Bayesian Nonparametric Unmixing of Hyperspectral Images

Hyperspectral imaging is an important tool in remote sensing, allowing for accurate analysis of vast areas. Due to a low spatial resolution, a pixel of a hyperspectral image rarely represents a single material, but rather a mixture of different spectra. HSU aims at estimating the pure spectra present in the scene of interest, referred to as endmembers, and their fractions in each pixel, referred to as abundances. Today, many HSU algorithms have been proposed, based either on a geometrical or statistical model. While most methods assume that the number of endmembers present in the scene is known, there is only little work about estimating this number from the observed data. In this work, we propose a Bayesian nonparametric framework that jointly estimates the number of endmembers, the endmembers itself, and their abundances, by making use of the Indian Buffet Process as a prior for the endmembers. Simulation results and experiments on real data demonstrate the effectiveness of the proposed algorithm, yielding results comparable with state-of-the-art methods while being able to reliably infer the number of endmembers. In scenarios with strong noise, where other algorithms provide only poor results, the proposed approach tends to overestimate the number of endmembers slightly. The additional endmembers, however, often simply represent noisy replicas of present endmembers and could easily be merged in a post-processing step

A convex formulation for hyperspectral image superresolution via subspace-based regularization

Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, respectively, is a data fusion problem that has been the focus of recent active research due to the increasing availability of HSIs and MSIs retrieved from the same geographical area. We formulate this problem as the minimization of a convex objective function containing two quadratic data-fitting terms and an edge-preserving regularizer. The data-fitting terms account for blur, different resolutions, and additive noise. The regularizer, a form of vector Total Variation, promotes piecewise-smooth solutions with discontinuities aligned across the hyperspectral bands. The downsampling operator accounting for the different spatial resolutions, the non-quadratic and non-smooth nature of the regularizer, and the very large size of the HSI to be estimated lead to a hard optimization problem. We deal with these difficulties by exploiting the fact that HSIs generally "live" in a low-dimensional subspace and by tailoring the Split Augmented Lagrangian Shrinkage Algorithm (SALSA), which is an instance of the Alternating Direction Method of Multipliers (ADMM), to this optimization problem, by means of a convenient variable splitting. The spatial blur and the spectral linear operators linked, respectively, with the HSI and MSI acquisition processes are also estimated, and we obtain an effective algorithm that outperforms the state-of-the-art, as illustrated in a series of experiments with simulated and real-life data.Comment: IEEE Trans. Geosci. Remote Sens., to be publishe

Application of spectral and spatial indices for specific class identification in Airborne Prism EXperiment (APEX) imaging spectrometer data for improved land cover classification

Hyperspectral remote sensing's ability to capture spectral information of targets in very narrow bandwidths gives rise to many intrinsic applications. However, the major limiting disadvantage to its applicability is its dimensionality, known as the Hughes Phenomenon. Traditional classification and image processing approaches fail to process data along many contiguous bands due to inadequate training samples. Another challenge of successful classification is to deal with the real world scenario of mixed pixels i.e. presence of more than one class within a single pixel. An attempt has been made to deal with the problems of dimensionality and mixed pixels, with an objective to improve the accuracy of class identification. In this paper, we discuss the application of indices to cope with the disadvantage of the dimensionality of the Airborne Prism EXperiment (APEX) hyperspectral Open Science Dataset (OSD) and to improve the classification accuracy using the Possibilistic c–Means (PCM) algorithm. This was used for the formulation of spectral and spatial indices to describe the information in the dataset in a lesser dimensionality. This reduced dimensionality is used for classification, attempting to improve the accuracy of determination of specific classes. Spectral indices are compiled from the spectral signatures of the target and spatial indices have been defined using texture analysis over defined neighbourhoods. The classification of 20 classes of varying spatial distributions was considered in order to evaluate the applicability of spectral and spatial indices in the extraction of specific class information. The classification of the dataset was performed in two stages; spectral and a combination of spectral and spatial indices individually as input for the PCM classifier. In addition to the reduction of entropy, while considering a spectral-spatial indices approach, an overall classification accuracy of 80.50% was achieved, against 65% (spectral indices only) and 59.50% (optimally determined principal component

Spectral mixture analysis of EELS spectrum-images

Recent advances in detectors and computer science have enabled the acquisition and the processing of multidimensional datasets, in particular in the field of spectral imaging. Benefiting from these new developments, earth scientists try to recover the reflectance spectra of macroscopic materials (e.g., water, grass, mineral types...) present in an observed scene and to estimate their respective proportions in each mixed pixel of the acquired image. This task is usually referred to as spectral mixture analysis or spectral unmixing (SU). SU aims at decomposing the measured pixel spectrum into a collection of constituent spectra, called endmembers, and a set of corresponding fractions (abundances) that indicate the proportion of each endmember present in the pixel. Similarly, when processing spectrum-images, microscopists usually try to map elemental, physical and chemical state information of a given material. This paper reports how a SU algorithm dedicated to remote sensing hyperspectral images can be successfully applied to analyze spectrum-image resulting from electron energy-loss spectroscopy (EELS). SU generally overcomes standard limitations inherent to other multivariate statistical analysis methods, such as principal component analysis (PCA) or independent component analysis (ICA), that have been previously used to analyze EELS maps. Indeed, ICA and PCA may perform poorly for linear spectral mixture analysis due to the strong dependence between the abundances of the different materials. One example is presented here to demonstrate the potential of this technique for EELS analysis.Comment: Manuscript accepted for publication in Ultramicroscop

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

Joint & Progressive Learning from High-Dimensional Data for Multi-Label Classification

Despite the fact that nonlinear subspace learning techniques (e.g. manifold learning) have successfully applied to data representation, there is still room for improvement in explainability (explicit mapping), generalization (out-of-samples), and cost-effectiveness (linearization). To this end, a novel linearized subspace learning technique is developed in a joint and progressive way, called \textbf{j}oint and \textbf{p}rogressive \textbf{l}earning str\textbf{a}teg\textbf{y} (J-Play), with its application to multi-label classification. The J-Play learns high-level and semantically meaningful feature representation from high-dimensional data by 1) jointly performing multiple subspace learning and classification to find a latent subspace where samples are expected to be better classified; 2) progressively learning multi-coupled projections to linearly approach the optimal mapping bridging the original space with the most discriminative subspace; 3) locally embedding manifold structure in each learnable latent subspace. Extensive experiments are performed to demonstrate the superiority and effectiveness of the proposed method in comparison with previous state-of-the-art methods.Comment: accepted in ECCV 201

Parsimonious Mahalanobis Kernel for the Classification of High Dimensional Data

The classification of high dimensional data with kernel methods is considered in this article. Exploit- ing the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its inversion is unstable or impossible. Using a parsimonious statistical model, namely the High Dimensional Discriminant Analysis model, the specific signal and noise subspaces are estimated for each considered class making the inverse of the class specific covariance matrix explicit and stable, leading to the definition of a parsimonious Mahalanobis kernel. A SVM based framework is used for selecting the hyperparameters of the parsimonious Mahalanobis kernel by optimizing the so-called radius-margin bound. Experimental results on three high dimensional data sets show that the proposed kernel is suitable for classifying high dimensional data, providing better classification accuracies than the conventional Gaussian kernel