Multiscale Algorithms for the Geometric Analysis of Hyperspectral Data

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Hyperspectral imaging is a sensing technique that collects hundreds of narrowband images from across the electromagnetic spectrum. By both going beyond the visible spectrum and accurately discriminating wavelengths within the visible range, this technology can be remarkably powerful for distinguishing different materials when standard imagery is ineffective. As a result, hyperspectral remote sensing offers unique capabilities for tasks that include monitoring the development and health of crops, mapping oil spills and invasive species, and detecting objects that may be camouflaged. With modern remote sensing applications not being constrained to satellite images, however, the image acquisition in many scenarios is no longer under controlled conditions, because illumination, physical parameters, and viewing angles may change over time and objects of interest may be partially occluded. This investigation introduces a new generation of mathematical and algorithmic tools that are designed to provide robust classification of hyperspectral data under such realistic conditions. The project aims to develop a new class of analysis and classification algorithms for hyperspectral data that are robust with respect to changes of illumination, viewpoint, and physical conditions. The results are intended to have direct application to the monitoring of environmental conditions in coastal wetlands and to other observations of societal, economic, and national security interest.While hyperspectral imaging and image processing have been well developed within the remote-sensing community, image acquisition in remote sensing may occur in conditions where illumination, physical parameters, and viewing angle change over time. This research program combines ideas from sparse representations, multilayer convolutional networks, and machine learning to address the challenges to imaging posed by such changing conditions. A novelty of the approach is the adaptation of methods from sparse representations and shearlets, an anisotropic multiscale system that is particularly effective at capturing the directional content of multidimensional data. This approach provides the basis for constructing a deep learning neural convolutional network tailored to hyperspectral data and designed to generate stable and robust feature vectors. This investigation aims to develop an efficient multiscale representation that is customized to the specifics of hyperspectral data. The scattering transform will be adapted in combination with shearlets by exploiting the covariance properties of shearlets under affine transformations to build stable and viewpoint-invariant features for hyperspectral data. A novel hierarchical scheme for classification optimized for the specific structure of hyperspectral data and sparsity-based inpainting methods to restore hyperspectral data corrupted by occlusions will be developed. These new algorithms will be used for the analysis of hyperspectral data to monitor environmental conditions of coastal wetlands, a challenging case study of great social and economic importance.