基于运动补偿的光学遥感单像素压缩成像方法研究

Single-pixel compressive imaging is an important approach that makes the optical remote imaging be with high resolution, high signal-to-noise rate, ultra-wide spectrum, high dynamic range and high sensitivity, which has significant research value. To solve the problem of single-pixel compressive imaging in motion condition for optical remote sensing, we follow the idea of “analysis of theory and engineering background→mathematical modeling and solution→analysis of the solution’s well-posedness→validation by simulated experiments” and research on single-pixel compressive imaging method based on motion compensation. The motion compensation begins from the engineering background of optical remote sensing and compressive sensing theory, takes compressive sampling model based on spatial-time joint coding as breakthrough point, and regards image blind recovery that simultaneously estimates the unknown motion and reconstructs the original image as kernel. Moreover, the analysis of the solution’s well-posedness by reconstruction conditions of the projected measurement matrix and the mathematical and physical simulated experiments are regarded as the condition and approach, respectively. Based on motion compensation, the single-pixel compressive imaging in motion condition is realized. Research achievements can develop the compressive imaging theory and promote the practicality of the single-pixel compressive imaging in optical remote sensing.

单像素压缩成像是光学遥感走向高分辨率、高信噪比、超宽谱段、高动态范围与高灵敏度成像的重要途径，具有重要的研究价值。本项目针对运动条件下光学遥感单像素压缩成像问题，按照“理论与工程背景分析→数学建模与求解→解的适定性分析→仿真实验验证”的思路，开展基于运动补偿的光学遥感单像素压缩成像方法研究。运动补偿以光学遥感工程背景与压缩成像理论为出发点，以建立基于空时联合编码的压缩采样模型为突破口，以同时进行运动估计与图像重构的图像盲重构为核心，以利用投影测量矩阵的可重构条件分析解的适定性为条件，以数字、物理仿真实验验证为途径，实现运动条件下单像素压缩成像。研究成果可丰富发展压缩成像理论，推进光学遥感单像素压缩成像实用化进程。

单像素压缩成像是满足与适应光学遥感成像发展需求的重要研究领域，具有重要的研究价值。本项目针对运动条件下光学遥感单像素压缩成像问题，从光学遥感工程背景与压缩成像理论出发，首先建立了基于空时联合编码的运动压缩采样模型，重点在于建立空时联合编码投影测量测量矩阵的具体表达形式。建模考虑了单像素压缩成像的时序测量机理、平台运动特性、噪声统计规律等，同时结合了投影测量、数理统计、数学建模等数学工具的综合运用。其次，考虑到运动条件下图像重构的高度病态性，需要在重构逆问题中加入图像以及降质因素的先验约束。因此，通过稀疏约束、低秩约束、变分PDE约束等实现了图像先验信息的开采，进而结合模型特点设计数值算法，实现了图像的快速、稳健的重构。再次，测量矩阵可重构条件是使得图像先验约束重构能够精确、稳定恢复原信号所需的条件，一般通过测量矩阵的某种性质度量给出。本项目利用约束等距性质、互相关性、累加互相关性分析了运动条件下投影测量矩阵的可重构条件。最后，结合数字仿真与物理仿真实验验证了模型与算法的有效性。仿真结果表明，伯努利矩阵和特普利兹矩阵皆可用作投影测量矩阵，同时针对成像场景的复杂程度，需要采用不同的采样率。此外，为了后续将光学遥感压缩成像应用于实际星载光学成像环境，课题组针对光学遥感成像平台的运动特性设计了压缩成像系统方案，即推扫式光学压缩成像系统方案，这种新的压缩成像方案可以充分利用星载光学遥感成像的运动环境，同时降低采样数据量，提高了系统稳定度。