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Graph-based denoising and classification of hyperspectral imagery using nonlocal operators

Several studies have shown that the use of nonlocal operators can significantly remove noise and improve the quality of natural images. These operators are built on similarities between small local neighborhoods that are not necessarily spatially close, which plays a very important role in preserving the image structure, and are closely related to the kernel methods used in manifold learning and nonlinear dimension reduction. This serves as our motivation for exploring the use of nonlocal, linear, and nonlinear diffusion processes on high dimensional imagery (e.g. hyperspectral) that do not require the computation of eigenfunctions. We utilize the same iterative scheme to perform a semi-supervised multi-class classification and segmentation, only by changing the initial conditions. Furthermore, we compare the denoising performance of these algorithms with other PDE-based methods like anisotropic diffusion and compare classification accuracies for different materials on real Hyperspectral Image (HSI) cubes.