Minimum-volume transforms for remotely sensed data

Craig, Maurice

doi:10.1109/36.297973

Cited by 444 publications

(349 citation statements)

References 8 publications

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“…Geometric approaches have been used whenever pure pixels are present in data [66]- [70]. In most cases, however, pure pixels can not be found in data.…”

Section: Discussionmentioning

confidence: 99%

Does Independent Component Analysis Play a~Role in Unmixing Hyperspectral Data?

Nascimento

Dias

2003

Pattern Recognition and Image Analysis

114

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Abstract-Independent component analysis (ICA) has recently been proposed as a tool to unmix hyperspectral data. ICA is founded on two assumptions: 1) the observed spectrum vector is a linear mixture of the constituent spectra (endmember spectra) weighted by the correspondent abundance fractions (sources); 2) sources are statistically independent. Independent factor analysis (IFA) extends ICA to linear mixtures of independent sources immersed in noise. Concerning hyperspectral data, the first assumption is valid whenever the multiple scattering among the distinct constituent substances (endmembers) is negligible, and the surface is partitioned according to the fractional abundances. The second assumption, however, is violated, since the sum of abundance fractions associated to each pixel is constant due to physical constraints in the data acquisition process. Thus, sources cannot be statistically independent, this compromising the performance of ICA/IFA algorithms in hyperspectral unmixing. This paper studies the impact of hyperspectral source statistical dependence on ICA and IFA performances. We conclude that the accuracy of these methods tends to improve with the increase of the signature variability, of the number of endmembers, and of the signal-to-noise ratio. In any case, there are always endmembers incorrectly unmixed. We arrive to this conclusion by minimizing the mutual information of simulated and real hyperspectral mixtures. The computation of mutual information is based on fitting mixtures of Gaussians to the observed data. A method to sort ICA and IFA estimates in terms of the likelihood of being correctly unmixed is proposed.Index Terms-Independent component analysis (ICA), independent factor analysis (IFA), mixture of Gaussians, unmixing hyperspectral data.

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“…Geometric approaches have been used whenever pure pixels are present in data [66]- [70]. In most cases, however, pure pixels can not be found in data.…”

Section: Discussionmentioning

confidence: 99%

Does Independent Component Analysis Play a~Role in Unmixing Hyperspectral Data?

Nascimento

Dias

2003

Pattern Recognition and Image Analysis

114

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“…Several approaches [14,15,16] exploited this geometric feature of hyperspectral mixtures. The minimum volume transform (MVT) algorithm [16] determines the simplex of a minimal volume that contains the data.…”

Section: Related Workmentioning

confidence: 99%

“…The minimum volume transform (MVT) algorithm [16] determines the simplex of a minimal volume that contains the data. The method presented in [17] is also of MVT type, but by introducing the notion of bundles, it takes into account the endmember variability that is usually present in hyperspectral mixtures.…”

Section: Related Workmentioning

confidence: 99%

Two Linear Unmixing Algorithms to Recognize Targets Using Supervised Classification and Orthogonal Rotation in Airborne Hyperspectral Images

Averbuch

Zheludev

2012

Remote Sensing

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The goal of the paper is to detect pixels that contain targets of known spectra. The target can be present in a sub-or above pixel. Pixels without targets are classified as background pixels. Each pixel is treated via the content of its neighborhood. A pixel whose spectrum is different from its neighborhood is classified as a "suspicious point". In each suspicious point there is a mix of target(s) and background. The main objective in a supervised detection (also called "target detection") is to search for a specific given spectral material (target) in hyperspectral imaging (HSI) where the spectral signature of the target is known a priori from laboratory measurements. In addition, the fractional abundance of the target is computed. To achieve this we present two linear unmixing algorithms that recognize targets with known (given) spectral signatures. The CLUN is based on automatic feature extraction from the target's spectrum. These features separate the target from the background. The ROTU algorithm is based on embedding the spectra space into a special space by random orthogonal transformation and on the statistical properties of the embedded result. Experimental results demonstrate that the targets' locations were extracted correctly and these algorithms are robust and efficient.

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“…. , R max ) have been for instance identified by one of the numerous endmember extraction algorithms such as N-FINDR [14], MVT [15] or ICE [16].…”

Section: Problem Formulationmentioning

confidence: 99%

Library-based linear unmixing for hyperspectral imagery via reversible jump MCMC sampling

Dobigeon

Tourneret²

2009

2009 IEEE Aerospace Conference

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Abstract-This paper studies a semi-supervised algorithm for linear hyperspectral unmixing. The proposed unmixing method assumes that the pure material spectra denoted as endmembers belong to a library that is a priori available. However, the number and the nature of endmembers appearing in the pixel are not known a priori, resulting in a model selection problem. This paper proposes to handle this model selection problem within a fully Bayesian framework. First, appropriate distributions are elected as prior distributions for the unknown parameters. Particularly, a distribution defined on a simplex is chosen as prior for an appropriate partial abundance vector to ensure the positivity and the sum-to-one constraints of the mixing coefficients. Due to the complexity of the posterior distribution, a reversible jump Markov chain Monte Carlo algorithm is proposed to estimate the number and the nature of the macroscopic materials, as well as their respective proportions in the pixel. The accuracy of the proposed method is illustrated by simulations on synthetic hyperspectral data.

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Minimum-volume transforms for remotely sensed data

Cited by 444 publications

References 8 publications

Does Independent Component Analysis Play a~Role in Unmixing Hyperspectral Data?

Does Independent Component Analysis Play a~Role in Unmixing Hyperspectral Data?

Two Linear Unmixing Algorithms to Recognize Targets Using Supervised Classification and Orthogonal Rotation in Airborne Hyperspectral Images

Library-based linear unmixing for hyperspectral imagery via reversible jump MCMC sampling

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