Learning Endmember Dynamics in Multitemporal Hyperspectral Data Using A State-Space Model Formulation

Hyperspectral image unmixing is an inverse problem aiming at recovering the spectral signatures of pure materials of interest (called endmembers) and estimating their proportions (called abundances) in every pixel of the image. However, in spite of a tremendous applicative potential and the avent of new satellite sensors with high temporal resolution, multitemporal hyperspectral unmixing is still a relatively underexplored research avenue in the community, compared to standard image unmixing. In this paper, we propose a new framework for multitemporal unmixing and endmember extraction based on a state-space model, and present a proof of concept on simulated data to show how this representation can be used to inform multitemporal unmixing with external prior knowledge, or on the contrary to learn the dynamics of the quantities involved from data using neural network architectures adapted to the identification of dynamical systems.

[1]  Bertrand Chapron,et al.  Learning Latent Dynamics for Partially-Observed Chaotic Systems , 2019, Chaos.

[2]  Antonio J. Plaza,et al.  Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches , 2012, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[3]  K. C. Ho,et al.  Endmember Variability in Hyperspectral Analysis: Addressing Spectral Variability During Spectral Unmixing , 2014, IEEE Signal Processing Magazine.

[4]  Jean-Yves Tourneret,et al.  A Hierarchical Bayesian Model Accounting for Endmember Variability and Abrupt Spectral Changes to Unmix Multitemporal Hyperspectral Images , 2016, IEEE Transactions on Computational Imaging.

[5]  S. Brunton,et al.  Discovering governing equations from data by sparse identification of nonlinear dynamical systems , 2015, Proceedings of the National Academy of Sciences.

[6]  Paul D. Gader,et al.  A Review of Nonlinear Hyperspectral Unmixing Methods , 2014, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[7]  R. Bannister.  A review of operational methods of variational and ensemble‐variational data assimilation , 2017 .

[8]  Naoto Yokoya,et al.  Multisensor Coupled Spectral Unmixing for Time-Series Analysis , 2017, IEEE Transactions on Geoscience and Remote Sensing.

[9]  Patrick Hostert,et al.  The EnMAP Spaceborne Imaging Spectroscopy Mission for Earth Observation , 2015, Remote. Sens..

[10]  B. Hapke.  Theory of reflectance and emittance spectroscopy , 1993 .

[11]  Cédric Herzet,et al.  Bilinear residual Neural Network for the identification and forecasting of dynamical systems , 2017, ArXiv.

[12]  José M. Bioucas-Dias,et al.  Vertex component analysis: a fast algorithm to unmix hyperspectral data , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[13]  Ronan Fablet,et al.  EM-like Learning Chaotic Dynamics from Noisy and Partial Observations , 2019, ArXiv.

[14]  G. Evensen.  Data Assimilation: The Ensemble Kalman Filter , 2006 .

[15]  Jocelyn Chanussot,et al.  Dynamical Spectral Unmixing of Multitemporal Hyperspectral Images , 2015, IEEE Transactions on Image Processing.

[16]  Jocelyn Chanussot,et al.  Blind Hyperspectral Unmixing Using an Extended Linear Mixing Model to Address Spectral Variability , 2016, IEEE Transactions on Image Processing.

[17]  Jocelyn Chanussot,et al.  Spectral Unmixing: A Derivation of the Extended Linear Mixing Model From the Hapke Model , 2019, IEEE Geoscience and Remote Sensing Letters.

[18]  Ronan Fablet,et al.  Residual Networks as Flows of Diffeomorphisms , 2019, Journal of Mathematical Imaging and Vision.

[19]  Qian Du,et al.  Hyperspectral and LiDAR Data Fusion: Outcome of the 2013 GRSS Data Fusion Contest , 2014, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[20]  Cédric Herzet,et al.  Bilinear Residual Neural Network for the Identification and Forecasting of Geophysical Dynamics , 2018, 2018 26th European Signal Processing Conference (EUSIPCO).