Technical Report: Band selection for nonlinear unmixing of hyperspectral images as a maximal clique problem
This is an incremental improvement for hyperspectral image analysis, addressing computational load in large-scale applications.
The paper tackles the computational challenge of kernel-based nonlinear unmixing in hyperspectral images by proposing a band selection method based on coherence in RKHS, showing it is equivalent to solving a maximum clique problem, with simulation results demonstrating its efficiency.
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.