Linear–Quadratic Mixing Model for Reflectances in Urban Environments

Meganem, Inès; Déliot, Philippe; Briottet, Xavier; Deville, Yannick; Hosseini, Shahram

doi:10.1109/tgrs.2013.2242475

Cited by 110 publications

(76 citation statements)

References 24 publications

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“…Moreover, it generalizes the GBM model [7,24] by accounting for self-interaction between the endmembers, and also generalizes the PPNMM [6] by considering different weights for the bilinear terms. Overall, model (1) is of a similar polynomial form as the bilinear models (GBM [7], PPNMM [6], Nascimento [8], Fan [9], and Meganem [10] models) with the main difference due to the introduction of higher order interaction terms, and the non-negativity and sum-to-one constraints associated with each model. In contrast with the model described in [25], which accounts for all the interactions by using only one parameter, the model (1) includes a different coefficient for each interaction term, which enables analysis of the interaction between any specific physical components (i.e., availability of interaction maps).…”

Section: Nonlinear Mixture Modelmentioning

confidence: 99%

“…Nonlinear mixture models are an alternative to better account for those effects [3,4]. We distinguish between signal processing based models and physical based models, which include the intimate mixture models [5] and those accounting for bilinear interactions [6][7][8][9][10]. This paper considers a physical based nonlinearity that generalizes the bilinear formulation in [11,12] to account for multiple scattering effects.…”

Section: Introductionmentioning

confidence: 99%

“…A clear motivation for this new formulation is the simplification it introduces in the unmixing problem thanks to the linear expression for both the LMM term and the residual term. Note finally that the resulting formulation is general, and covers many NL models [6][7][8][9][10]15].…”

Section: Introductionmentioning

confidence: 99%

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Fast hyperspectral unmixing in presence of sparse multiple scattering nonlinearities

Halimi

Bioucas-Dias

Dobigeon

et al. 2017

2017 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 : 18923The contribution was presented at ICASSP 2017 : http://www.ieee-icassp2017.org/ ABSTRACT This paper presents a novel nonlinear hyperspectral mixture model and its associated supervised unmixing algorithm. The model assumes a linear mixing model corrupted by an additive term which accounts for multiple scattering nonlinearities (NL). The proposed model generalizes bilinear models by taking into account higher order interaction terms. The inference of the abundances and nonlinearity coefficients of this model is formulated as a convex optimization problem suitable for fast estimation algorithms. This formulation accounts for constraints such as the sum-to-one and nonnegativity of the abundances, the non-negativity of the nonlinearity coefficients, and the spatial sparseness of the residuals. The resulting convex problem is solved using the alternating direction method of multipliers (ADMM) whose convergence is ensured theoretically. The proposed mixture model and its unmixing algorithm are validated on both synthetic and real images showing competitive results regarding the quality of the inference and the computational complexity when compared to the state-of-the-art algorithms.

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Section: Nonlinear Mixture Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fast hyperspectral unmixing in presence of sparse multiple scattering nonlinearities

Halimi

Bioucas-Dias

Dobigeon

et al. 2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…To relax the dependency on physical parameters, analytical formulations based on bilinear models have been successfully applied to represent the multiple scattering phenomenon which is the interactions of light with several materials. Efficient associated techniques can be found in [15]- [18].…”

Section: A Hyperspectral Unmixing 1) Overviewmentioning

confidence: 99%

Joint Anomaly Detection and Spectral Unmixing for Planetary Hyperspectral Images

Nakhostin

Clénet

Corpetti

et al. 2016

IEEE Trans. Geosci. Remote Sensing

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Abstract-Hyperspectral images are commonly used in the context of planetary exploration, especially for the analysis of the composition of planets. As several instruments have been sent throughout the Solar System, a huge quantity of data is getting available for the research community. Among classical problems in the analysis of hyperspectral images, a crucial one is unsupervised non-linear spectral unmixing, which aims at estimating the spectral signatures of elementary materials and determining their relative contribution at a sub-pixel level. While the unmixing problem is well studied for earth observation, some of the traditional problems encountered with earth images are somehow magnified in planetary exploration. Among them, large image sizes, strong non-linearities in the mixing (often different from those found in the earth images) and presence of anomalies are usually impairing the unmixing algorithms. This paper presents a new method that scales favorably with the problem posed by this analysis. It performs an unsupervised unmixing jointly with anomaly detection capacities, and has a global linear complexity. Non linearities are handled by decomposing the hyperspectral data on an overcomplete set of spectra, combined with a specific sparse projection, which guarantees the interpretability of the analysis. A theoretical study is proposed on synthetic datasets, and results are presented over the challenging 4-Vesta asteroid dataset.

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“…This class of models includes the bilinear models [8], the quadratic-linear model [9], the post-nonlinear model [10] and the bilinear-bilinear model [11]. However, to the authors' knowledge, the accuracy and the ability of these models to properly describe real mixtures have never been carefully investigated.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear unmixing of vegetated areas: A model comparison based on simulated and real hyperspectral data

Dobigeon¹,

Tits

Somers

et al. 2014

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

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When analyzing remote sensing hyperspectral images, numerous works dealing with spectral unmixing assume the pixels result from linear combinations of the endmember signatures. However, this assumption cannot be fulfilled, in particular when considering images acquired over vegetated areas. As a consequence, several nonlinear mixing models have been recently derived to take various nonlinear effects into account when unmixing hyperspectral data. Unfortunately, these models have been empirically proposed and without thorough validation. This paper attempts to fill this gap by taking advantage of two sets of real and physical-based simulated data. The accuracy of various linear and nonlinear models and the corresponding unmixing algorithms is evaluated with respect to their ability of fitting the sensed pixels and of providing accurate estimates of the abundances.

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Linear–Quadratic Mixing Model for Reflectances in Urban Environments

Cited by 110 publications

References 24 publications

Fast hyperspectral unmixing in presence of sparse multiple scattering nonlinearities

Fast hyperspectral unmixing in presence of sparse multiple scattering nonlinearities

Joint Anomaly Detection and Spectral Unmixing for Planetary Hyperspectral Images

Nonlinear unmixing of vegetated areas: A model comparison based on simulated and real hyperspectral data

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