On Using Projection Onto Convex Sets for Solving the Hyperspectral Unmixing Problem

Heylen, Rob; Akhter, Muhammad Awais; Scheunders, Paul

doi:10.1109/lgrs.2013.2261276

Cited by 11 publications

(9 citation statements)

References 14 publications

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“…• D t is closed and convex as the (non-empty) intersection of two closed balls. The projection onto D t can be approximated by the Dykstra algorithm [22], [24]. Besides, the projection on a Frobenius ball is given by [28] P BF(X,r) (Y) = X + min 1,…”

Section: Discussionmentioning

confidence: 99%

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Online Unmixing of Multitemporal Hyperspectral Images Accounting for Spectral Variability

Thouvenin

Dobigeon

Tourneret

2016

IEEE Trans. on Image Process.

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Hyperspectral unmixing is aimed at identifying the reference spectral signatures composing an hyperspectral image and their relative abundance fractions in each pixel. In practice, the identified signatures may vary spectrally from an image to another due to varying acquisition conditions, thus inducing possibly significant estimation errors. Against this background, hyperspectral unmixing of several images acquired over the same area is of considerable interest. Indeed, such an analysis enables the endmembers of the scene to be tracked and the corresponding endmember variability to be characterized. Sequential endmember estimation from a set of hyperspectral images is expected to provide improved performance when compared to methods analyzing the images independently.However, the significant size of hyperspectral data precludes the use of batch procedures to jointly estimate the mixture parameters of a sequence of hyperspectral images. Provided that each elementary component is present in at least one image of the sequence, we propose to perform an online hyperspectral unmixing accounting for temporal endmember variability. The online hyperspectral unmixing is formulated as a two-stage stochastic program, which can be solved using a stochastic approximation. The performance of the proposed method is evaluated on synthetic and real data.A comparison with independent unmixing algorithms finally illustrates the interest of the proposed strategy. Index TermsHyperspectral imagery, perturbed linear unmixing (PLMM), endmember temporal variability, two-stage stochastic program, stochastic approximation (SA).

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Section: Discussionmentioning

confidence: 99%

“…Note that the projection P Dt can be efficiently approximated using the Dykstra algorithm (see [22]- [24]). The resulting algorithm is summarized in Algo.…”

Section: ) Abundance and Variability Estimationmentioning

confidence: 99%

Online Unmixing of Multitemporal Hyperspectral Images Accounting for Spectral Variability

Thouvenin

Dobigeon

Tourneret

2016

IEEE Trans. on Image Process.

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“…This projection is computed by the Dykstra algorithm [17,18]. Indeed, we can introduce an auxiliary variable Et and observe that Dt = BF(0, σ) ∩ {dMt : dMt + Et−1 F ≤ κ}…”

Section: Abundance and Variability Estimationmentioning

confidence: 99%

Unmixing multitemporal hyperspectral images with variability: An online algorithm

Thouvenin

Dobigeon

Tourneret

2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 16914The contribution was presented at ICASSP 2016 :http://www.icassp2016.org/ ABSTRACTHyperspectral unmixing consists in determining the reference spectral signatures composing a hyperspectral image and their relative abundance fractions in each pixel. In practice, the identified signatures may be affected by a significant spectral variability resulting for instance from the temporal evolution of the imaged scene. This phenomenon can be accounted for by using a perturbed linear mixing model. This paper studies an online estimation algorithm for the parameters of this extended linear mixing model. This algorithm is of interest for the practical applications where the size of the hyperspectral images precludes the use of batch procedures. The performance of the proposed method is evaluated on synthetic data.Index Terms-Multi-temporal hyperspectral image, linear unmixing, endmember variability, online estimation, two-stage stochastic program.

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“…In [31], the underlying constrained least-squares problem is solved using a primaldual interior-point method claimed to be amenable to parallel computing. In [32], Dykstra's algorithm for finding projections onto the intersection of convex sets is employed to estimate the abundances, which are required to satisfy the nonnegativity and sum-to-one constraints.…”

Section: Introductionmentioning

confidence: 99%

Spectral Unmixing With Perturbed Endmembers

Arablouei

2019

IEEE Trans. Geosci. Remote Sensing

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Abstract-We consider the problem of supervised spectral unmixing with a fully-perturbed linear mixture model where the given endmembers, as well as the observations of the spectral image, are subject to perturbation due to noise, error, mismatch, etc. We calculate the Fisher information matrix and the CramerRao lower bound associated with the estimation of the abundance matrix in the considered fully-perturbed linear spectral unmixing problem. We develop an algorithm for estimating the abundance matrix by minimizing a constrained and regularized maximumlog-likelihood objective function using the block coordinatedescend iterations and the alternating direction method of multipliers. We analyze the convergence of the proposed algorithm theoretically and perform simulations with real hyperspectral image datasets to evaluate its performance. The simulation results corroborate the efficacy of the proposed algorithm in mitigating the adverse effects of perturbation in the endmembers.

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On Using Projection Onto Convex Sets for Solving the Hyperspectral Unmixing Problem

Cited by 11 publications

References 14 publications

Online Unmixing of Multitemporal Hyperspectral Images Accounting for Spectral Variability

Online Unmixing of Multitemporal Hyperspectral Images Accounting for Spectral Variability

Unmixing multitemporal hyperspectral images with variability: An online algorithm

Spectral Unmixing With Perturbed Endmembers

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