José Carlos Moreira Bermudez — Page 2

arXiv2016

Technical Report: Band selection for nonlinear unmixing of hyperspectral images as a maximal clique problem

Kernel-based nonlinear mixing models have been applied to unmix spectral information of hyperspectral images when the type of mixing occurring in the scene is too complex or unknown. Such methods, however, usually require the inversion of matrices of sizes equal to the number of spectral bands. Reducing the computational load of these methods remains a challenge in large scale applications. This paper proposes a centralized method for band selection (BS) in the reproducing kernel Hilbert space (RKHS). It is based upon the coherence criterion, which sets the largest value allowed for correlations between the basis kernel functions characterizing the unmixing model. We show that the proposed BS approach is equivalent to solving a maximum clique problem (MCP), that is, searching for the biggest complete subgraph in a graph. Furthermore, we devise a strategy for selecting the coherence threshold and the Gaussian kernel bandwidth using coherence bounds for linearly independent bases. Simulation results illustrate the efficiency of the proposed method.

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arXiv2015

Nonparametric Detection of Nonlinearly Mixed Pixels and Endmember Estimation in Hyperspectral Images

Mixing phenomena in hyperspectral images depend on a variety of factors such as the resolution of observation devices, the properties of materials, and how these materials interact with incident light in the scene. Different parametric and nonparametric models have been considered to address hyperspectral unmixing problems. The simplest one is the linear mixing model. Nevertheless, it has been recognized that mixing phenomena can also be nonlinear. The corresponding nonlinear analysis techniques are necessarily more challenging and complex than those employed for linear unmixing. Within this context, it makes sense to detect the nonlinearly mixed pixels in an image prior to its analysis, and then employ the simplest possible unmixing technique to analyze each pixel. In this paper, we propose a technique for detecting nonlinearly mixed pixels. The detection approach is based on the comparison of the reconstruction errors using both a Gaussian process regression model and a linear regression model. The two errors are combined into a detection statistics for which a probability density function can be reasonably approximated. We also propose an iterative endmember extraction algorithm to be employed in combination with the detection algorithm. The proposed Detect-then-Unmix strategy, which consists of extracting endmembers, detecting nonlinearly mixed pixels and unmixing, is tested with synthetic and real images.

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