Multiscale Algorithms for the Geometric Analysis of Hyperspectral Data

高光谱成像是一种传感技术，从整个电磁频谱中收集数百个窄带图像。通过超越可见光谱和在可见范围内精确区分波长，当标准图像无效时，该技术可以非常强大地区分不同的材料。因此，高光谱遥感提供了独特的功能，包括监测作物的发育和健康，绘制石油泄漏和入侵物种的地图，以及探测可能被伪装的物体。然而，随着现代遥感应用不再局限于卫星图像，许多情况下的图像采集不再处于受控条件下，因为照明、物理参数和视角可能随时间而变化，感兴趣的物体可能部分被遮挡。本研究介绍了新一代数学和算法工具，旨在提供在这种现实条件下高光谱数据的稳健分类。该项目旨在为高光谱数据开发一种新的分析和分类算法，该算法对光照、视点和物理条件的变化具有鲁棒性。研究结果旨在直接应用于沿海湿地环境状况的监测以及其他社会、经济和国家安全利益的观察。虽然高光谱成像和图像处理在遥感领域已经得到了很好的发展，但遥感中的图像采集可能发生在光照、物理参数和视角随时间变化的条件下。该研究项目结合了稀疏表示、多层卷积网络和机器学习的思想，以解决这种变化条件对成像带来的挑战。该方法的新颖之处在于对稀疏表示和shearlet方法的适应，shearlet是一种各向异性多尺度系统，在捕获多维数据的定向内容方面特别有效。该方法为构建适合高光谱数据的深度学习神经卷积网络提供了基础，该网络旨在生成稳定且鲁棒的特征向量。本研究旨在开发一种高效的多尺度表示，该表示是根据高光谱数据的具体情况定制的。利用剪切小波在仿射变换下的协方差特性，将散射变换与剪切小波相结合，构建高光谱数据的稳定和视点不变特征。针对高光谱数据的特殊结构，提出了一种新的分层分类方案，并提出了基于稀疏性的高光谱数据修复方法。这些新算法将用于分析高光谱数据，以监测沿海湿地的环境状况，这是一个具有重大社会和经济意义的具有挑战性的案例研究。

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.