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

Abstract

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.

Biobjective Nonnegative Matrix Factorization: Linear Versus Kernel-Based Models

“…More recently, the abundances are incorporated in the nonlinear model, with a post-nonlinear model as studied in [25] and a Bayesian approach is used in [27] with the so-called residual component analysis. Another model is proposed in [19] in the context of supervised learning.…”

“…Many studies have shown the limits of a linear decomposition, as opposed to a nonlinear one [17], [18], [19]. While most research activities have been concentrated on the linear NMF, a few works have considered the nonlinear case.…”

Nonlinear unmixing of hyperspectral images using a semiparametric model and spatial regularization

“…This results from the use of the matrix V . Let us now solve the local optimization problem αn 0 and α n 1R = 1 (11) By introducing the Lagrange multipliers β n, , γ n, and λn, where the superscript (k) of these variables has been omitted for simplicity of notation, the Lagrange function associated with (11) is equal to…”

“…Post-nonlinear mixing models were discussed in [7,8]. Unmixing algorithms using geodesic distances and other manifold learning based techniques were investigated in [9][10][11][12]. In addition, algorithms operating in reproducing kernel Hilbert spaces (RKHS) have been proposed for hyperspectral unmixing.…”

Estimating the Intrinsic Dimension of Hyperspectral Images Using a Noise-Whitened Eigengap Approach

“…This model assumes that each spectrum is a convex combination of the endmember spectra. Unmixing hyperspectral images consists of three stages: (i) determining the number of endmembers and possibly projecting the data onto a subspace of reduced dimension [6], [7], (ii) extracting endmember spectra [8], [9] and (iii) estimating their abundances [10]- [12]. These stages can be performed separately or jointly [13]- [15].…”