Non-Linear Spectral Unmixing by Geodesic Simplex Volume Maximization

Heylen, Rob; Burazerovic, Dzevdet; Scheunders, Paul

doi:10.1109/jstsp.2010.2088377

Cited by 103 publications

(82 citation statements)

References 29 publications

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“…First, vertex component analysis (VCA) [17] has been used as an endmember extraction algorithm to recover the spectral signatures of the pure components. For comparison, endmembers were also extracted from images using the nonlinear endmember extraction algorithm proposed in [18], denoted as Heylen's algorithm in what follows. Then, in an inversion step, the mixing coefficients have been estimated by algorithms dedicated to the LMM, FM, GBM and PNLMM, respectively.…”

Section: Synthetic Datamentioning

confidence: 99%

Robust nonnegative matrix factorization for nonlinear unmixing of hyperspectral images

Dobigeon

Févotte

2013

2013 5th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS)

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To cite this version:Nicolas Dobigeon, Cédric Févotte. ABSTRACT This paper introduces a robust linear model to describe hyperspectral data arising from the mixture of several pure spectral signatures. This new model not only generalizes the commonly used linear mixing model but also allows for possible nonlinear effects to be handled, relying on mild assumptions regarding these nonlinearities. Based on this model, a nonlinear unmixing procedure is proposed. The standard nonnegativity and sum-to-one constraints inherent to spectral unmixing are coupled with a group-sparse constraint imposed on the nonlinearity component. The resulting objective function is minimized using a multiplicative algorithm. Simulation results obtained on synthetic and real data show that the proposed strategy competes with state-of-the-art linear and nonlinear unmixing methods.

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Section: Synthetic Datamentioning

confidence: 99%

Robust nonnegative matrix factorization for nonlinear unmixing of hyperspectral images

Dobigeon

Févotte

2013

2013 5th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS)

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“…A number of remote sensing studies have estimated FVC in multispectral or hyperspectral images using a Linear Spectral Unmixing (LSU) approach with two or more endmembers [2][3][4][5][7][8][9][10][11][12]. Non-linear unmixing approaches also exist (e.g., [13][14][15]), but the linear approach is used most often due to its simplicity, rationality, and feasibility in practical applications [16]. The number of spectral bands in an image limits the number of endmembers that can be used for unmixing [17], so for images with relatively few spectral bands, a common approach is to assume that FVC can be estimated by the linear combination of two endmembers: bare soil and 100% green vegetation cover [3,6,7,12,18].…”

Section: Introductionmentioning

confidence: 99%

Remote Sensing of Fractional Green Vegetation Cover Using Spatially-Interpolated Endmembers

2012

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Abstract:Fractional green vegetation cover (FVC) is a useful parameter for many environmental and climate-related applications. A common approach for estimating FVC involves the linear unmixing of two spectral endmembers in a remote sensing image; bare soil and green vegetation. The spectral properties of these two endmembers are typically determined based on field measurements, estimated using additional data sources (e.g., soil databases or land cover maps), or extracted directly from the imagery. Most FVC estimation approaches do not consider that the spectral properties of endmembers may vary across space. However, due to local differences in climate, soil type, vegetation species, etc., the spectral characteristics of soil and green vegetation may exhibit positive spatial autocorrelation. When this is the case, it may be useful to take these local variations into account for estimating FVC. In this study, spatial interpolation (Inverse Distance Weighting and Ordinary Kriging) was used to predict variations in the spectral characteristics of bare soil and green vegetation across space. When the spatially-interpolated values were used in place of scene-invariant endmember values to estimate FVC in an Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) image, the accuracy of FVC estimates increased, providing evidence that it may be useful to consider the effects of spatial autocorrelation for spectral mixture analysis.

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“…A significant amount of research has been developed in unmixing methods [1,2] and, among them, sparse regression-based unmixing (SRU) approaches have received much attention in recent years [3][4][5][6]. SRU takes the benefit of the availability of a large library (or dictionary) of candidate endmembers, and then recovers those contributing to the observed mixed spectra.…”

Section: Introductionmentioning

confidence: 99%

Performance guarantees for sparse regression-based unmixing

Itoh

Duarte

Parente

2015

2015 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS)

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Sparse regression-based unmixing has received much attention in recent years; however, its theoretical performance has not been explored in the literature. In this work, we present theoretical guarantees for the performance of a sparse regression based unmixing (in short, sparse unmixing) implemented in the form of a Lasso optimization with non-negativity constraints. We provide a sufficient condition required for the exact recovery of the endmembers and validate it both theoretically and through experiments. In cases in which the condition is not verified, we explore the performance of sparse unmixing in relation to the exact recovery coefficient (ERC).

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Non-Linear Spectral Unmixing by Geodesic Simplex Volume Maximization

Cited by 103 publications

References 29 publications

Robust nonnegative matrix factorization for nonlinear unmixing of hyperspectral images

Robust nonnegative matrix factorization for nonlinear unmixing of hyperspectral images

Remote Sensing of Fractional Green Vegetation Cover Using Spatially-Interpolated Endmembers

Performance guarantees for sparse regression-based unmixing

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