镜像综合孔径微波辐射成像方法研究
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摘要
综合孔径微波辐射计采用稀疏的小口径天线阵列合成一个等效的大口径天线,可有效降低天线的体积与重量,且无需机械扫描即可实现对整个视场的瞬时成像,为提高星载被动微波遥感的空间分辨率提供了一种可行的途径。但是综合孔径辐射计的优点是以系统结构和信号处理复杂度为代价的,特别是对于大型星载综合孔径辐射计,由于阵元数目过多,系统结构和信号处理非常复杂。为了降低大型综合孔径辐射计系统结构和信号处理的复杂度,本文首次提出“镜像综合孔径微波辐射成像”这一新的成像方法,旨在使用较少的天线单元和简单的接收机结构获取更高的空间分辨率。本文将阐述镜像综合孔径微波辐射成像的基本原理及其关键问题,主要内容如下：
(1)一维镜像综合孔径微波辐射成像原理及成像性能。首先阐述了一维镜像综合孔径辐射成像的基本原理：镜像双天线接收信号的相关输出可以表示为两个余弦可见度的差,通过求解联系余弦可见度和双天线接收信号相关输出的线性方程组可以获得所有基线上的余弦可见度,然后通过反余弦变换重建场景亮温分布图像；接着分析了一维镜像综合孔径辐射成像的空间分辨率和灵敏度,提出了多次联合测量的方法解决基线完整性问题；然后以具体一维镜像综合孔径系统为例,通过仿真验证了一维镜像综合孔径成像的原理、空间分辨率以及灵敏度,仿真结果与理论分析一致；最后从多个方面对一维镜像综合孔径和一维传统综合孔径进行了比较。在同样的空间分辨率下,理论分析和仿真结果均表明一维镜像综合孔径能够大大减少天线、模数转换器(ADC)以及相关器的数目,简化接收机结构。
(2)二维镜像综合孔径微波辐射成像原理及成像性能。首先阐述了从一维镜像综合孔径扩展到二维镜像综合孔径的思路,然后与一维镜像综合孔径的过程一样,阐述二维镜像综合孔径成像的原理,分析其成像性能,通过仿真验证其原理、空间分辨率以及灵敏度。理论分析和仿真结果表明二维镜像综合孔径可以在两个维度上提供高分辨率。
(3)系统误差对镜像综合孔径成像性能的影响。首先建立了镜像综合孔径系统中反演亮温准确度与镜像双天线相关误差之间的关系,在此基础上结合Parseval定理提出了图像均方误差评价准则,并从矩阵范数的角度给出了镜像双天线相关误差造成亮温反演准确度的上限。然后分别针对反射面误差、天线误差以及通道误差进行建模,并在该误差评价准则下仿真分析了误差对成像性能的影响。
(4)镜像综合孔径辐射成像的图象重建方法。受系统误差的影响,利用反余弦变换重建的图像质量较差,为此引入了基于系统冲激响应G矩阵的图像重建方法。镜像综合孔径辐射成像的图象重建是一个病态的反问题,受误差和系统噪声的影响,常用的广义逆图像重建方法稳定性较差,导致结果会远远偏离真实解,丧失其物理意义。为了解决解的稳定性问题,引入了正则化的图象重建方法：截断奇异值求解正则化和Tikhonov正则化,并通过仿真验证了这两种正则化图像重建方法。
本文从成像原理、成像性能、误差分析以及图像重建等方面对镜像综合孔径辐射成像方法进行了全方位阐述,可为镜像综合孔径辐射成像理论的发展和实际系统的设计提供理论指导,也为星载被动微波遥感的高分辨率成像观测提供了一种可选途径。
An aperture synthesis radiometer has the advantage of reducing antenna volume and weight needed for a given spatial resolution and the advantage of covering a large field of view without mechanical scanning. It provides a means for the radiometers operated at low frequencies to obtain high spatial resolution for the earth observation from space. But the superiority in spatial resolution of the technology is at the price of the complexity of system and signal processing. For a spaceborne aperture synthesis radiometer with hundrends of antennas and thousands of corrleators, the system and the signal processing are very complex, which are obstacles to achieve the required system performance. In this paper, mirrored interferometric aperture synthesis (MIAS) is proposed, which can achieve the same spatial resolution as a large traditional aperture synthesis system but needs fewer antennas and simple receiver structure. The fundamental principle and key problems of MIAS imaging are presented. The main aspects are as follows:
(1) The fundamental principle and the performances of one-dimansional MIAS. Firstly the pricinple of MIAS imaging is presented. The correlation between the signals collected by a pair of antennas can be represented by the subtraction of the cosine visibility at different two baselines. The cosine visibility can be obtained by solving the linear equations, and the brightness temperature image can be reconstructed from the cosine visibility by the inverse cosine transform. Then the spatial resolution and the sensitivity of MIAS imaging are analyzed, and the method, combing the linear equations at different distances from the array to the reflector, is proposed to guarantee the baseline integrity. Moreover, simulation experiments are conducted to demonstrate the principle of MIAS, the spatial resolution, and the sensitivity. The results are in good agreement with the theoretical. Finally, comparison between MIAS and traditional interferometric aperture synthesis is made. With the same spatial resolution, theoretical analysis and simulation results show that MIAS can greatly reduce the number of antennas, analog-to-digital converters (ADC), and correlators, and simplify the receiver structure.
(2) The fundamental principle and the performances of two-dimansional MIAS. Firstly, the process how to expand the one-dimensional MIAS to two-dimensional MIAS is presented. Then as the one-dimensional MIAS, the imaging principle and the system performances are presented. Simulation experiments for it are also conducted. The theoretical analysis and the simulation results show that two-dimensional MIAS can provide high spatial resolution in the two dimensional.
(3) The impacts of system errors on the performances of MIAS The relationship between the system errors and the system performances is established. Based on it and combining the Parseval principle, the root-mean-square rule is proposed to evaluate the impacts, and the upper limit of the impacts on the accuracy is given according to the matrix nrom. Then the model for the reflector imperfection, antenna errors, and channel errors are established, and the impacts of these errors are quantified through simulation.
(4) Image reconstruction method of MIAS imaging. Due to the impacts of system errors, the reconstructed image by inverse cosine transform is with bad quality. And reconstruction methods based on the impulse response matrix, the G operator, are introduced. The image reconstruction is an ill-posed inverse problem, and due to the impacts of system errors and noise, the common generalized inverse reconstruction is not robust, which cause the solution deviating from the real one severely. In order to solve the problem, two regularization methods, truncated singular value decomposition and tikhonov regularization, are introduced, and the simulation results demonstrate the validity of the two regularization methods.
In this paper, main aspects of MIAS, including imaging principle, imaging performances, error analysis, and image reconstruction are presented, which provide good references for the evolution of MIAS imaging and the design of a MIAS radiometer. MIAS also provides a means for the earth observation with high spatial resolution from space.
(1)一维镜像综合孔径微波辐射成像原理及成像性能。首先阐述了一维镜像综合孔径辐射成像的基本原理：镜像双天线接收信号的相关输出可以表示为两个余弦可见度的差,通过求解联系余弦可见度和双天线接收信号相关输出的线性方程组可以获得所有基线上的余弦可见度,然后通过反余弦变换重建场景亮温分布图像；接着分析了一维镜像综合孔径辐射成像的空间分辨率和灵敏度,提出了多次联合测量的方法解决基线完整性问题；然后以具体一维镜像综合孔径系统为例,通过仿真验证了一维镜像综合孔径成像的原理、空间分辨率以及灵敏度,仿真结果与理论分析一致；最后从多个方面对一维镜像综合孔径和一维传统综合孔径进行了比较。在同样的空间分辨率下,理论分析和仿真结果均表明一维镜像综合孔径能够大大减少天线、模数转换器(ADC)以及相关器的数目,简化接收机结构。
(2)二维镜像综合孔径微波辐射成像原理及成像性能。首先阐述了从一维镜像综合孔径扩展到二维镜像综合孔径的思路,然后与一维镜像综合孔径的过程一样,阐述二维镜像综合孔径成像的原理,分析其成像性能,通过仿真验证其原理、空间分辨率以及灵敏度。理论分析和仿真结果表明二维镜像综合孔径可以在两个维度上提供高分辨率。
(3)系统误差对镜像综合孔径成像性能的影响。首先建立了镜像综合孔径系统中反演亮温准确度与镜像双天线相关误差之间的关系,在此基础上结合Parseval定理提出了图像均方误差评价准则,并从矩阵范数的角度给出了镜像双天线相关误差造成亮温反演准确度的上限。然后分别针对反射面误差、天线误差以及通道误差进行建模,并在该误差评价准则下仿真分析了误差对成像性能的影响。
(4)镜像综合孔径辐射成像的图象重建方法。受系统误差的影响,利用反余弦变换重建的图像质量较差,为此引入了基于系统冲激响应G矩阵的图像重建方法。镜像综合孔径辐射成像的图象重建是一个病态的反问题,受误差和系统噪声的影响,常用的广义逆图像重建方法稳定性较差,导致结果会远远偏离真实解,丧失其物理意义。为了解决解的稳定性问题,引入了正则化的图象重建方法：截断奇异值求解正则化和Tikhonov正则化,并通过仿真验证了这两种正则化图像重建方法。
本文从成像原理、成像性能、误差分析以及图像重建等方面对镜像综合孔径辐射成像方法进行了全方位阐述,可为镜像综合孔径辐射成像理论的发展和实际系统的设计提供理论指导,也为星载被动微波遥感的高分辨率成像观测提供了一种可选途径。
An aperture synthesis radiometer has the advantage of reducing antenna volume and weight needed for a given spatial resolution and the advantage of covering a large field of view without mechanical scanning. It provides a means for the radiometers operated at low frequencies to obtain high spatial resolution for the earth observation from space. But the superiority in spatial resolution of the technology is at the price of the complexity of system and signal processing. For a spaceborne aperture synthesis radiometer with hundrends of antennas and thousands of corrleators, the system and the signal processing are very complex, which are obstacles to achieve the required system performance. In this paper, mirrored interferometric aperture synthesis (MIAS) is proposed, which can achieve the same spatial resolution as a large traditional aperture synthesis system but needs fewer antennas and simple receiver structure. The fundamental principle and key problems of MIAS imaging are presented. The main aspects are as follows:
(1) The fundamental principle and the performances of one-dimansional MIAS. Firstly the pricinple of MIAS imaging is presented. The correlation between the signals collected by a pair of antennas can be represented by the subtraction of the cosine visibility at different two baselines. The cosine visibility can be obtained by solving the linear equations, and the brightness temperature image can be reconstructed from the cosine visibility by the inverse cosine transform. Then the spatial resolution and the sensitivity of MIAS imaging are analyzed, and the method, combing the linear equations at different distances from the array to the reflector, is proposed to guarantee the baseline integrity. Moreover, simulation experiments are conducted to demonstrate the principle of MIAS, the spatial resolution, and the sensitivity. The results are in good agreement with the theoretical. Finally, comparison between MIAS and traditional interferometric aperture synthesis is made. With the same spatial resolution, theoretical analysis and simulation results show that MIAS can greatly reduce the number of antennas, analog-to-digital converters (ADC), and correlators, and simplify the receiver structure.
(2) The fundamental principle and the performances of two-dimansional MIAS. Firstly, the process how to expand the one-dimensional MIAS to two-dimensional MIAS is presented. Then as the one-dimensional MIAS, the imaging principle and the system performances are presented. Simulation experiments for it are also conducted. The theoretical analysis and the simulation results show that two-dimensional MIAS can provide high spatial resolution in the two dimensional.
(3) The impacts of system errors on the performances of MIAS The relationship between the system errors and the system performances is established. Based on it and combining the Parseval principle, the root-mean-square rule is proposed to evaluate the impacts, and the upper limit of the impacts on the accuracy is given according to the matrix nrom. Then the model for the reflector imperfection, antenna errors, and channel errors are established, and the impacts of these errors are quantified through simulation.
(4) Image reconstruction method of MIAS imaging. Due to the impacts of system errors, the reconstructed image by inverse cosine transform is with bad quality. And reconstruction methods based on the impulse response matrix, the G operator, are introduced. The image reconstruction is an ill-posed inverse problem, and due to the impacts of system errors and noise, the common generalized inverse reconstruction is not robust, which cause the solution deviating from the real one severely. In order to solve the problem, two regularization methods, truncated singular value decomposition and tikhonov regularization, are introduced, and the simulation results demonstrate the validity of the two regularization methods.
In this paper, main aspects of MIAS, including imaging principle, imaging performances, error analysis, and image reconstruction are presented, which provide good references for the evolution of MIAS imaging and the design of a MIAS radiometer. MIAS also provides a means for the earth observation with high spatial resolution from space.
引文
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