#### DMCA

## Estimating abundance fractions of materials in hyperspectral images by fitting a post-nonlinear mixing model (2013)

Venue: | in Proc. IEEE WHISPERS |

Citations: | 5 - 3 self |

### Citations

963 | Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends
- Boyd, Parikh, et al.
- 2011
(Show Context)
Citation Context ...tive parameter and ν ∈ RR is the dual variable associated to the constraint u = α. For simplicity, the function Joa can also be written in an equivalent scaled form Ja with d the scaled dual variable =-=[9]-=- Ja(ψ,α,u, e,d) = J(ψ,α,u, e) + 1 2ζ ‖u−α− d‖2 Minimizing the above cost function can be performed by iterating the following three steps: • Step 1: Update the variables α, ψ and e by α(k+1), ψ(k+1), ... |

166 | Fully constrained least squares linear spectral mixture analysis method for material quantification in hyperspectral imagery
- Heinz, Chang
- 2001
(Show Context)
Citation Context ... by the post-nonlinear model. Typical evolutions of the abundance vector α and its counterpart u are shown in Figure 1. Our approach was compared with the fully constrained least square method (FCLS) =-=[10]-=-, the extended endmember matrix method (ExtM) [2], and our previously proposed K-Hype method [5]. The root mean square error of the estimated abundances was used to compare these algorithms. The compa... |

99 | Hyperspectral unmixing overview: Geometrical, statistical, and sparse regression-based approaches,”
- Bioucas-Dias, Plaza, et al.
- 2012
(Show Context)
Citation Context ...r unmixing techniques, as nonlinear models may provide more accurate estimations of mixtures, in particular when there are significant physical interactions of photons scattered by multiple materials =-=[1]-=-. Several algorithms have been proposed to address the nonlinear unmixing problem. For instance, bilinear models were considered to handle complex scenarios such as multilayered scenes [2, 3], by intr... |

41 | Unmixing hyperspectral images using a generalized bilinear model
- Halimi, Altmann, et al.
- 2011
(Show Context)
Citation Context ...e materials [1]. Several algorithms have been proposed to address the nonlinear unmixing problem. For instance, bilinear models were considered to handle complex scenarios such as multilayered scenes =-=[2, 3]-=-, by introducing additional interaction terms in the linear model. An unmixing algorithm based on a manifold learning process was investigated in [4], under the assumption that hyperspectral data may ... |

40 |
Exploiting manifold geometry in hyperspectral imagery
- Bachmann, Ainsworth, et al.
- 2005
(Show Context)
Citation Context ...e complex scenarios such as multilayered scenes [2, 3], by introducing additional interaction terms in the linear model. An unmixing algorithm based on a manifold learning process was investigated in =-=[4]-=-, under the assumption that hyperspectral data may be embedded into a low-dimensional manifold. Kernel methods aim to avoid high computational complexity by using more simple physics-inspired models. ... |

15 | Nonlinear unmixing of hyperspectral data based on a linear-mixture/nonlinear-fluctuation model
- Chen, Richard, et al.
- 2013
(Show Context)
Citation Context ...ernel methods aim to avoid high computational complexity by using more simple physics-inspired models. Some kernels were designed to be sufficiently flexible for matching various nonlinearity degrees =-=[5]-=-. Finally, artificial neural networks were considered to conduct unmixing with training data [6]. More recently, it has been argued that both linear and nonlinear mixtures can be present in a single p... |

13 |
Nonlinear spectral mixture analysis for hyperspectral imagery in an unknown environment
- Raksuntorn, Du
- 2010
(Show Context)
Citation Context ...e materials [1]. Several algorithms have been proposed to address the nonlinear unmixing problem. For instance, bilinear models were considered to handle complex scenarios such as multilayered scenes =-=[2, 3]-=-, by introducing additional interaction terms in the linear model. An unmixing algorithm based on a manifold learning process was investigated in [4], under the assumption that hyperspectral data may ... |

11 | Nonlinear neural network mixture models for fractional abundance estimation - Plaza, Martinez, et al. - 2004 |

9 |
A novel kernel-based nonlinear unmixing scheme of hyperspectral images
- Chen, Richard, et al.
- 2011
(Show Context)
Citation Context ...ally, artificial neural networks were considered to conduct unmixing with training data [6]. More recently, it has been argued that both linear and nonlinear mixtures can be present in a single pixel =-=[5, 7, 8]-=-, meaning that partially linear models may be advantageously used. In [7], we proposed a kernel-based nonlinear unmixing technique based on the partially linear assumption. In [8], the authors combine... |

4 |
An improved training algorithm for nonlinear kernel discriminants
- Abdallah, Richard, et al.
- 2004
(Show Context)
Citation Context ...ious algorithms to estimate abundances in each pixel. The abundance vectors were used as features with an SVM classifier, based on a Gaussian kernel. Note that other classification algorithms such as =-=[11]-=- could have been used. This max β,γ,λ Ga(β,γ, λ) = −ρ 2 βγ λ > 1ρ (K + µI) M −M1M> I −1 −1>M> −1 R βγ λ + r − ρ ζ M(u(k) − d(k)) − ρ ζ (u(k) − d(k)) ρ ζ 1>(u(k) − d(k))− 1 > βγ... |

1 |
Estimating the percentage of linear and nonlinear mixing at the subpixel level in hyperspectral imaging
- Close, Gader
- 2012
(Show Context)
Citation Context ...ally, artificial neural networks were considered to conduct unmixing with training data [6]. More recently, it has been argued that both linear and nonlinear mixtures can be present in a single pixel =-=[5, 7, 8]-=-, meaning that partially linear models may be advantageously used. In [7], we proposed a kernel-based nonlinear unmixing technique based on the partially linear assumption. In [8], the authors combine... |