Multiscale Algorithms for the Geometric Analysis of Hyperspectral Data

高光谱成像是一种传感技术，它从整个电磁光谱中收集数百幅窄带图像。通过超越可见光光谱并准确区分可见光范围内的波长，当标准图像无效时，这项技术可以非常强大地区分不同的材料。因此，高光谱遥感为监测农作物的发育和健康、绘制石油泄漏和入侵物种的地图以及检测可能伪装的物体等任务提供了独特的能力。然而，随着现代遥感应用不再局限于卫星图像，许多场景中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会随着时间的推移而变化，感兴趣的对象可能会被部分遮挡。这项研究引入了新一代数学和算法工具，旨在在这样的现实条件下提供稳健的高光谱数据分类。该项目旨在开发一类新的高光谱数据分析和分类算法，该算法对光照、视点和物理条件的变化具有健壮性。这些结果旨在直接应用于滨海湿地环境条件的监测以及其他社会、经济和国家安全利益的观测。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。这项研究计划结合了稀疏表示法、多层卷积网络和机器学习的思想，以应对这种变化的条件对成像带来的挑战。该方法的一个新奇之处是采用了稀疏表示和剪切片的方法，这是一种各向异性的多尺度系统，在捕获多维数据的方向性内容方面特别有效。这种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和健壮的特征向量。这项研究旨在开发一种针对高光谱数据细节而定制的高效多尺度表示法。通过利用仿射变换下的剪切片的协方差特性，将散射变换与剪切片相结合，为高光谱数据建立稳定的、视点不变的特征。针对高光谱数据的特定结构优化了一种新的分级分类方案，并开发了基于稀疏性的修复方法来恢复被遮挡破坏的高光谱数据。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.