基于哈达玛矩阵与压缩感知的超亚采样成像方法研究

Compressive imaging plays an important role in deep space exploration, spacecraft docking, life science, disaster warning, space environment monitoring, automatic drive, remote sensing, and the like. Among them, the preferred display of important patterns and the structured fast computation are the key problems to be solved and the main bottlenecks restricting the practicality of the technology, also are the research hotspots in the field of imaging. In this project, on the basis of the complementary/differential measurement techniques proposed in our previous study, we plan to present a sorting approach of Hadamard basis patterns which can satisfy the conditions of high-flux measurement and compressive imaging, in order to make the patterns with the significant contributions to the reconstruction be modulated firstly. By using the structural characteristics of the Hadamard matrix, the calculation can be simplified, which reduces the computational complexity and the memory consumption. The high-speed compressive imaging with super sub-sampling and high-spatial-resolution will be realized through the optical experiments. The research contents include: research on the contribution of the block feature of the patterns to the image reconstruction, the fast computation method based on the structural characteristics of the Hadamard matrix, research on the technology fusion problem of pattern sorting and total variation, and so on. The project aims to provide a universal new idea for realizing low-sampling-ratio high-spatial-resolution high-quality fast compressive imaging, by introducing the differential pattern sorting idea and fast computation method in compressed sensing. The key performance indicator of imaging: the sampling ratio is less than or equal to 5%. Therefore, this project has scientific significance and will finally promote the practicality of the technology.

压缩成像在深空探测、航天器对接、生命科学、灾害预警、空间环境监测、自动驾驶、遥感等领域发挥着重要作用，其中，重要掩模优先显示和结构化快速计算是亟待解决的关键问题和制约该技术实用化的主要瓶颈，也是成像领域的研究热点。本项目在前期研究所提出的互补/差分测量技术基础上，拟提出能满足高通量测量和压缩成像条件的哈达玛差分掩模排序的方案，使对图像重建贡献大的掩模优先显示，并利用哈达玛矩阵的结构化特征简化计算，降低计算复杂度和内存消耗，拟通过实验实现超亚采样高空间分辨率的高速压缩成像。研究内容包括：掩模区块特征对图像重建的贡献研究、基于哈达玛矩阵结构化特征的快速计算方法、掩模排序与全变分技术融合问题研究等。本项目旨在压缩感知中引入差分掩模排序思想和快速计算方法，为实现低采样率、高空间分辨率、高质量的快速压缩成像方案提供普适新思路。成像主要指标：采样率≤5%。因而本项目具有科学意义，能促进该技术实用化。

单像素计算成像为图像信息获取提供了一种新型非直接探测方式，近年来广受学者关注。由于它需要对物体进行多帧测量，在实时成像应用中就希望尽可能优先显示对重构贡献大的重要掩模和设计出方便计算的重构方法，以满足日益增长的瞬时探测需求。为此，本项目重点研究了Hadamard差分调制与掩模排序方法、基于Hadamard矩阵结构化特征的快速计算方法、掩模调制次序与全变分算法相结合的方法、单像素计算成像基础问题和相关应用扩展。主要研究成果：1）构建了基于切蛋糕和折纸排序的极限高维高阶光场多尺度时空变换理论体系，在单光子源下得到实验验证，采样率最高可降至0.2%，提高了1–2个数量级，空间分辨率提升至1024×1024像素，计算时间降至百秒量级，存储消耗降至MB量级；2）通过构建光场与掩模之间的联合概率密度模型，推演出掩模连通域对重建贡献的一般规律；3）发展了连续微分测量技术来提高测量信噪比；4）设计出了类梯度下降的快速重构算法；5）针对重构噪声提出了多尺度小波剩余密度卷积神经网络去噪方法；6）探索了在安全通信和运动目标场景中的相关应用。因而，本项目对于探索新型掩模构造和快速计算方法具有重要科学意义，为高性能单像素计算成像提供了普适新思路，在最大程度上促进了技术实用化进程。在本项目资助下，发表了10篇SCI论文、1篇北大中文核心期刊论文和1篇EI论文；获批授权6项发明专利；在国防工业出版社出版一本译著；部分成果得到转化应用和推广；衍生出包括北京市自然科学基金项目面上项目、北京市科学技术协会青年人才托举工程项目在内的主持项目6项；超额完成了任务指标，在单像素计算成像基础理论上取得了突破创新。