Nonlinear Unmixing of Hyperspectral Data With Vector-Valued Kernel Functions

Abstract

This paper presents a kernel-based nonlinear mixing model for hyperspectral data, where the nonlinear function belongs to a Hilbert space of vector valued functions. The proposed model extends the existing ones by accounting for band-dependent and neighboring nonlinear contributions. The key idea is to work under the assumption that nonlinear contributions are dominant in some parts of the spectrum, while they are less pronounced in other parts. In addition to this, we motivate the need for taking into account nonlinear contributions originating from the ground covers of neighboring pixels by practical considerations, precisely the adjacency effect. The relevance of the proposed model is that the nonlinear function is associated with a matrix valued kernel that allows to jointly model a wide range of nonlinearities and includes prior information regarding band dependences. Furthermore, the choice of the nonlinear function input allows to incorporate neighboring effects. The optimization problem is strictly convex and the corresponding iterative algorithm is based on the alternating direction method of multipliers. Finally, experiments conducted using synthetic and real data demonstrate the effectiveness of the proposed approach.

Hyperspectral Unmixing with Bandwise Generalized Bilinear Model

“…HySime [47] can be also adopted to estimate the number of endmembers for the gulf of Lion HSI. Besides, according to [24], the selected Cuprite HSI mainly has three materials, i.e., water, agricultural areas, and forests and semi natural areas. Moreover, the Corine Land Cover classification map of gulf of Lion HSI is shown in the first row of Figure 7, which can be used as potential visual ground truth to to interpret and evaluate the unmixing performance of different methods.…”

“…Besides, the alternative direction method of multipliers (ADMM) is adopted to solve the proposed NU-BGBM. Finally, extensive experiments are conducted to demonstrate the effectiveness of the proposed NU-BGBM compared with some other state-of-the-art unmixing methods.Keywords: additive white Gaussian noise (AWGN); hyperspectral images (HSIs); mixed noise; bandwise generalized bilinear model (BGBM); alternative direction method of multipliers (ADMM) some flexible models based on signal processing, such as post-nonlinear model [22], neural network model [23] and kernel model [24]. The second category includes some physical based models, such as intimate mixture model [25], bilinear mixture model (BMM) [26][27][28][29][30][31][32][33] and multilinear mixing model [34][35][36].…”

Human settlement and infrastructure monitoring with hyperspectral imaging

“…Following the same line, in [37] a multilinear mixture model including all orders of interactions is used to describe the reflectance of hyperspectral images. Alternatively, the methods introduced in [38] and [39] can be used to retrieve a feasible description of the effects resulting from additive terms assumed to corrupt an originally linear mixture term.…”

Kernel-Based Nonlinear Spectral Unmixing with Dictionary Pruning

“…Post-nonlinear models as well as some robust unmixing models that consider such a fluctuation are presented in [37]. In [38], the authors extended this method by accounting for band-dependent and neighboring nonlinear contributions using separable kernels. Further, kernel-based nonnegative matrix factorization (NMF) techniques are studied to simultaneously capture nonlinear dependence features and estimate the abundance.…”

“…The parameter µ K−Hype controls the trade-off between the fitting and the functional regularity. •The nonlinear neighbor and band dependent unmixing (NDU)[38]: This method extends the K-Hype by accounting for band-dependent and neighboring nonlinear contributions with vector-valued kernel function. The separable (Sp.)…”