2,119 research outputs found

    Correntropy Maximization via ADMM - Application to Robust Hyperspectral Unmixing

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    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

    Quantum-inspired computational imaging

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    Computational imaging combines measurement and computational methods with the aim of forming images even when the measurement conditions are weak, few in number, or highly indirect. The recent surge in quantum-inspired imaging sensors, together with a new wave of algorithms allowing on-chip, scalable and robust data processing, has induced an increase of activity with notable results in the domain of low-light flux imaging and sensing. We provide an overview of the major challenges encountered in low-illumination (e.g., ultrafast) imaging and how these problems have recently been addressed for imaging applications in extreme conditions. These methods provide examples of the future imaging solutions to be developed, for which the best results are expected to arise from an efficient codesign of the sensors and data analysis tools.Y.A. acknowledges support from the UK Royal Academy of Engineering under the Research Fellowship Scheme (RF201617/16/31). S.McL. acknowledges financial support from the UK Engineering and Physical Sciences Research Council (grant EP/J015180/1). V.G. acknowledges support from the U.S. Defense Advanced Research Projects Agency (DARPA) InPho program through U.S. Army Research Office award W911NF-10-1-0404, the U.S. DARPA REVEAL program through contract HR0011-16-C-0030, and U.S. National Science Foundation through grants 1161413 and 1422034. A.H. acknowledges support from U.S. Army Research Office award W911NF-15-1-0479, U.S. Department of the Air Force grant FA8650-15-D-1845, and U.S. Department of Energy National Nuclear Security Administration grant DE-NA0002534. D.F. acknowledges financial support from the UK Engineering and Physical Sciences Research Council (grants EP/M006514/1 and EP/M01326X/1). (RF201617/16/31 - UK Royal Academy of Engineering; EP/J015180/1 - UK Engineering and Physical Sciences Research Council; EP/M006514/1 - UK Engineering and Physical Sciences Research Council; EP/M01326X/1 - UK Engineering and Physical Sciences Research Council; W911NF-10-1-0404 - U.S. Defense Advanced Research Projects Agency (DARPA) InPho program through U.S. Army Research Office; HR0011-16-C-0030 - U.S. DARPA REVEAL program; 1161413 - U.S. National Science Foundation; 1422034 - U.S. National Science Foundation; W911NF-15-1-0479 - U.S. Army Research Office; FA8650-15-D-1845 - U.S. Department of the Air Force; DE-NA0002534 - U.S. Department of Energy National Nuclear Security Administration)Accepted manuscrip

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

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    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

    Composition of Jupiter irregular satellites sheds light on their origin

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    Irregular satellites of Jupiter with their highly eccentric, inclined and distant orbits suggest that their capture took place just before the giant planet migration. We aim to improve our understanding of the surface composition of irregular satellites of Jupiter to gain insight into a narrow time window when our Solar System was forming. We observed three Jovian irregular satellites, Himalia, Elara, and Carme, using a medium-resolution 0.8-5.5 micro m spectrograph on the National Aeronautics and Space Administration (NASA) Infrared Telescope Facility (IRTF). Using a linear spectral unmixing model we have constrained the major mineral phases on the surface of these three bodies. Our results confirm that the surface of Himalia, Elara, and Carme are dominated by opaque materials such as those seen in carbonaceous chondrite meteorites. Our spectral modeling of NIR spectra of Himalia and Elara confirm that their surface composition is the same and magnetite is the dominant mineral. A comparison of the spectral shape of Himalia with the two large main C-type asteroids, Themis (D 176 km) and Europa (D 352 km), suggests surface composition similar to Europa. The NIR spectrum of Carme exhibits blue slope up to 1.5 microm and is spectrally distinct from those of Himalia and Elara. Our model suggests that it is compositionally similar to amorphous carbon. Himalia and Elara are compositionally similar but differ significantly from Carme. These results support the hypotheses that the Jupiter irregular satellites are captured bodies that were subject to further breakup events and clustered as families based on their similar physical and surface compositions

    Bayesian Nonparametric Unmixing of Hyperspectral Images

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    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

    Minimum mean square distance estimation of a subspace

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    We consider the problem of subspace estimation in a Bayesian setting. Since we are operating in the Grassmann manifold, the usual approach which consists of minimizing the mean square error (MSE) between the true subspace UU and its estimate U^\hat{U} may not be adequate as the MSE is not the natural metric in the Grassmann manifold. As an alternative, we propose to carry out subspace estimation by minimizing the mean square distance (MSD) between UU and its estimate, where the considered distance is a natural metric in the Grassmann manifold, viz. the distance between the projection matrices. We show that the resulting estimator is no longer the posterior mean of UU but entails computing the principal eigenvectors of the posterior mean of UUTU U^{T}. Derivation of the MMSD estimator is carried out in a few illustrative examples including a linear Gaussian model for the data and a Bingham or von Mises Fisher prior distribution for UU. In all scenarios, posterior distributions are derived and the MMSD estimator is obtained either analytically or implemented via a Markov chain Monte Carlo simulation method. The method is shown to provide accurate estimates even when the number of samples is lower than the dimension of UU. An application to hyperspectral imagery is finally investigated
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