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

Sketch-based subspace clustering of hyperspectral images

Sparse subspace clustering (SSC) techniques provide the state-of-the-art in clustering of hyperspectral images (HSIs). However, their computational complexity hinders their applicability to large-scale HSIs. In this paper, we propose a large-scale SSC-based method, which can effectively process large HSIs while also achieving improved clustering accuracy compared to the current SSC methods. We build our approach based on an emerging concept of sketched subspace clustering, which was to our knowledge not explored at all in hyperspectral imaging yet. Moreover, there are only scarce results on any large-scale SSC approaches for HSI. We show that a direct application of sketched SSC does not provide a satisfactory performance on HSIs but it does provide an excellent basis for an effective and elegant method that we build by extending this approach with a spatial prior and deriving the corresponding solver. In particular, a random matrix constructed by the Johnson-Lindenstrauss transform is first used to sketch the self-representation dictionary as a compact dictionary, which significantly reduces the number of sparse coefficients to be solved, thereby reducing the overall complexity. In order to alleviate the effect of noise and within-class spectral variations of HSIs, we employ a total variation constraint on the coefficient matrix, which accounts for the spatial dependencies among the neighbouring pixels. We derive an efficient solver for the resulting optimization problem, and we theoretically prove its convergence property under mild conditions. The experimental results on real HSIs show a notable improvement in comparison with the traditional SSC-based methods and the state-of-the-art methods for clustering of large-scale images

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Spectral Target Detection using Physics-Based Modeling and a Manifold Learning Technique

Identification of materials from calibrated radiance data collected by an airborne imaging spectrometer depends strongly on the atmospheric and illumination conditions at the time of collection. This thesis demonstrates a methodology for identifying material spectra using the assumption that each unique material class forms a lower-dimensional manifold (surface) in the higher-dimensional spectral radiance space and that all image spectra reside on, or near, these theoretic manifolds. Using a physical model, a manifold characteristic of the target material exposed to varying illumination and atmospheric conditions is formed. A graph-based model is then applied to the radiance data to capture the intricate structure of each material manifold, followed by the application of the commute time distance (CTD) transformation to separate the target manifold from the background. Detection algorithms are then applied in the CTD subspace. This nonlinear transformation is based on a random walk on a graph and is derived from an eigendecomposition of the pseudoinverse of the graph Laplacian matrix. This work provides a geometric interpretation of the CTD transformation, its algebraic properties, the atmospheric and illumination parameters varied in the physics-based model, and the influence the target manifold samples have on the orientation of the coordinate axes in the transformed space. This thesis concludes by demonstrating improved detection results in the CTD subspace as compared to detection in the original spectral radiance space

Hyperspectral Data Acquisition and Its Application for Face Recognition

Current face recognition systems are rife with serious challenges in uncontrolled conditions: e.g., unrestrained lighting, pose variations, accessories, etc. Hyperspectral imaging (HI) is typically employed to counter many of those challenges, by incorporating the spectral information within different bands. Although numerous methods based on hyperspectral imaging have been developed for face recognition with promising results, three fundamental challenges remain: 1) low signal to noise ratios and low intensity values in the bands of the hyperspectral image specifically near blue bands; 2) high dimensionality of hyperspectral data; and 3) inter-band misalignment (IBM) correlated with subject motion during data acquisition. This dissertation concentrates mainly on addressing the aforementioned challenges in HI. First, to address low quality of the bands of the hyperspectral image, we utilize a custom light source that has more radiant power at shorter wavelengths and properly adjust camera exposure times corresponding to lower transmittance of the filter and lower radiant power of our light source. Second, the high dimensionality of spectral data imposes limitations on numerical analysis. As such, there is an emerging demand for robust data compression techniques with lows of less relevant information to manage real spectral data. To cope with these challenging problems, we describe a reduced-order data modeling technique based on local proper orthogonal decomposition in order to compute low-dimensional models by projecting high-dimensional clusters onto subspaces spanned by local reduced-order bases. Third, we investigate 11 leading alignment approaches to address IBM correlated with subject motion during data acquisition. To overcome the limitations of the considered alignment approaches, we propose an accurate alignment approach ( A3) by incorporating the strengths of point correspondence and a low-rank model. In addition, we develop two qualitative prediction models to assess the alignment quality of hyperspectral images in determining improved alignment among the conducted alignment approaches. Finally, we show that the proposed alignment approach leads to promising improvement on face recognition performance of a probabilistic linear discriminant analysis approach

Hyperspectral Sensors as a Management Tool to Prevent the Invasion of the Exotic Cordgrass Spartina densiflora in the Doñana Wetlands

We test the use of hyperspectral sensors for the early detection of the invasive dense-flowered cordgrass (Spartina densiflora Brongn.) in the Guadalquivir River marshes, Southwestern Spain. We flew in tandem a CASI-1500 (368–1052 nm) and an AHS (430–13,000 nm) airborne sensors in an area with presence of S. densiflora. We simplified the processing of hyperspectral data (no atmospheric correction and no data-reduction techniques) to test if these treatments were necessary for accurate S. densiflora detection in the area. We tested several statistical signal detection algorithms implemented in ENVI software as spectral target detection techniques (matched filtering, constrained energy minimization, orthogonal subspace projection, target-constrained interference minimized filter, and adaptive coherence estimator) and compared them to the well-known spectral angle mapper, using spectra extracted from ground-truth locations in the images. The target S. densiflora was easy to detect in the marshes by all algorithms in images of both sensors. The best methods (adaptive coherence estimator and target-constrained interference minimized filter) on the best sensor (AHS) produced 100% discrimination (Kappa = 1, AUC = 1) at the study site and only some decline in performance when extrapolated to a new nearby area. AHS outperformed CASI in spite of having a coarser spatial resolution (4-m vs. 1-m) and lower spectral resolution in the visible and near-infrared range, but had a better signal to noise ratio. The larger spectral range of AHS in the short-wave and thermal infrared was of no particular advantage. Our conclusions are that it is possible to use hyperspectral sensors to map the early spread S. densiflora in the Guadalquivir River marshes. AHS is the most suitable airborne hyperspectral sensor for this task and the signal processing techniques target-constrained interference minimized filter (TCIMF) and adaptive coherence estimator (ACE) are the best performing target detection techniques that can be employed operationally with a simplified processing of hyperspectral images.This study has been funded by the Spanish Ministry of Science and Innovation through the research projects HYDRA (No. CGL2006-02247/BOS) and HYDRA2 (CGL2009-09801/BOS), by the National Parks Authority (Organismo Autonomo de Parques Nacionales) of the Spanish Ministry of Environment to project OAPN 042/2007, and by funding from the European Union (EU) Horizon 2020 research and innovation program under grant agreement No. 641762 to ECOPOTENTIAL project. The Espacio Natural de Doñana provided permits for field work in protected areas with restricted access. We are grateful to the Instituto Nacional de Técnica Aeroespacial (INTA), Spain, for performing the airborne campaign and the geometric correction of the images. J.B. has to acknowledge a sabbatical stay at Pye Laboratory of the Commonwealth Scientific and Research Organization (CSIRO) Marine and Atmospheric Sciences, Australia, and at the Climate Change Cluster (C3) of the University of Technology Sydney, Australia, funded by the Spanish Ministry of Education, during data analysis and writing of this paper. This publication is a contribution from CEIMAR and also a contribution from CEICAMBIO. We acknowledge support by the CSIC Open Access Publication Initiative through its Unit of Information Resources for Research (URICI