An efficient methodology to simulate mixed spectral signatures of land covers through Field Radiometry data

An efficient methodology to simulate mixed spectral signatures of land covers, from endmember data, using linear statistical modelling based on the least squares estimation approach, is proposed. The optimal set of endmember has been obtained by measurements in situ with a field spectroradiometer GER 1500. Also, it is proposed the use of new sub-pixel methods based on statistics and certain “units of sampling” to apply to the landscapes. The resultant point estimations for these new units will be the “observations” and all of them will carry out an special role to simulate the final spectral signature. This methodology is used to simulate spectral signatures of a Mediterranean forest landscape near to Madrid (Spain). Furthermore the spectral signature model obtained through Field Radiometry data will be correlated with the image data of the same zone provided by the Landsat 7 Enhaced Thematic Mapper Plus (ETM+) sensor once corrected. The results obtained in correlation studies seem to conclude its efficiency. At the same time, the results open new research guidelines

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

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

Semi-supervised linear spectral unmixing using a hierarchical Bayesian model for hyperspectral imagery

This paper proposes a hierarchical Bayesian model that can be used for semi-supervised hyperspectral image unmixing. The model assumes that the pixel reflectances result from linear combinations of pure component spectra contaminated by an additive Gaussian noise. The abundance parameters appearing in this model satisfy positivity and additivity constraints. These constraints are naturally expressed in a Bayesian context by using appropriate abundance prior distributions. The posterior distributions of the unknown model parameters are then derived. A Gibbs sampler allows one to draw samples distributed according to the posteriors of interest and to estimate the unknown abundances. An extension of the algorithm is finally studied for mixtures with unknown numbers of spectral components belonging to a know library. The performance of the different unmixing strategies is evaluated via simulations conducted on synthetic and real data

Nonlinear unmixing of hyperspectral images: Models and algorithms

When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid, and other nonlinear models need to be considered, for instance, when there are multiscattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this article, we present an overview of recent advances in nonlinear unmixing modeling

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

Distributed Unmixing of Hyperspectral Data With Sparsity Constraint

Spectral unmixing (SU) is a data processing problem in hyperspectral remote sensing. The significant challenge in the SU problem is how to identify endmembers and their weights, accurately. For estimation of signature and fractional abundance matrices in a blind problem, nonnegative matrix factorization (NMF) and its developments are used widely in the SU problem. One of the constraints which was added to NMF is sparsity constraint that was regularized by L 1/2 norm. In this paper, a new algorithm based on distributed optimization has been used for spectral unmixing. In the proposed algorithm, a network including single-node clusters has been employed. Each pixel in hyperspectral images considered as a node in this network. The distributed unmixing with sparsity constraint has been optimized with diffusion LMS strategy, and then the update equations for fractional abundance and signature matrices are obtained. Simulation results based on defined performance metrics, illustrate advantage of the proposed algorithm in spectral unmixing of hyperspectral data compared with other methods. The results show that the AAD and SAD of the proposed approach are improved respectively about 6 and 27 percent toward distributed unmixing in SNR=25dB.Comment: 6 pages, conference pape

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