Deep Generative Endmember Modeling: An Application to Unsupervised Spectral Unmixing

Abstract

Endmember (EM) spectral variability can greatly impact the performance of standard hyperspectral image analysis algorithms. Extended parametric models have been successfully applied to account for the EM spectral variability. However, these models still lack the compromise between flexibility and low-dimensional representation that is necessary to properly explore the fact that spectral variability is often confined to a low-dimensional manifold in real scenes. In this paper we propose to learn a spectral variability model directly from the observed data, instead of imposing it a priori. This is achieved through a deep generative EM model, which is estimated using a variational autoencoder (VAE). The encoder and decoder that compose the generative model are trained using pure pixel information extracted directly from the observed image, what allows for an unsupervised formulation. The proposed EM model is applied to the solution of a spectral unmixing problem, which we cast as an alternating nonlinear least-squares problem that is solved iteratively with respect to the abundances and to the low-dimensional representations of the EMs in the latent space of the deep generative model. Simulations using both synthetic and real data indicate that the proposed strategy can outperform the competing state-of-the-art algorithms.

A Data Dependent Multiscale Model for Hyperspectral Unmixing With Spectral Variability

“…This assumption can compromise the accuracy of estimated abundances in many circumstances due to the spectral variability existing in a typical scene. Recently, variations of the LMM have been proposed to cope with the variability phenomenon [8], [9], [10], [28], [11]. This work considers models that are linear on the abundances.…”

“…, e N ] is the noise. Different models have been recently proposed to represent endmember variability as a parametric function of some reference endmember spectral signatures [8], [9], [10], [28]. These models are generically denoted by…”

“…. , N where matrices M Dn are given in (28) and (29). Note that this cost function is again equivalent to a standard FCLS problem, which can be solved efficiently.…”

A Blind Multiscale Spatial Regularization Framework for Kernel-Based Spectral Unmixing

“…Problem (7) is solved using standard dual formulation based on the Lagrangian [20]. Although problem (7) presents an effective way of modeling both the linear trend and the nonlinear mixing occurring in a given pixel, it fails to impose any smooth structure over the abundance estimation within neighboring pixels.…”

“…The LMM is effective in accurately modelling mixtures occurring in scenes where the materials of interest cover a large area with respect to the pixel size [2]. It however disregards more complex mixing phenomena such as non-linearity [2], [3] and spectral variability [4], [5], [6], [7], which often results in estimation errors being propagated throughout the unmixing process [8].…”