基于对称三对角矩阵的宽带滤波调制光谱观测编码设计  

Broadband Filtering Modulation Based on Symmetric Tridiagonal Matrix for Spectral Observation Coding Design

作　　者：魏磊[1] 王晓旭 杨林[1] 徐拓奇 岳品良 王夺 Wei Lei;Wang Xiaoxu;Yang Lin;Xu Tuoqi;Yue Pinliang;Wang Duo(Institute of Space Sciences,Institute of Frontier and Interdisciplinary Science,Shandong University,Qingdao,Shandong 266273,China;Changchun Institute of Optics,Fine Mechanics and Physics,Chinese Academy of Sciences,Changchun,Jilin 130033,China)

机构地区：[1]山东大学空间科学研究院山东大学前沿交叉科学研究院,山东青岛266273 [2]中国科学院长春光学精密机械与物理研究所,吉林长春130033

出　　处：《光学学报》2022年第7期117-125,共9页Acta Optica Sinica

基　　金：国家自然科学基金(41774180);中国博士后科学基金面上项目(2020M672053)。

摘　　要：基于压缩感知及深度学习理论的光谱观测编码方案存在滤光器件设计与光谱重建过程复杂、设计光谱透过率难以硬件实现等问题,因此从简化光谱观测系统的思路出发,考虑常见干涉滤光器件的制造难度,提出基于对称三对角Toeplitz矩阵的光谱透过率观测编码方案;采用矩阵理论讨论光谱观测矩阵的适定性,并采用数值仿真方法研究其容差能力。理论分析结果表明,随着光谱观测矩阵规模的增大,对称三对角矩阵的条件数增长较慢,上限可控。数值仿真结果表明,采用非负最小二乘算法进行光谱重建,并在保证特定约束的情况下,增加观测矩阵的规模对对称三对角矩阵光谱观测编码方案适定性的影响较小,仍然可以保证很高的光谱测量重建准确度。The spectral observation coding scheme based on compressed sensing and deep learning theory has some problems,such as the complex process of filter design and spectral reconstruction,and the difficulty of hardware implementation of the designed spectral transmittance.Therefore,in order to simplify the spectral observation system,considering the manufacturing difficulty of common interference filters,a spectral transmittance observation coding scheme based on symmetrical tridiagonal Toeplitz matrix is proposed.The well-posedness of spectral observation matrix is discussed by matrix theory,and its tolerance is studied by numerical simulation.The theoretical analysis results show that with the increase of the size of the spectral observation matrix,the condition number of the symmetric tridiagonal matrix increases slowly and the upper limit can be controlled.The numerical simulation results show that the non-negative least squares algorithm is used for spectral reconstruction,and under certain constraints,increasing the size of the observation matrix has little influence on the suitability of the spectral observation coding scheme of the symmetric tridiagonal matrix,which can still guarantee the high accuracy of spectral measurement reconstruction.

关 键 词：成像系统 宽带滤波 计算光谱测量 光谱编码 观测矩阵 光谱重建 

分 类 号：TH744[机械工程—光学工程]