Online Unmixing of Multitemporal Hyperspectral Images Accounting for Spectral Variability

Abstract

Hyperspectral unmixing is aimed at identifying the reference spectral signatures composing an hyperspectral image and their relative abundance fractions in each pixel. In practice, the identified signatures may vary spectrally from an image to another due to varying acquisition conditions, thus inducing possibly significant estimation errors. Against this background, hyperspectral unmixing of several images acquired over the same area is of considerable interest. Indeed, such an analysis enables the endmembers of the scene to be tracked and the corresponding endmember variability to be characterized. Sequential endmember estimation from a set of hyperspectral images is expected to provide improved performance when compared to methods analyzing the images independently.However, the significant size of hyperspectral data precludes the use of batch procedures to jointly estimate the mixture parameters of a sequence of hyperspectral images. Provided that each elementary component is present in at least one image of the sequence, we propose to perform an online hyperspectral unmixing accounting for temporal endmember variability. The online hyperspectral unmixing is formulated as a two-stage stochastic program, which can be solved using a stochastic approximation. The performance of the proposed method is evaluated on synthetic and real data.A comparison with independent unmixing algorithms finally illustrates the interest of the proposed strategy. Index TermsHyperspectral imagery, perturbed linear unmixing (PLMM), endmember temporal variability, two-stage stochastic program, stochastic approximation (SA).

Unmixing multitemporal hyperspectral images accounting for smooth and abrupt variations

“…The proposed algorithm has been compared to VCA/FCLS [18], [19], SISAL/FCLS [20], the robust LMM (rLMM) [21] applied to each HS image independently, and the online unmixing (OU) described in [15] (in the setting [15, Table I quadratic reconstruction error (RE), respectively defined as…”

“…Section IV presents some simulation results obtained on synthetic data. The performance of the proposed method is appreciated in comparison with the VCA/FCLS algorithm [18], [19], the SISAL/FCLS algorithm [20], the robust LMM (rLMM) described in [21] and the online unmixing (OU) method of [15]. Conclusions and research perspectives are finally reported in Section V.…”

“…Even if endmember spatial variability in a given HS image has been extensively considered in the literature (using statistical [3]- [5] and deterministic [6]- [12] approaches) fewer works have considered temporal variability by exploiting multitemporal HS (MTHS) images. However, MTHS images, which are composed of images successively acquired over the same area, allow information redundancies between consecutive images to be exploited (e.g, via features exhibiting smooth temporal variations) [13]- [15]. While these approaches allow smooth, moderate temporal variations of the mixture parameters to be represented, they do not address abrupt spectral changes affecting HS images, either resulting from the presence of outliers or from significant time intervals between consecutive acquisitions.…”

“…On the other hand, endmembers appearing in only a few images are considered as outliers with respect to the commonly shared materials. Based on these observations, a new instance of the perturbed linear mixing model (PLMM) [15] is investigated to account for temporal variability and additive outliers. The resulting problem is formulated within a Bayesian framework and solved with an MCMC method.…”

Low-Rank Decomposition and Total Variation Regularization of Hyperspectral Video Sequences

“…improvements of sensor technologies, HVSs are currently being developed, opening the door to new research avenues and application, involving critical new methodological developments [5][6][7][8].…”