”