Nonlinear unmixing of hyperspectral images using radial basis functions and orthogonal least squares

Abstract

This paper studies a linear radial basis function network (RBFN) for unmixing hyperspectral images. The proposed RBFN assumes that the observed pixel reflectances are nonlinear mixtures of known endmembers (extracted from a spectral library or estimated with an endmember extraction algorithm), with unknown proportions (usually referred to as abundances). We propose to estimate the model abundances using a linear combination of radial basis functions whose weights are estimated using training samples. The main contribution of this paper is to study an orthogonal least squares algorithm which allows the number of RBFN centers involved in the abundance estimation to be significantly reduced. The resulting abundance estimator is combined with a fully constrained estimation procedure ensuring positivity and sum-to-one constraints for the abundances. The performance of the nonlinear unmixing strategy is evaluated with simulations conducted on synthetic and real data.

Supervised Nonlinear Spectral Unmixing Using a Postnonlinear Mixing Model for Hyperspectral Imagery

“…1) Conditional pdf : Straightforward computations lead to (13) where . Since it is not easy to sample according to (13) [mainly because of the indicator function ], we propose to update the abundance using a Metropolis-Hasting move.…”

“…Since it is not easy to sample according to (13) [mainly because of the indicator function ], we propose to update the abundance using a Metropolis-Hasting move. More precisely, a new abundance coefficient is proposed following a Gaussian random walk procedure (the variance of the proposal distribution has been adjusted to obtain an acceptance rate close to 0.5, as recommended in [26, p. 8]).…”

“…Conversely, the bilinear models recently studied in [8]- [11] address the problem of scattering effects, mainly observed in vegetation areas. Other more flexible unmixing techniques have been also proposed to handle a wider class of nonlinearity, including radial basis function networks [12], [13] Manuscript received June 23, 2011; revised November 28, 2011; accepted January 29,2012. Date of publication February 13, 2012; date of current version May 11, 2012.…”

Unsupervised nonlinear unmixing of hyperspectral images using Gaussian processes

“…Bilinear models recently studied in [3,4] have shown interesting properties for images subjected to scattering effects, i.e., observed in wooded areas. Other more flexible unmixing techniques have also been proposed to handle wider class of nonlinearities, including radial basis function networks [5,6] and kernel-based models [7]. This paper considers a kernel-based approach for unsupervised SU based on a nonlinear dimension reduction method referred to as Gaussian process latent variable model (GP-LVM).…”

Fractional Snow-Cover Mapping Based on MODIS and UAV Data over the Tibetan Plateau

“…In addition, several hyperspectral imaging-based spectral unmixing algorithms have been gradually introduced into MODIS FSC mapping. Zhang et al (2015) produced MODIS FSC maps using a fully constrained least squares spectral mixture analysis method (FCLS) [30], fully constrained scaled gradient method (FCSGM) [31], a sparse regression method (SPARSE) [32] and a polynomial nonlinear method (POLY) [33,34] for the Tibetan Plateau. Although they found that all of these algorithms can improve the accuracy of snow-cover mapping compared with the MOD10A1 FSC, they also showed that complex terrain can greatly reduce the accuracy of these spectral unmixing algorithms [35].…”