Minimum Volume Simplex Analysis: A Fast Algorithm to Unmix Hyperspectral Data

Li, Jun; Bioucas-Dias, José M.

doi:10.1109/igarss.2008.4779330

Cited by 334 publications

(250 citation statements)

References 14 publications

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“…• Use the preconditioning to enhance other blind hyperspectral unmixing algorithms; for example algorithms which do not require the pure-pixel assumption to hold, e.g., [17,7,4].…”

Section: Conclusion and Further Researchmentioning

confidence: 99%

Enhancing pure-pixel identification performance via preconditioning

Gillis

2014

2014 6th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS)

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In this paper, we analyze different preconditionings designed to enhance robustness of pure-pixel search algorithms, which are used for blind hyperspectral unmixing and which are equivalent to near-separable nonnegative matrix factorization algorithms. Our analysis focuses on the successive projection algorithm (SPA), a simple, efficient and provably robust algorithm in the pure-pixel algorithm class. Recently, a provably robust preconditioning was proposed by Gillis and Vavasis (arXiv:1310.2273) which requires the resolution of a semidefinite program (SDP) to find a data points-enclosing minimum volume ellipsoid. Since solving the SDP in high precisions can be time consuming, we generalize the robustness analysis to approximate solutions of the SDP, that is, solutions whose objective function values are some multiplicative factors away from the optimal value. It is shown that a high accuracy solution is not crucial for robustness, which paves the way for faster preconditionings (e.g., based on first-order optimization methods). This first contribution also allows us to provide a robustness analysis for two other preconditionings. The first one is pre-whitening, which can be interpreted as an optimal solution of the same SDP with additional constraints. We analyze robustness of pre-whitening which allows us to characterize situations in which it performs competitively with the SDP-based preconditioning. The second one is based on SPA itself and can be interpreted as an optimal solution of a relaxation of the SDP. It is extremely fast while competing with the SDP-based preconditioning on several synthetic data sets.

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“…• Use the preconditioning to enhance other blind hyperspectral unmixing algorithms; for example algorithms which do not require the pure-pixel assumption to hold, e.g., [17,7,4].…”

Section: Conclusion and Further Researchmentioning

confidence: 99%

Enhancing pure-pixel identification performance via preconditioning

Gillis

2014

2014 6th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS)

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“…An image of P = 625 synthetic pixels has been generated from the mixture of R = 6 endmembers, with s 2 = 10 −4 (SNR ≈ 30dB). The MVSA algorithm [3] has been used to estimate the endmember spectra. Finally, the material abundances have been estimated using the proposed variational algorithm and the MCMC strategy of [6].…”

Section: Synthetic Datamentioning

confidence: 99%

“…In practical applications, they can be obtained by an endmember extraction procedure such as the well-known N-FINDR algorithm developed by Winter [2] or the minimum volume simplex analysis (MVSA) algorithm presented in [3]. Once the endmembers have been determined, the abundances have to be estimated in the so-called inversion step.…”

Section: Introductionmentioning

confidence: 99%

Variational methods for spectral unmixing of hyperspectral images

Eches¹,

Dobigeon²,

Tourneret³

et al. 2011

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper studies a variational Bayesian unmixing algorithm for hyperspectral images based on the standard linear mixing model. Each pixel of the image is modeled as a linear combination of endmembers whose corresponding fractions or abundances are estimated by a Bayesian algorithm. This approach requires to define prior distributions for the parameters of interest and the related hyperparameters. After defining appropriate priors for the abundances (uniform priors on the interval (0, 1)), the joint posterior distribution of the model parameters and hyperparameters is derived. The complexity of this distribution is handled by using variational methods that allow the joint distribution of the unknown parameters and hyperparameter to be approximated. Simulation results conducted on synthetic and real data show similar performances than those obtained with a previously published unmixing algorithm based on Markov chain Monte Carlo methods, with a significantly reduced computational cost.Index Terms-Bayesian inference, variational methods, spectral unmixing, hyperspectral images.

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“…Geometry based methods usually require that pixel observations of hyperspectral data are within a simplex and their vertices correspond to the endmember [10]. This class of methods includes N-FINDR [11], vertex component analysis [12], minimum-volume simplex analysis [13], simplex growing algorithm [14], etc. In general, these methods require the estimation of the number of the endmembers or the presence of pure pixels.…”

Section: Introductionmentioning

confidence: 99%

Double Reweighted Sparse Regression and Graph Regularization for Hyperspectral Unmixing

et al. 2018

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Hyperspectral unmixing, aiming to estimate the fractional abundances of pure spectral signatures in each mixed pixel, has attracted considerable attention in analyzing hyperspectral images. Plenty of sparse unmixing methods have been proposed in the literature that achieved promising performance. However, many of these methods overlook the latent geometrical structure of the hyperspectral data which limit their performance to some extent. To address this issue, a double reweighted sparse and graph regularized unmixing method is proposed in this paper. Specifically, a graph regularizer is employed to capture the correlation information between abundance vectors, which makes use of the property that similar pixels in a spectral neighborhood have higher probability to share similar abundances. In this way, the latent geometrical structure of the hyperspectral data can be transferred to the abundance space. In addition, a double weighted sparse regularizer is used to enhance the sparsity of endmembers and the fractional abundance maps, where one weight is introduced to promote the sparsity of endmembers as a hyperspectral image typically contains fewer endmembers compared to the overcomplete spectral library and the other weight is exploited to improve the sparsity of the abundance matrix. The weights of the double weighted sparse regularizer used for the next iteration are adaptively computed from the current abundance matrix. The experimental results on synthetic and real hyperspectral data demonstrate the superiority of our method compared with some state-of-the-art approaches.

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Minimum Volume Simplex Analysis: A Fast Algorithm to Unmix Hyperspectral Data

Cited by 334 publications

References 14 publications

Enhancing pure-pixel identification performance via preconditioning

Enhancing pure-pixel identification performance via preconditioning

Variational methods for spectral unmixing of hyperspectral images

Double Reweighted Sparse Regression and Graph Regularization for Hyperspectral Unmixing

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