Unsupervised Post-Nonlinear Unmixing of Hyperspectral Images Using a Hamiltonian Monte Carlo Algorithm

Abstract

This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are post-nonlinear functions of unknown pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomials leading to a polynomial post-nonlinear mixing model. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding an unsupervised nonlinear unmixing algorithm. Due to the large number of parameters to be estimated, an efficient Hamiltonian Monte Carlo algorithm is investigated. The classical leapfrog steps of this algorithm are modified to handle the parameter constraints. The performance of the unmixing strategy, including convergence and parameter tuning, is first evaluated on synthetic data. Simulations conducted with real data finally show the accuracy of the proposed unmixing strategy for the analysis of hyperspectral images.

References in corpus (1)

• Nonlinear unmixing of hyperspectral images: models and algorithms

Cited by in corpus (8)

• Nonlinear unmixing of hyperspectral images: models and algorithms
• Unsupervised Unmixing of Hyperspectral Images Accounting for Endmember Variability
• Hyperspectral Unmixing in Presence of Endmember Variability, Nonlinearity or Mismodelling Effects
• Residual component analysis of hyperspectral images -- Application to joint nonlinear unmixing and nonlinearity detection
• Estimating the Intrinsic Dimension of Hyperspectral Images Using an Eigen-Gap Approach
• Nonparametric Detection of Nonlinearly Mixed Pixels and Endmember Estimation in Hyperspectral Images
• Spectral unmixing of Multispectral Lidar signals
• Identifiability-Guaranteed Simplex-Structured Post-Nonlinear Mixture Learning via Autoencoder