Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

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 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.

/pdf/hyperspectral-unmixing-overview-geometrical-statistical-and-2lb11fr9l4.pdf

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

IEEE Transactions on Pattern Analysis and Machine Intelligence

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.

Hyperspectral remote sensing technology has advanced significantly in the past two decades. Current sensors onboard airborne and spaceborne platforms cover large areas of the Earth surface with unprecedented spectral, spatial, and temporal resolutions. These characteristics enable a myriad of applications requiring fine identification of materials or estimation of physical parameters. Very often, these applications rely on sophisticated and complex data analysis methods. The sources of difficulties are, namely, the high dimensionality and size of the hyperspectral data, the spectral mixing (linear and nonlinear), and the degradation mechanisms associated to the measurement process such as noise and atmospheric effects. This paper presents a tutorial/overview cross section of some relevant hyperspectral data analysis methods and algorithms, organized in six main topics: data fusion, unmixing, classification, target detection, physical parameter retrieval, and fast computing. In all topics, we describe the state-of-the-art, provide illustrative examples, and point to future challenges and research directions.

/pdf/hyperspectral-remote-sensing-data-analysis-and-future-1cxk3zgg98.pdf

Hyperspectral Remote Sensing Data Analysis and Future Challenges

Nonlinear models have recently shown interesting properties for spectral unmixing. This paper studies a generalized bilinear model and a hierarchical Bayesian algorithm for unmixing hyperspectral images. The proposed model is a generalization not only of the accepted linear mixing model but also of a bilinear model that has been recently introduced in the literature. Appropriate priors are chosen for its parameters to satisfy the positivity and sum-to-one constraints for the abundances. The joint posterior distribution of the unknown parameter vector is then derived. Unfortunately, this posterior is too complex to obtain analytical expressions of the standard Bayesian estimators. As a consequence, a Metropolis-within-Gibbs algorithm is proposed, which allows samples distributed according to this posterior to be generated and to estimate the unknown model parameters. The performance of the resulting unmixing strategy is evaluated via simulations conducted on synthetic and real data.

/pdf/nonlinear-unmixing-of-hyperspectral-images-using-a-12b3zqb9r9.pdf

Nonlinear Unmixing of Hyperspectral Images Using a Generalized Bilinear Model

Depth and intensity profiling of targets at a range of up to 10 km is demonstrated using time-of-flight time-correlated single-photon counting technique. The system comprised a pulsed laser source at 1550 nm wavelength, a monostatic scanning transceiver and a single-element InGaAs/InP single-photon avalanche diode (SPAD) detector. High-resolution three-dimensional images of various targets acquired over ranges between 800 metres and 10.5 km demonstrate long-range depth and intensity profiling, feature extraction and the potential for target recognition. Using a total variation restoration optimization algorithm, the acquisition time necessary for each pixel could be reduced by at least a factor of ten compared to a pixel-wise image processing approach. Kilometer range depth profiles are reconstructed with average signal returns of less than one photon per pixel.

Single-photon three-dimensional imaging at up to 10 kilometers range.

This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model. The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data.

/pdf/supervised-nonlinear-spectral-unmixing-using-a-postnonlinear-2d73wwigqm.pdf

Supervised Nonlinear Spectral Unmixing Using a Postnonlinear Mixing Model for Hyperspectral Imagery

This paper studies a generalized bilinear model and a hierarchical Bayesian algorithm for unmixing hyperspectral images. The proposed model is a generalization of the accepted linear mixing model but also of a bilinear model recently introduced in the literature. Appropriate priors are chosen for its parameters in particular to satisfy the positivity and sum-to-one constraints for the abundances. The joint posterior distribution of the unknown parameter vector is then derived. A Metropolis-within-Gibbs algorithm is proposed which allows samples distributed according to the posterior of interest to be generated and to estimate the unknown model parameters. The performance of the resulting unmixing strategy is evaluated via simulations conducted on synthetic and real data.

/pdf/nonlinear-unmixing-of-hyperspectral-images-using-a-3959qubkho.pdf

Nonlinear unmixing of hyperspectral images using a generalized bilinear model

We investigate the depth imaging of objects through various densities of different obscurants (water fog, glycol-based vapor, and incendiary smoke) using a time-correlated single-photon detection system which had an operating wavelength of 1550 nm and an average optical output power of approximately 1.5 mW. It consisted of a monostatic scanning transceiver unit used in conjunction with a picosecond laser source and an individual Peltier-cooled InGaAs/InP single-photon avalanche diode (SPAD) detector. We acquired depth and intensity data of targets imaged through distances of up to 24 meters for the different obscurants. We compare several statistical algorithms which reconstruct both the depth and intensity images for short data acquisition times, including very low signal returns in the photon-starved regime.

/pdf/three-dimensional-single-photon-imaging-through-obscurants-20odeqoh95.pdf

Abderrahim Halimi

Papers

Nonlinear Unmixing of Hyperspectral Images Using a Generalized Bilinear Model

Single-photon three-dimensional imaging at up to 10 kilometers range.

Supervised Nonlinear Spectral Unmixing Using a Postnonlinear Mixing Model for Hyperspectral Imagery

Nonlinear unmixing of hyperspectral images using a generalized bilinear model

Three-dimensional single-photon imaging through obscurants