16 research outputs found
Supervised nonlinear spectral unmixing using a post-nonlinear mixing model for hyperspectral imagery
This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model. The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data
Correntropy Maximization via ADMM - Application to Robust Hyperspectral Unmixing
In hyperspectral images, some spectral bands suffer from low signal-to-noise
ratio due to noisy acquisition and atmospheric effects, thus requiring robust
techniques for the unmixing problem. This paper presents a robust supervised
spectral unmixing approach for hyperspectral images. The robustness is achieved
by writing the unmixing problem as the maximization of the correntropy
criterion subject to the most commonly used constraints. Two unmixing problems
are derived: the first problem considers the fully-constrained unmixing, with
both the non-negativity and sum-to-one constraints, while the second one deals
with the non-negativity and the sparsity-promoting of the abundances. The
corresponding optimization problems are solved efficiently using an alternating
direction method of multipliers (ADMM) approach. Experiments on synthetic and
real hyperspectral images validate the performance of the proposed algorithms
for different scenarios, demonstrating that the correntropy-based unmixing is
robust to outlier bands.Comment: 23 page
Spectral unmixing of Multispectral Lidar signals
In this paper, we present a Bayesian approach for spectral unmixing of
multispectral Lidar (MSL) data associated with surface reflection from targeted
surfaces composed of several known materials. The problem addressed is the
estimation of the positions and area distribution of each material. In the
Bayesian framework, appropriate prior distributions are assigned to the unknown
model parameters and a Markov chain Monte Carlo method is used to sample the
resulting posterior distribution. The performance of the proposed algorithm is
evaluated using synthetic MSL signals, for which single and multi-layered
models are derived. To evaluate the expected estimation performance associated
with MSL signal analysis, a Cramer-Rao lower bound associated with model
considered is also derived, and compared with the experimental data. Both the
theoretical lower bound and the experimental analysis will be of primary
assistance in future instrument design
Nonlinear spectral unmixing of hyperspectral images using Gaussian processes
This paper presents an unsupervised algorithm for nonlinear unmixing of
hyperspectral images. The proposed model assumes that the pixel reflectances
result from a nonlinear function of the abundance vectors associated with the
pure spectral components. We assume that the spectral signatures of the pure
components and the nonlinear function are unknown. The first step of the
proposed method consists of the Bayesian estimation of the abundance vectors
for all the image pixels and the nonlinear function relating the abundance
vectors to the observations. The endmembers are subsequently estimated using
Gaussian process regression. The performance of the unmixing strategy is
evaluated with simulations conducted on synthetic and real data
Bayesian nonlinear hyperspectral unmixing with spatial residual component analysis
This paper presents a new Bayesian model and algorithm for nonlinear unmixing
of hyperspectral images. The model proposed represents the pixel reflectances
as linear combinations of the endmembers, corrupted by nonlinear (with respect
to the endmembers) terms and additive Gaussian noise. Prior knowledge about the
problem is embedded in a hierarchical model that describes the dependence
structure between the model parameters and their constraints. In particular, a
gamma Markov random field is used to model the joint distribution of the
nonlinear terms, which are expected to exhibit significant spatial
correlations. An adaptive Markov chain Monte Carlo algorithm is then proposed
to compute the Bayesian estimates of interest and perform Bayesian inference.
This algorithm is equipped with a stochastic optimisation adaptation mechanism
that automatically adjusts the parameters of the gamma Markov random field by
maximum marginal likelihood estimation. Finally, the proposed methodology is
demonstrated through a series of experiments with comparisons using synthetic
and real data and with competing state-of-the-art approaches