乘性及矩阵噪声环境下的压缩感知测量方法研究

Compression sensing achieves observations far below the Nyquist frequency, which indicates significant potential for improving the test speed and resolution in the test area. However，the existing prototype systems of compressive sensing have a poor performance in practice because of the interference of the environment and the system noise. The traditional noisy observation model mostly considers the additive white Gaussian noise introduced by the signal interference and quantization error, but ignores the observation matrix related noise caused by the non-negative, drift and jitter of the template-type devices used to realize the matrix and the multiplicative noise introduced by non-linear devices. Even if such a slight noise can damage the Restricted Isometry Property of the observation matrix, resulting in reconstruction failure. In this project, we first study the mathematical properties and influence of multiplicative and matrix noise. Secondly, we propose the anti-noise compensation algorithm from the aspects of observation vector correction and equivalent matrix design, and propose a new observation method which corresponding to a negative valued sensing matrix. These contributions can effectively improve the compression perception of the anti-noise performance of the observation system. Finally, the compression efficiency measurement of photoelectric efficiency of photovoltaic devices is used as an example to verify the effect and performance of the algorithm. The research of this subject will expand the understanding and solution of the compressed perceptual noise, which has certain theoretical significance and wide application value in the fields of signal processing and test measurement.

压缩感知能实现远低于奈奎斯特频率的观测，在测试领域有大幅提高测试速度及分辨率的潜力。但已有压缩感知原型系统在实践中受环境和系统噪声的干扰而性能欠佳。传统含噪观测模型大多考虑由信号干扰及量化误差引入的加性高斯白噪声，却忽略了用于实现观测矩阵的模板类器件在物理上的非负性、漂移、抖动造成的与矩阵元素强相关的噪声以及器件的非线性引入的乘性噪声。即使轻微的这类噪声也能破坏观测矩阵的约束等距离性，导致重构失败。针对此类问题，本课题首先对乘性及矩阵噪声的数学性质和影响展开研究；其次从观测向量修正和等效矩阵设计两方面提出抗噪补偿算法，并提出可对应含负值观测矩阵的观测方法，能有效的提高压缩感知观测系统的抗噪性能。最后以光伏器件光电效率的压缩感知测量为应用实例，对算法的改进效果和性能进行实际验证。本课题的研究将拓展对压缩感知噪声的认识和解决方法，在信号处理和测试计量等领域具有一定的理论意义和广泛的应用价值。

压缩感知能实现远低于奈奎斯特频率的观测，在测试领域有大幅提高测试速度及分辨率的潜力。但已有压缩感知原型系统在实践中受环境和系统噪声的干扰而性能欠佳。.　　本项目针对实际压缩感知测量系统中面临的噪声问题，以太阳能电池板表面缺陷测量为应用，搭建了“压缩感知-光感生电流”（CS-LBIC）太阳能电池板缺陷的快速检测系统，分析了压缩感知测量系统的噪声特性，提出了基于测量向量修正的压缩感知测量算法，实现了对大幅面光伏器件表面稀疏坏点的压缩采样，以20%的测量样本数，实现了对表面转换效率缺陷点的有效检测，加之省去了机械运动部件，其扫描速度相比传统机械式光感生电流（LBIC）扫描速度提高了15倍以上。.在此基础上，利用光学相机获取太阳能电池板表面图像，采用数字图像处理方法提取表面栅极线特征信息作为先验信息，提出了基于信息增强的压缩感知-光感生电流（CECS-LBIC）测量算法，有效改善待测信号结构特征，降低了信号复杂度，进一步提升了太阳能电池板的检测效率，将测量样本数的典型需求降低至2%~6%，需要耗费3小时的传统10000点测量，采用CECS-LBIC检测系统，可在20秒以内完成。.　　本项目得出的压缩感知测量系统的噪声特性、提出的基于辅助测量的观测向量抗噪修正算法、基于先验信息的大信号剔除算法可推广至大部分基于压缩感知的测量系统，本项目搭建的CECS-LBIC检测系统，使得大面积精细检测以及工业在线检测成为可能，非常适用于需要频繁进行检测评估的新产品研发场景以及太阳能电池片的品质细分和质量控制场景，具有广阔的应用前景和潜在经济效益。