218 research outputs found
Robust Linear Spectral Unmixing using Anomaly Detection
This paper presents a Bayesian algorithm for linear spectral unmixing of
hyperspectral images that accounts for anomalies present in the data. The model
proposed assumes that the pixel reflectances are linear mixtures of unknown
endmembers, corrupted by an additional nonlinear term modelling anomalies and
additive Gaussian noise. A Markov random field is used for anomaly detection
based on the spatial and spectral structures of the anomalies. This allows
outliers to be identified in particular regions and wavelengths of the data
cube. A Bayesian algorithm is proposed to estimate the parameters involved in
the model yielding a joint linear unmixing and anomaly detection algorithm.
Simulations conducted with synthetic and real hyperspectral images demonstrate
the accuracy of the proposed unmixing and outlier detection strategy for the
analysis of hyperspectral images
Bayesian estimation of linear mixtures using the normal compositional model. Application to hyperspectral imagery
This paper studies a new Bayesian unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of so-called endmembers. These endmembers are supposed to be random in order to model uncertainties regarding their knowledge. More precisely, we model endmembers as Gaussian vectors whose means have been determined using an endmember extraction algorithm such as the famous N-finder (N-FINDR) or Vertex Component Analysis (VCA) algorithms. This paper proposes to estimate the mixture coefficients (referred to as abundances) using a Bayesian algorithm. Suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters. A hybrid Gibbs sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances. The performance of the proposed methodology is evaluated by comparison with other unmixing algorithms on synthetic and real images
Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery
This paper studies a fully Bayesian algorithm for endmember extraction and
abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral
image is decomposed as a linear combination of pure endmember spectra following
the linear mixing model. The estimation of the unknown endmember spectra is
conducted in a unified manner by generating the posterior distribution of
abundances and endmember parameters under a hierarchical Bayesian model. This
model assumes conjugate prior distributions for these parameters, accounts for
non-negativity and full-additivity constraints, and exploits the fact that the
endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is
proposed to overcome the complexity of evaluating the resulting posterior
distribution. This sampler generates samples distributed according to the
posterior distribution and estimates the unknown parameters using these
generated samples. The accuracy of the joint Bayesian estimator is illustrated
by simulations conducted on synthetic and real AVIRIS images
Adaptive Markov random fields for joint unmixing and segmentation of hyperspectral image
Linear spectral unmixing is a challenging problem in hyperspectral imaging that consists of decomposing an observed pixel into a linear combination of pure spectra (or endmembers) with their corresponding proportions (or abundances). Endmember extraction algorithms can be employed for recovering the spectral signatures while abundances are estimated using an inversion step. Recent works have shown that exploiting spatial dependencies between image pixels can improve spectral unmixing. Markov random fields (MRF) are classically used to model these spatial correlations and partition the image into multiple classes with homogeneous abundances. This paper proposes to define the MRF sites using similarity regions. These regions are built using a self-complementary area filter that stems from the morphological theory. This kind of filter divides the original image into flat zones where the underlying pixels have the same spectral values. Once the MRF has been clearly established, a hierarchical Bayesian algorithm is proposed to estimate the abundances, the class labels, the noise variance, and the corresponding hyperparameters. A hybrid Gibbs sampler is constructed to generate samples according to the corresponding posterior distribution of the unknown parameters and hyperparameters. Simulations conducted on synthetic and real AVIRIS data demonstrate the good performance of the algorithm
Enhancing hyperspectral image unmixing with spatial correlations
This paper describes a new algorithm for hyperspectral image unmixing. Most
of the unmixing algorithms proposed in the literature do not take into account
the possible spatial correlations between the pixels. In this work, a Bayesian
model is introduced to exploit these correlations. The image to be unmixed is
assumed to be partitioned into regions (or classes) where the statistical
properties of the abundance coefficients are homogeneous. A Markov random field
is then proposed to model the spatial dependency of the pixels within any
class. Conditionally upon a given class, each pixel is modeled by using the
classical linear mixing model with additive white Gaussian noise. This strategy
is investigated the well known linear mixing model. For this model, the
posterior distributions of the unknown parameters and hyperparameters allow
ones to infer the parameters of interest. These parameters include the
abundances for each pixel, the means and variances of the abundances for each
class, as well as a classification map indicating the classes of all pixels in
the image. To overcome the complexity of the posterior distribution of
interest, we consider Markov chain Monte Carlo methods that generate samples
distributed according to the posterior of interest. The generated samples are
then used for parameter and hyperparameter estimation. The accuracy of the
proposed algorithms is illustrated on synthetic and real data.Comment: Manuscript accepted for publication in IEEE Trans. Geoscience and
Remote Sensin
Estimating the number of endmembers in hyperspectral images using the normal compositional model and a hierarchical Bayesian algorithm.
This paper studies a semi-supervised Bayesian unmixing algorithm for hyperspectral images. This algorithm is based on the normal compositional model recently introduced by Eismann and Stein. The normal compositional model assumes that each pixel of the image is modeled as a linear combination of an unknown number of pure materials, called endmembers. However, contrary to the classical linear mixing model, these endmembers are supposed to be random in order to model uncertainties regarding their knowledge. This paper proposes to estimate the mixture coefficients of the Normal Compositional Model (referred to as abundances) as well as their number using a reversible jump Bayesian algorithm. The performance of the proposed methodology is evaluated thanks to simulations conducted on synthetic and real AVIRIS images
Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing
This paper presents a new Bayesian collaborative sparse regression method for
linear unmixing of hyperspectral images. Our contribution is twofold; first, we
propose a new Bayesian model for structured sparse regression in which the
supports of the sparse abundance vectors are a priori spatially correlated
across pixels (i.e., materials are spatially organised rather than randomly
distributed at a pixel level). This prior information is encoded in the model
through a truncated multivariate Ising Markov random field, which also takes
into consideration the facts that pixels cannot be empty (i.e, there is at
least one material present in each pixel), and that different materials may
exhibit different degrees of spatial regularity. Secondly, we propose an
advanced Markov chain Monte Carlo algorithm to estimate the posterior
probabilities that materials are present or absent in each pixel, and,
conditionally to the maximum marginal a posteriori configuration of the
support, compute the MMSE estimates of the abundance vectors. A remarkable
property of this algorithm is that it self-adjusts the values of the parameters
of the Markov random field, thus relieving practitioners from setting
regularisation parameters by cross-validation. The performance of the proposed
methodology is finally demonstrated through a series of experiments with
synthetic and real data and comparisons with other algorithms from the
literature
Implementation strategies for hyperspectral unmixing using Bayesian source separation
Bayesian Positive Source Separation (BPSS) is a useful unsupervised approach
for hyperspectral data unmixing, where numerical non-negativity of spectra and
abundances has to be ensured, such in remote sensing. Moreover, it is sensible
to impose a sum-to-one (full additivity) constraint to the estimated source
abundances in each pixel. Even though non-negativity and full additivity are
two necessary properties to get physically interpretable results, the use of
BPSS algorithms has been so far limited by high computation time and large
memory requirements due to the Markov chain Monte Carlo calculations. An
implementation strategy which allows one to apply these algorithms on a full
hyperspectral image, as typical in Earth and Planetary Science, is introduced.
Effects of pixel selection, the impact of such sampling on the relevance of the
estimated component spectra and abundance maps, as well as on the computation
times, are discussed. For that purpose, two different dataset have been used: a
synthetic one and a real hyperspectral image from Mars.Comment: 10 pages, 6 figures, submitted to IEEE Transactions on Geoscience and
Remote Sensing in the special issue on Hyperspectral Image and Signal
Processing (WHISPERS
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