Nonlinear Unmixing of Hyperspectral Images: Models and Algorithms

Abstract

When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM).However, the LMM may be not valid and other nonlinear models need to be considered, for instance, when there are multi-scattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM.In this paper, we present an overview of recent advances in nonlinear unmixing modeling.arXiv:1304.1875v2 [physics.data-an]

A global optimization approach for rational sparsity promoting criteria

“…T and hence the polynomials corresponding to the inequalities g t (x t ) = −(x t + B)(x t − B) ≥ 0 can be included in the polynomials in (5). Details on these technical conditions are out of the scope of this paper and can be found in [18,19].…”

“…For a long time, attempts have been made in order to deal with more general nonlinear models. For example, one can mention the works undertaken by using Volterra models [4], which may be useful in some application areas [5]. Secondly, convex regularization terms may be limited, especially for capturing the sparse structure of a signal.…”

Detection of nonlinear mixtures using Gaussian processes: Application to hyperspectral imaging

“…Such analysis aims at unmixing the spectral information present in the hyperspectral image to identify the composing materials (endmembers) and their abundances in the region from which the data has been acquired. Most unmixing techniques rely on a parametric mixing model, from which the parameters must be estimated [4]. The simplest of these models assumes linear mixing of the endmember contributions [3] (Linear Mixing Model -LMM).…”

“…However, it has been recognized that the mixing in some pixels of a region is actually nonlinear [3][4][5][6][7][8][9][10][11]. This finding has triggered a plethora of techniques for analyzing nonlinearly mixed pixels (see for instance [4,5] and references therein). Though nonlinear unmixing permits a better understanding of the endmember contributions, the corresponding analysis techniques are necessarily more complex than linear unmixing.…”

Residual component analysis of hyperspectral images for joint nonlinear unmixing and nonlinearity detection

“…Nonlinear mixing models (NLMMs) provide an interesting alternative to overcoming the inherent limitations of the LMM. They have been proposed in the hyperspectral image literature and can be divided into two main classes [3]. The first class of NLMMs consists of physical models based on the nature of the environment (e.g., intimate mixtures [4] and multiple scattering effects [5,6,7]).…”