Fast Constrained Least Squares Spectral Unmixing Using Primal-Dual Interior-Point Optimization

Chouzenoux, Émilie; Legendre, Maxime; Moussaoui, Saïd; Idier, Jérôme

doi:10.1109/jstars.2013.2266732

Cited by 42 publications

(41 citation statements)

References 46 publications

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“…Such images are widely used in many application areas, such as medical imaging and remote sensing [69][70][71]. Several medical modalities provide color images, including cervicography, dermoscopy, and gastrointestinal endoscopy [72].…”

Section: Application To Multichannel Image Recovery In the Presence Omentioning

confidence: 99%

An Auxiliary Variable Method for Markov Chain Monte Carlo Algorithms in High Dimension

Marnissi

Chouzenoux

Benazza-Benyahia

et al. 2018

Entropy

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Abstract:In this paper, we are interested in Bayesian inverse problems where either the data fidelity term or the prior distribution is Gaussian or driven from a hierarchical Gaussian model. Generally, Markov chain Monte Carlo (MCMC) algorithms allow us to generate sets of samples that are employed to infer some relevant parameters of the underlying distributions. However, when the parameter space is high-dimensional, the performance of stochastic sampling algorithms is very sensitive to existing dependencies between parameters. In particular, this problem arises when one aims to sample from a high-dimensional Gaussian distribution whose covariance matrix does not present a simple structure. Another challenge is the design of Metropolis-Hastings proposals that make use of information about the local geometry of the target density in order to speed up the convergence and improve mixing properties in the parameter space, while not being too computationally expensive. These two contexts are mainly related to the presence of two heterogeneous sources of dependencies stemming either from the prior or the likelihood in the sense that the related covariance matrices cannot be diagonalized in the same basis. In this work, we address these two issues. Our contribution consists of adding auxiliary variables to the model in order to dissociate the two sources of dependencies. In the new augmented space, only one source of correlation remains directly related to the target parameters, the other sources of correlations being captured by the auxiliary variables. Experiments are conducted on two practical image restoration problems-namely the recovery of multichannel blurred images embedded in Gaussian noise and the recovery of signal corrupted by a mixed Gaussian noise. Experimental results indicate that adding the proposed auxiliary variables makes the sampling problem simpler since the new conditional distribution no longer contains highly heterogeneous correlations. Thus, the computational cost of each iteration of the Gibbs sampler is significantly reduced while ensuring good mixing properties.

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Section: Application To Multichannel Image Recovery In the Presence Omentioning

confidence: 99%

An Auxiliary Variable Method for Markov Chain Monte Carlo Algorithms in High Dimension

Marnissi

Chouzenoux

Benazza-Benyahia

et al. 2018

Entropy

Self Cite

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“…To do so, the algorithm systematically explores all possible combinations of spectral endmembers, which is the only way to provide the best fit from explicitly solving the whole system of linear equations (Sabol et al, 1992;Rodricks and Kirkland, 2004a, b). Equivalent results could be obtained by linear unmixing under constraints, which allows all combinations to be tested in one run (Heinz and Chang, 2001;Chouzenoux et al, 2014), as performed by Schmidt et al (2014). Perfect fit is never achieved however, because of instrument noise, non-linear effects and the non-exhaustive representativity of the few reference spectra used as spectral endmembers.…”

Section: Algorithmmentioning

confidence: 99%

Composition of the northern regions of Vesta analyzed by the Dawn mission

Combe

McCord

McFadden

et al. 2015

Icarus

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“…This is because the objects we classify are not pixels in the image but point sources of space debris which are independent of one another. The minimization is solved by an Interior Point Least Squares solver [34,35]. The proposed algorithm for all the stages is summarized as Algorithm 2.…”

Section: Stage 3: Multispectral Classification Of Point Sourcesmentioning

confidence: 99%

Joint 3D localization and classification of space debris using a multispectral rotating point spread function

et al. 2019

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We consider the problem of joint three-dimensional (3D) localization and material classification of unresolved space debris using a multispectral rotating point spread function (RPSF). The use of RPSF allows one to estimate the 3D locations of point sources from their rotated images acquired by a single 2D sensor array, since the amount of rotation of each source image about its x, y location depends on its axial distance z. Using multi-spectral images, with one RPSF per spectral band, we are able not only to localize the 3D positions of the space debris but also classify their material composition. We propose a three-stage method for achieving joint localization and classification. In Stage 1, we adopt an optimization scheme for localization in which the spectral signature of each material is assumed to be uniform, which significantly improves efficiency and yields better localization results than possible with a single spectral band. In Stage 2, we estimate the spectral signature and refine the localization result via an alternating approach. We process classification in the final stage. Both Poisson noise and Gaussian noise models are considered, and the implementation of each is discussed. Numerical tests using multispectral data from NASA show the efficiency of our three-stage approach and illustrate the improvement of point source localization and spectral classification from using multiple bands over a single band.

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Fast Constrained Least Squares Spectral Unmixing Using Primal-Dual Interior-Point Optimization

Cited by 42 publications

References 46 publications

An Auxiliary Variable Method for Markov Chain Monte Carlo Algorithms in High Dimension

An Auxiliary Variable Method for Markov Chain Monte Carlo Algorithms in High Dimension

Composition of the northern regions of Vesta analyzed by the Dawn mission

Joint 3D localization and classification of space debris using a multispectral rotating point spread function

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