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

Non-negative mixtures

This is the author's accepted pre-print of the article, first published as M. D. Plumbley, A. Cichocki and R. Bro. Non-negative mixtures. In P. Comon and C. Jutten (Ed), Handbook of Blind Source Separation: Independent Component Analysis and Applications. Chapter 13, pp. 515-547. Academic Press, Feb 2010. ISBN 978-0-12-374726-6 DOI: 10.1016/B978-0-12-374726-6.00018-7file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.26file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.2

Multimodal methods for blind source separation of audio sources

The enhancement of the performance of frequency domain convolutive blind source separation (FDCBSS) techniques when applied to the problem of separating audio sources recorded in a room environment is the focus of this thesis. This challenging application is termed the cocktail party problem and the ultimate aim would be to build a machine which matches the ability of a human being to solve this task. Human beings exploit both their eyes and their ears in solving this task and hence they adopt a multimodal approach, i.e. they exploit both audio and video modalities. New multimodal methods for blind source separation of audio sources are therefore proposed in this work as a step towards realizing such a machine. The geometry of the room environment is initially exploited to improve the separation performance of a FDCBSS algorithm. The positions of the human speakers are monitored by video cameras and this information is incorporated within the FDCBSS algorithm in the form of constraints added to the underlying cross-power spectral density matrix-based cost function which measures separation performance. [Continues.

A geometrically constrained multimodal time domain approach for convolutive blind source separation

A novel time domain constrained multimodal approach for convolutive blind source separation is presented which incorporates geometrical 3-D cordinates of both the speakers and the microphones. The semi-blind separation is performed in time domain and the constraints are incorporated through an alternative least squares optimization. Orthogonal source model and gradient based optimization concepts have been used to construct and estimate the model parameters which fits the convolutive mixture signals. Moreover, the majorization concept has been used to incorporate the geometrical information for estimating the mixing channels for different time lags. The separation results show a considerable improvement over time domain convolutive blind source separation systems. Having diagonal or quasi diagonal covariance matrices for different source segments and also having independent profiles for different sources (which implies nonstationarity of the sources) are the requirements for our method. We evaluated the method using synthetically mixed real signals. The results show high capability of the method for separating speech signals. © 2011 EURASIP

Non-Negative Blind Source Separation Algorithm Based on Minimum Aperture Simplicial Cone

International audienceWe address the problem of Blind Source Separation (BSS) when the hidden sources are Nonnegative (N-BSS). In this case, the scatter plot of the mixed data is contained within the simplicial cone generated by the columns of the mixing matrix. The proposed method, termed SCSA-UNS for Simplicial Cone Shrinking Algorithm for Unmixing Non-negative Sources, aims at estimating the mixing matrix and the sources by fitting a Minimum Aperture Simplicial Cone (MASC) to the cloud of mixed data points. SCSA-UNS is evaluated on both independent and correlated synthetic data and compared to other N-BSS methods. Simulations are also performed on real Liquid Chromatography-Mass Spectrum (LC-MS) data for the metabolomic analysis of a chemical sample, and on real dynamic Positron Emission Tomography (PET) images, in order to study the pharmacokinetics of the [18F]-FDG (FluoroDeoxyGlucose) tracer in the brain

Evaluation of emerging frequency domain convolutive blind source separation algorithms based on real room recordings

This paper presents a comparative study of three of the emerging frequency domain convolutive blind source separation (FDCBSS) techniques i.e. convolutive blind separation of non-stationary sources due to Parra and Spence, penalty function-based joint diagonalization approach for convolutive blind separation of nonstationary sources due to Wang et al. and a geometrically constrained multimodal approach for convolutive blind source separation due to Sanei et al. Objective evaluation is performed on the basis of signal to interference ratio (SIR), performance index (PI) and solution to the permutation problem. The results confirm that a multimodal approach is necessary to properly mitigate the permutation in BSS and ultimately to solve the cocktail party problem. In other words, it is to make BSS semiblind by exploiting prior geometrical information, and thereby providing the framework to find robust solutions for more challenging source separation with moving speakers

Self-Localization of Ad-Hoc Arrays Using Time Difference of Arrivals

This work was supported by the U.K. Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/K007491/1