单像素压缩成像高质量图像重建特征函数  

High-Quality Image Reconstruction Characteristic Function forSingle-Pixel Compressive Imaging

作　　者：居世昌 蔡俊杰 龚文林 Ju Shichang;Cai Junjie;Gong Wenlin(School of Optoelectronic Science and Engineering,Soochow University,Suzhou 215006,Jiangsu,China)

机构地区：[1]苏州大学光电科学与工程学院,江苏苏州215006

出　　处：《光学学报》2024年第7期61-73,共13页Acta Optica Sinica

基　　金：江苏省高等学校自然科学研究项目(21KJA140001);苏州大学引进人才科研启动项目(NH15901123)。

摘　　要：通过测量矩阵获取Gram矩阵,梳理了Gram矩阵与系统点扩散函数的关系,进而基于点扩散函数提出最强旁瓣峰值大小、叠加旁瓣峰值大小、空间距离和频谱余弦相似度4个特征参量。在此基础上,构建了一种单像素压缩成像高质量图像重建的特征函数,建立了可重建的目标稀疏度与特征函数的关系,并通过数值模拟和实验验证了所提特征函数的有效性,该工作对于单像素成像系统测量矩阵的优化设计具有重要借鉴意义。Objective The property of the measurement matrix has a great influence on the image reconstruction quality of singlepixel compressive imaging.Optimizing the measurement matrices is a core and crucial technology for single-pixel imaging.However,current optimization methods for measurement matrices often face the problems of local optimization and limited applicability.Additionally,existing analytical theories and methods based on the measurement matrix often fail to explain or predict the image reconstruction quality in many scenarios,and the quantitative relationship among measurement matrix characteristics,target properties,and image reconstruction results is unclear.For example,the reconstruction results vary obviously among different kinds of Hadamard encoding measurement matrices.Therefore,after combining optical imaging systems with compressive sensing theory,it has become an urgent issue for single-pixel compressive imaging to construct a characteristic function that can predict image reconstruction quality.We propose a characteristic function of high-quality image reconstruction for single-pixel compressive imaging to predict the imaging quality of targets with different sparsity,which is helpful for the optimal design of measurement matrices in single-pixel imaging systems.Methods Under the same sampling rate,the image reconstruction quality is significantly different for various kinds of Hadamard encoding measurement matrices,which can not be explained by existing compressive sensing theories.By combining compressive sensing theory with the characteristic parameters described in Ref.[23],the Gram matrix is obtained from the measurement matrix and then the relationship between the Gram matrix and the system s point spread function is clarified.Next,according to the point spread function and compressive sensing theory,four characteristic parameters are proposed,including the peak value of the strongest sidelobe,overlapped sidelobe peak value,spatial distance,and spectral cosine similarity.Based on these pa

关 键 词：成像系统 单像素成像 压缩感知 测量矩阵 特征函数 

分 类 号：O436[机械工程—光学工程]