基于多尺度几何分析的三维表面稀疏表示和快速重构方法研究

This project focuses on the visual measurement and sparse representation of 3D surface. The traditional measuring method of 3D surface has the disadvantages of high cost, complicated operation and large amounts of data. In this project, a novel compressed sensing theory is introduced for grain information monitoring and processing. The shape and temperature, humidity tomographic images of stored grain can be represented as 3D surfaces. With the method of multiscale geometric analysis, the key scientific issues are studied for surface sparse representation and compressed sensing. A split Bregman recovery algorithm is proposed for surfacelet transformed surfaces. Novel methods for image denoising, quantity estimation, temperature and humidity anomaly detection and location are researched and discussed. Experiments carry out to verify the convergence, computational efficiency, and robustness of the proposed methods. Research of this project indicates a new acquisition protocol for surface metrology and leads to building new measurement instruments for compressed sensing.

本项目以三维表面的视觉测量和稀疏表示为研究对象，针对三维表面信息监测设备成本高、测量过程复杂、数据量巨大等问题，提出了基于曲面稀疏重构的粮情监测和处理方法。利用多尺度几何分析方法，对粮堆轮廓曲面和层析温湿度三维曲面进行稀疏表示和压缩测量，设计了基于分裂Bregman迭代算法的曲面重构算法，建立了粮情监测的压缩感知测量机制。项目重点对曲面稀疏变换模型及重构算法的有效性进行分析，还对粮食测量图像去噪、储粮数量估计、温湿度异常检测与定位等问题的解决方法进行研究和探讨。为三维表面测量的数据获取机制和压缩感知测量设备的研制奠定了理论基础。

三维表面测量面临着设备成本高、操作复杂、数据量巨大等问题。本项目研究了三维表面视觉测量系统结构、数据转换及处理方法，并对三维表面的稀疏表示和快速重构算法进行了理论分析和实验验证。提出了基于Contourlet和Surfacelet等多尺度、多方向的三维表面稀疏变换方法，有利于获得图像的稀疏表示，将图像稀疏重构转化为l1范数正则化问题，为了获得稳定、快速的重建结果，采用分裂 Bregman迭代算法进行求解。项目还对基于微波探测的粮食密度三维分布的测量及其在粮食数量估计方面的应用进行了探讨，为三维表面压缩测量的实际应用奠定了基础。