Spectral unmixing of hyperspectral images consists of estimating pure material spectra with their corresponding proportions (or abundances). Nonlinear mixing models for spectral unmixing are of very recent interest within the signal and image processing community. This letter proposes a new nonlinear unmixing approach using the Fan bilinear-bilinear model and nonnegative matrix factorization method that takes into account physical constraints on spectra (positivity) and abundances (positivity and sum-to-one). The proposed method is tested using a projected-gradient algorithm on synthetic and real data. The performances of this method are compared to the linear approach and to the recent nonlinear approach.

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.

Spectral unmixing of hyperspectral remote sensing reflectance data is a challenging task, being the subject of many recent researches, and aims to retrieve both endmembers spectra and abundances. It turns out to be hardly feasible when the data are attenuated by additional mediums such as water column in the case of seabed estimation. In this case, a possible solution is to first correct the attenuation due to the water column and then proceed to the unmixing process. This paper presents a new approach, jointly estimating the attenuation, the endmembers spectra and the abundances with a triple non-negative matrix factorization (tri-NMF) method. The method has been tested on synthetic and real data and allow one to obtain accurate abundance maps of the seabed.

This paper studies a variational Bayesian unmixing algorithm for hyperspectral images based on the standard linear mixing model. Each pixel of the image is modeled as a linear combination of endmembers whose corresponding fractions or abundances are estimated by a Bayesian algorithm. This approach requires to define prior distributions for the parameters of interest and the related hyperparameters. After defining appropriate priors for the abundances (uniform priors on the interval (0,1)), the joint posterior distribution of the model parameters and hyperparameters is derived. The complexity of this distribution is handled by using variational methods that allow the joint distribution of the unknown parameters and hyperparameter to be approximated. Simulation results conducted on synthetic and real data show similar performances than those obtained with a previously published unmixing algorithm based on Markov chain Monte Carlo methods, with a significantly reduced computational cost.

This paper describes a new algorithm for hyperspectral image unmixing. Most unmixing algorithms proposed in the literature do not take into account the possible spatial correlations between the pixels. In this paper, 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 dependencies between 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. For this model, the posterior distributions of the unknown parameters and hyperparameters allow the parameters of interest to be inferred. 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, we consider a Markov chain Monte Carlo method that generates samples asymptotically distributed according to the posterior. The generated samples are then used for parameter and hyperparameter estimation. The accuracy of the proposed algorithms is illustrated on synthetic and real data.

In this paper, we address the problem of unmixing hyperspectral images in a semi-supervised framework using the normal compositional model recently introduced by Eismann and Stein. Each pixel of the image is modeled as a linear combination of random endmembers. More precisely, endmembers are modeled as Gaussian vectors whose means belong to a known spectral library. This paper proposes to estimate the number of endmembers involved in the mixture, as well as the mixture coefficients (referred to as abundances) using a trans-dimensional algorithm. Appropriate prior distributions are assigned to the abundance vector (to satisfy constraints inherent to hyperspectral imagery), the noise variance and the number of components involved in the mixture model. The computational complexity of the resulting posterior distribution is alleviated by constructing an hybrid Gibbs algorithm which generates samples distributed according to this posterior distribution. As the number of endmembers is unknown, the sampler has to jump between spaces of different dimensions. This is achieved by a reversible jump Markov chain Monte Carlo method that allows one to handle the model order selection problem. The performance of the proposed methodology is evaluated thanks to simulations conducted on synthetic data.

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.