基于压缩感知的定向遥感理论研究

It's very difficult to sample change area data directionally due to uncertainty and unpredictability of sampling objects. Conventional data collecting of entire zone leads to repeat work towards unchanged areas so that capital and resource are wasted. Compressive sensing (CS) theory can be used properly in directional remote sensing research of urban change area by virtue of the sparsity hypothesis of change area. It has been demonstrated in our early experiments that change area can be reconstructed losslessly by 3 times as much as its data based on the difference of unlike temporal CS measurement values. This study would solve primarily the basic theory problem of directional remote sensing through theoretical analysis, mathematical proof and experimental validation based on linear push-broom mode and the directional remote sensing ideally as the object of study. It lays the foundation for the future industrial application of directional sensing. In order to use change areas' prior information such as spatio-temporal continuity and structure, restricted direction property, reconstruction ability of optimal matrix, design of measurement matrix and novel reconstruction algorithm are studied by theory and experiment from two-dimension. Efficient acquisition and reconstruction of the massive measurement data would be implemented at last. This study not only provides a new theory and technology for remote sensing image acquisition and update, but also opens up new field for the research on compressed sensing. Therefore, the study, in addition to the great theoretical value, but also had a broad engineering application prospect and great economic value.

由于地表变化区域的不确定性和不可预知性，很难定向采集数据。传统的面向全域的数据采集又会导致对非变化区域的重复工作和资源资金等的严重浪费。基于变化区域的稀疏假设，可采用压缩感知理论研究变化区域的定向遥感问题。不同时相压缩感知测量数据的差值可用于无损重构变化区域，所需数据量仅为变化区域数据量的3倍。本研究拟基于线阵推扫模式，以理想情况下的定向遥感为研究对象，通过理论分析、数学证明和实验验证初步解决定向遥感的基础理论问题。为将来定向遥感的工业应用研究奠定基础。本研究拟充分利用变化区域时空连续性和结构等先验信息，从二维的角度开展约束等向性、优化矩阵重构性能、测量矩阵设计和新型重构算法的理论和实验研究。最终实现海量测量数据的高效采集和重构。本研究不仅为遥感影像的采集和更新提供新的理论和技术，还为压缩感知研究开辟新的领域。因此，本研究不但具有极大的理论价值，而且具有广阔的工程应用前景和巨大的经济价值。

由于地表变化区域的不确定性和不可预知性，很难定向采集数据。传统的面向全域的数据采集又会导致对非变化区域的重复工作和资源资金等的严重浪费。基于变化区域的稀疏假设，可采用压缩感知理论研究变化区域的定向遥感问题。不同时相压缩感知测量数据的差值可用于无损重构变化区域，所需数据量仅为变化区域数据量的3 倍。本研究基于线阵推扫模式，以理想情况下的定向遥感为研究对象，研究构建了：信号方向的保持和继承模型，即压缩感知的约束保角性、基于信号方向和结构先验信息的重构算法、优化矩阵重构能力分析模型、稀疏循环矩阵的设计理论，并整合研究成果。建立多种测量矩阵和重构算法的组合模型，实验验证分析和比较各种实现模型的综合性能。 取得的重要结果包括：压缩感知的约束保角性的提出、推导和证明；基于信号方向信息的二维压缩感知重构模型；基于先验信息、线阵推扫和等效二维稀疏变换的采集和重构模型；基于信号方向和结构先验信息的定向遥感理论；基于结构先验信息和分块对角矩阵的二维压缩感知采集和重构模型；压缩感知中的高斯矩阵优化模型；信号重构中测量矩阵性能的判据模型；基于点扩散函数的稀疏循环矩阵的优化和重构能力模型；基于单像素相机重构矩阵优化的影像采集和重构方法模型；稀疏循环矩阵设计和原始像素大小的关系模型；稀疏循环矩阵设计和基于低分辨原始图像插值关系模型，以及研究成果的整合。本研究不仅为遥感影像的采集和更新提供新的理论和技术，还为压缩感知研究开辟新的领域。因此，本研究不但具有极大的理论价值，而且具有广阔的工程应用前景和巨大的经济价值。为将来定向遥感的工业应用研究奠定基础。