Kernel fully constrained least squares abundance estimates

Broadwater, Joshua; Chellappa, Rama; Banerjee, Amit; Burlina, Philippe

doi:10.1109/igarss.2007.4423736

Cited by 87 publications

(70 citation statements)

References 11 publications

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“…The abundance estimatesâ for the model can be computed through constrained least squares regression. Alternatively, the linear model can also be posed as a special case of the kernel-based mixing model derived previously by Broadwater et al, 35 where the abundances of mixture components are estimated through the process E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 1 1 6 ; 1 5 1â ¼ argmin a 1 2 ½Kðx; xÞ − 2â t KðE; xÞ þâ t KðE; EÞâ…”

Section: Fully Constrained Least Squares and Linear Kernel-based Miximentioning

confidence: 99%

“…This was overcome by the development of a kernel fully constrained least squares (KFCLS) method that computes kernel-based abundance estimates to meet the physical (nonnegativity and sum-to-one) abundance constraints. 35 Further investigation of the KFCLS method has resulted in (1) the development of a generalized kernel for linear and intimate (nonlinear) mixtures 37 and (2) an adaptive kernel-based technique for mapping linear and intimate nonlinear mixtures. 38 The generalized kernel and adaptive techniques provide a way to adaptively estimate a mixture model suitable to the degree of nonlinearity that may be occurring at each pixel in a scene.…”

Section: Introductionmentioning

confidence: 99%

“…[32][33][34][35][36][37][38][39] Kernel functions provide a way to generalize linear algorithms to nonlinear data. 32,33 In the cases of detection and classification applications, they can induce high-dimensional feature spaces.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modeling linear and intimate mixtures of materials in hyperspectral imagery with single-scattering albedo and kernel approaches

Rand

Resmini

Allen

2017

J. Appl. Remote Sens

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Section: Fully Constrained Least Squares and Linear Kernel-based Miximentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modeling linear and intimate mixtures of materials in hyperspectral imagery with single-scattering albedo and kernel approaches

Rand

Resmini

Allen

2017

J. Appl. Remote Sens

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“…• The Kernel Fully Constrained Least Square method (KFCLS) (Broadwater et al 2007): This semi-supervised nonlinear algorithm is the kernel-based counterpart of FCLS, obtained by replacing all the inner products in FCLS by kernel functions. In the experiments, as for our pre-image algorithm, we used the Gaussian kernel with kernel bandwidth σ = 4.…”

Section: Experiments On Synthetic Images With Uniformly-distributed Amentioning

confidence: 99%

Supervised Nonlinear Unmixing of Hyperspectral Images Using a Pre-image Methods

Nguyen

Chen

Richard

et al. 2013

EAS Publications Series

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Abstract. Spectral unmixing is an important issue to analyze remotely sensed hyperspectral data. This involves the decomposition of each mixed pixel into its pure endmember spectra, and the estimation of the abundance value for each endmember. Although linear mixture models are often considered because of their simplicity, there are many situations in which they can be advantageously replaced by nonlinear mixture models. In this chapter, we derive a supervised kernel-based unmixing method that relies on a pre-image problem-solving technique. The kernel selection problem is also briefly considered. We show that partially-linear kernels can serve as an appropriate solution, and the nonlinear part of the kernel can be advantageously designed with manifold-learning-based techniques. Finally, we incorporate spatial information into our method in order to improve unmixing performance.

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“…The quality of training data for neural networks is responsible for their performance to a great extent. Nonlinear algorithms derived from linear ones have also been used for develop kernel-based nonlinear models [18][19][20] . In this case kernels have been applied to the spectral profile of each end-member, independent of radiation interactions between objects, consequently working as nonlinear distortion functions.…”

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confidence: 99%

Development of Higher-Order Model for Nonlinear Interactions in Hyperspectral Data of Mangrove Forests

Chakravortty¹,

Sinha²

2016

Current Science

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The present article analyses the accuracy of application of higher-order nonlinear interaction models on hyperspectral data to identify mangrove mixtures present in the Sunderbans Delta -a World Heritage Site in West Bengal, India. It is observed that intra-species interaction between similar mangrove species (interaction between the same type of end-members) in a homogeneous mangrove stand is more accurately modelled by the linear-quadratic model and hence results in more accurate fractional abundance estimations after unmixing when compared with linear-unmixing models. Specifically, we observe that quadratic models provide more accurate estimates than linear and bilinear models for the study area (Henry Island of Sunderbans), which is mostly dominated by pure and mixed mangrove species of Avicennia marina, Excoecaria agallocha, Avicennia alba, Phoenix paludosa, Avicennia officinalis, Ceriops decandra, Bruguiera cylindrica and Aegialitis. In this study, the quadratic nonlinear model successfully characterizes the interaction of endmember mixtures comprising E. agallocha, A. officinalis, B. cylindrica and A. alba in the study area.Keywords: Higher-order interaction models, hyperspectral data, mangrove species, nonlinear interactions.HYPERSPECTRAL remote sensing (HSRS) is a powerful tool for detailed spatio-temporal mapping and sustainable management of large forested lands. The wide spectral range of hyperspectral data and their high spectral resolution allows for accurate detection and classification of surface canopies and ground features through the application of hyperspectral image processing algorithms 1,2 . For example, the characteristic bio-optical properties of different mangrove species in a dense mangrove forest can be integrated into spectral libraries for improved discrimination and mapping of mangrove eco-types.Outside India, researchers have made a detailed study of mangroves at species level using hyperspectral data 3-5 . Studies in India have also established the capability of hyperspectral data for species-level discrimination of mangroves in distantly located islands of the Sunderban Delta. The Delta is well-known for its homogeneous and heterogeneous patches of mangrove species that include a particular form or various forms of mangrove species within the ecosystem. Application of remote sensing technologies for accurate identification and discrimination of mangrove species is being considerably encouraged in recent times. Homogeneous mangrove areas could be identified through linear spectral unmixing, which follows the principle of singular reflection with negligible multiple scattering 6 . However, in natural forests such as the Sunderban Biosphere Reserve, intra-and inter-species scattering occurs, thus making the reflections nonlinear in nature 7 . Nonlinear spectral unmixing is expected to provide a more accurate estimate of fractional abundance estimation of mangrove mixtures along with their identification.Nonlinear models have been developed at microscopic scale for materials which a...

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Kernel fully constrained least squares abundance estimates

Cited by 87 publications

References 11 publications

Modeling linear and intimate mixtures of materials in hyperspectral imagery with single-scattering albedo and kernel approaches

Modeling linear and intimate mixtures of materials in hyperspectral imagery with single-scattering albedo and kernel approaches

Supervised Nonlinear Unmixing of Hyperspectral Images Using a Pre-image Methods

Development of Higher-Order Model for Nonlinear Interactions in Hyperspectral Data of Mangrove Forests

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