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

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

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

Optimized kernel minimum noise fraction transformation for hyperspectral image classification

This paper presents an optimized kernel minimum noise fraction transformation (OKMNF) for feature extraction of hyperspectral imagery. The proposed approach is based on the kernel minimum noise fraction (KMNF) transformation, which is a nonlinear dimensionality reduction method. KMNF can map the original data into a higher dimensional feature space and provide a small number of quality features for classification and some other post processing. Noise estimation is an important component in KMNF. It is often estimated based on a strong relationship between adjacent pixels. However, hyperspectral images have limited spatial resolution and usually have a large number of mixed pixels, which make the spatial information less reliable for noise estimation. It is the main reason that KMNF generally shows unstable performance in feature extraction for classification. To overcome this problem, this paper exploits the use of a more accurate noise estimation method to improve KMNF. We propose two new noise estimation methods accurately. Moreover, we also propose a framework to improve noise estimation, where both spectral and spatial de-correlation are exploited. Experimental results, conducted using a variety of hyperspectral images, indicate that the proposed OKMNF is superior to some other related dimensionality reduction methods in most cases. Compared to the conventional KMNF, the proposed OKMNF benefits significant improvements in overall classification accuracy

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Dynamical spectral unmixing of multitemporal hyperspectral images

In this paper, we consider the problem of unmixing a time series of hyperspectral images. We propose a dynamical model based on linear mixing processes at each time instant. The spectral signatures and fractional abundances of the pure materials in the scene are seen as latent variables, and assumed to follow a general dynamical structure. Based on a simplified version of this model, we derive an efficient spectral unmixing algorithm to estimate the latent variables by performing alternating minimizations. The performance of the proposed approach is demonstrated on synthetic and real multitemporal hyperspectral images.Comment: 13 pages, 10 figure

Exploiting Structural Complexity for Robust and Rapid Hyperspectral Imaging

This paper presents several strategies for spectral de-noising of hyperspectral images and hypercube reconstruction from a limited number of tomographic measurements. In particular we show that the non-noisy spectral data, when stacked across the spectral dimension, exhibits low-rank. On the other hand, under the same representation, the spectral noise exhibits a banded structure. Motivated by this we show that the de-noised spectral data and the unknown spectral noise and the respective bands can be simultaneously estimated through the use of a low-rank and simultaneous sparse minimization operation without prior knowledge of the noisy bands. This result is novel for for hyperspectral imaging applications. In addition, we show that imaging for the Computed Tomography Imaging Systems (CTIS) can be improved under limited angle tomography by using low-rank penalization. For both of these cases we exploit the recent results in the theory of low-rank matrix completion using nuclear norm minimization