基于倾斜刃边法的遥感图像调制传递函数计算及图像复原技术研究
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摘要
高分辨对地观测是航天遥感领域的关键技术之一。在对地观测中,地面采样距离(ground sample distance, GSD)代表空间像元分辨率(空间相机探测器的像元尺寸)对应的地面采样间隔。高分辨对地观测,顾名思义,是指在对地观测中,追求更高GSD的遥感图像。GSD的大小取决于空间载体(人造卫星或航天飞机)的轨道高度,其上搭载的光学系统的焦距和空间相机探测器的像元尺寸。在像元尺寸一定的情况下,为了获得更小的GSD,就需增大系统的焦距和通光口径。然而,大的通光孔径一来会给光学系统的像差校正带来困难,二来会给光学系统的加工和装配增加麻烦,同时,载荷的增加也将大大提高其在航天领域的使用成本。目前,高分辨星载遥感光学系统大多采用反射式或折射一反射式结构,通常存在中心遮拦现象,降低了系统的成像质量。因此,当前高分辨对地观测系统呈现出两个主要发展趋势,一方面,使用小孔径光学系统配合图像后处理技术；另一方面,使用中心遮拦光学系统配合传递函数补偿(modulation transfer function compensation, MTFC)技术。本文开展了针对遥感成像系统MTF测量工作,意在对小孔径和中心遮拦光学系统进行MTFC,提高系统的成像质量,为系统的总体设计提供理论依据。
对于MTFC技术,如何精确估计系统的MTF乃是后期图像处理的基础和关键。首先,介绍了基于图像分析的各种传递函数测量方法,如针孔法,狭缝法和刃边法；其中,着重介绍了刃边法MTF测量的基本原理和计算流程；分析了成像器件的采样孔径,边缘扩散函数(edge spread function, ESF)的有限元差分,MTF的频率域压缩和刃边图像中的噪声等因素对MTF计算结果的影响,并给出了相应的校正方法；列举了已有的三种不同ESF函数模型,并从标量衍射理论出发,推导出一种新型的函数模型用于对ESF数据进行拟合,并通过它来计算得到系统的MTF。
其次,将成像过程看作是一个线性平移不变(linear shift-invariant, LSI)系统,建立了图像的退化和复原模型；介绍了常用的图像复原算法和图像质量客观评价方法,特别的,介绍了基于MTF的图像质量评价方法。
再次,分析了一个具有圆形光瞳的成像系统的退化机理,根据光学传递函数(optical transfer function, OTF)的自相关特性,推导了中心视场和边缘视场的OTF表达式；仿真实验中,针对不同噪声条件下(信噪比为∞,40和30 dB)的退化刃边图像,首先使用四种ESF函数模型和ISO 12233标准方法进行MTF计算,然后从计算精度和时间复杂度两个方面进行比较和分析；完成了一个小孔径成像系统的光学,结构和系统的设计与加工；实拍实验中,针对由该系统拍摄得到的两种不同类型的退化图像(分辨率板图和遥感图),基于四种ESF函数模型和ISO 12233标准方法计算系统的MTF,首先使用Lucy-Richardson (RL),总变分(total variation,TV)和稀疏反卷积(sparse deconvolution, SD)三种算法进行复原,然后使用灰度平均梯度(gray mean gradients, GMG),拉普拉斯算子和(Laplacian summation,LS),最大熵(large entropy, LE)和调制传递函数面积(modulation transfer function area, MTFA)四种客观评价方法对复原结果进行了评价。
最后,分析了一个具有中心遮拦的成像系统的退化机理,根据OTF的自相关特性,分别计算了系统在中心视场和边缘视场的OTF；完成了一个中心遮拦成像系统的光学,结构和系统的设计与加工；针对由该系统拍摄得到的不同遮拦比(原始,20%和30%)条件下的两种不同类型的退化图像(分辨率图和遥感图),计算系统的MTF,首先使用RL,TV和SD三种算法进行复原,然后使用GMG, LE, LS和MTFA四种客观评价方法对复原图进行了评价；针对由该系统拍摄得到的退化图像中的不同对比度(0.27,0.47和0.70)条件下的刃边区域,计算系统的MTF并使用SD算法进行复原,然后使用GMG,LE和LS三种客观评价方法对复原图进行评价。
High resolution earth observation is one of the key technologies in the space optical remote sensing. In remote sensing, ground sample distance (GSD) is the spacing of areas represented by each pixel in a digital photo of the ground from air or space. The purpose of high resolution earth observation is to seek a digital photo with a less GSD. GSD is determined by several factors, such as the pixel dimensions of the camera and the resolution of the optical system. To improve the resolution, we must enlarge the aperture of the system. However, a larger aperture will result in difficulties in aberration correction, fabrication and adjustment. Meanwhile, a larger aperture means more mass, which will increase the cost of launch. Therefore, the developments of high resolution earth observation focus on two aspects:one is to apply image processing to the optical system with a small aperture; the other is to use a reflection optical system combined with modulation transfer function compensation (MTFC).
How to estimate the MTF of the system accurately is the most important premise of MTFC. First, we introduce some methods that can be used to measure the MTF based on image analysis, such as pinhole method, slit method and edge method. Particularly, the slanted-edge method has been presented. Then, we analyze the factors, such as sample aperture of the sensor, finite differentiation of edge spread function (ESF), MTF compression in the frequency domain and noise in the image, which can affect the measurement. The corresponding correction methods have also been given. Finally, we propose a new analytical ESF fitting model to measure the MTF. By fitting the ESF data to the analytical expression, the LSF and the MTF can be easily calculated from the ESF fitting coefficients.
Second, we consider an optical system as a linear shift-invariant system (LSI), and establish a model to character its degradation and restoration. Some typical restoration algorithms and objective image quality metrics have been presented. Particularly, we introduce a method based on MTF.
Third, we analyze the degradation of an optical system with a circular aperture, and derive its optical transfer function (OTF) in both on-axis and off-axis fields. In simulation, four ESF fitting models and the ISO 12233 standard method have been used to estimate the MTF under different levels of noise (SNR=∞,30 and 20 dB). We compare them from both accuracy and complexity. Then we design and fabricate an imaging system, which is composed of a charge-coupled device (CCD) camera and an optical system with a small aperture. A resolution chart image and a remote sensing image have been used as objects, and we compute the MTF based on above five methods. Then, degraded images have been restored by Lucy-Richardson (RL), total variation (TV) and sparse deconvolution (SD), respectively. Finally, we assessed the restoration results by gray mean gradients (GMG), large entropy (LE), Laplacian summation (LS) and modulation transfer function area (MTFA), respectively.
At last, we analyze the degradation of an optical system with an obscuration aperture, and derive OTF of the system in both on-axis and off-axis fields. Then we design and fabricate an imaging system, which is composed of a digital camera and an optical system with an obscuration aperture. MTF under different levels of obscuration (10.56%,20% and 30%) have been computed. Then, degraded images have been restored by four restoration algorithms and evaluated by three objective image quality metrics, respectively. Similar processes have been applied to MTF calculation under different levels of contrast (0.27,0.47 and 0.70).
对于MTFC技术,如何精确估计系统的MTF乃是后期图像处理的基础和关键。首先,介绍了基于图像分析的各种传递函数测量方法,如针孔法,狭缝法和刃边法；其中,着重介绍了刃边法MTF测量的基本原理和计算流程；分析了成像器件的采样孔径,边缘扩散函数(edge spread function, ESF)的有限元差分,MTF的频率域压缩和刃边图像中的噪声等因素对MTF计算结果的影响,并给出了相应的校正方法；列举了已有的三种不同ESF函数模型,并从标量衍射理论出发,推导出一种新型的函数模型用于对ESF数据进行拟合,并通过它来计算得到系统的MTF。
其次,将成像过程看作是一个线性平移不变(linear shift-invariant, LSI)系统,建立了图像的退化和复原模型；介绍了常用的图像复原算法和图像质量客观评价方法,特别的,介绍了基于MTF的图像质量评价方法。
再次,分析了一个具有圆形光瞳的成像系统的退化机理,根据光学传递函数(optical transfer function, OTF)的自相关特性,推导了中心视场和边缘视场的OTF表达式；仿真实验中,针对不同噪声条件下(信噪比为∞,40和30 dB)的退化刃边图像,首先使用四种ESF函数模型和ISO 12233标准方法进行MTF计算,然后从计算精度和时间复杂度两个方面进行比较和分析；完成了一个小孔径成像系统的光学,结构和系统的设计与加工；实拍实验中,针对由该系统拍摄得到的两种不同类型的退化图像(分辨率板图和遥感图),基于四种ESF函数模型和ISO 12233标准方法计算系统的MTF,首先使用Lucy-Richardson (RL),总变分(total variation,TV)和稀疏反卷积(sparse deconvolution, SD)三种算法进行复原,然后使用灰度平均梯度(gray mean gradients, GMG),拉普拉斯算子和(Laplacian summation,LS),最大熵(large entropy, LE)和调制传递函数面积(modulation transfer function area, MTFA)四种客观评价方法对复原结果进行了评价。
最后,分析了一个具有中心遮拦的成像系统的退化机理,根据OTF的自相关特性,分别计算了系统在中心视场和边缘视场的OTF；完成了一个中心遮拦成像系统的光学,结构和系统的设计与加工；针对由该系统拍摄得到的不同遮拦比(原始,20%和30%)条件下的两种不同类型的退化图像(分辨率图和遥感图),计算系统的MTF,首先使用RL,TV和SD三种算法进行复原,然后使用GMG, LE, LS和MTFA四种客观评价方法对复原图进行了评价；针对由该系统拍摄得到的退化图像中的不同对比度(0.27,0.47和0.70)条件下的刃边区域,计算系统的MTF并使用SD算法进行复原,然后使用GMG,LE和LS三种客观评价方法对复原图进行评价。
High resolution earth observation is one of the key technologies in the space optical remote sensing. In remote sensing, ground sample distance (GSD) is the spacing of areas represented by each pixel in a digital photo of the ground from air or space. The purpose of high resolution earth observation is to seek a digital photo with a less GSD. GSD is determined by several factors, such as the pixel dimensions of the camera and the resolution of the optical system. To improve the resolution, we must enlarge the aperture of the system. However, a larger aperture will result in difficulties in aberration correction, fabrication and adjustment. Meanwhile, a larger aperture means more mass, which will increase the cost of launch. Therefore, the developments of high resolution earth observation focus on two aspects:one is to apply image processing to the optical system with a small aperture; the other is to use a reflection optical system combined with modulation transfer function compensation (MTFC).
How to estimate the MTF of the system accurately is the most important premise of MTFC. First, we introduce some methods that can be used to measure the MTF based on image analysis, such as pinhole method, slit method and edge method. Particularly, the slanted-edge method has been presented. Then, we analyze the factors, such as sample aperture of the sensor, finite differentiation of edge spread function (ESF), MTF compression in the frequency domain and noise in the image, which can affect the measurement. The corresponding correction methods have also been given. Finally, we propose a new analytical ESF fitting model to measure the MTF. By fitting the ESF data to the analytical expression, the LSF and the MTF can be easily calculated from the ESF fitting coefficients.
Second, we consider an optical system as a linear shift-invariant system (LSI), and establish a model to character its degradation and restoration. Some typical restoration algorithms and objective image quality metrics have been presented. Particularly, we introduce a method based on MTF.
Third, we analyze the degradation of an optical system with a circular aperture, and derive its optical transfer function (OTF) in both on-axis and off-axis fields. In simulation, four ESF fitting models and the ISO 12233 standard method have been used to estimate the MTF under different levels of noise (SNR=∞,30 and 20 dB). We compare them from both accuracy and complexity. Then we design and fabricate an imaging system, which is composed of a charge-coupled device (CCD) camera and an optical system with a small aperture. A resolution chart image and a remote sensing image have been used as objects, and we compute the MTF based on above five methods. Then, degraded images have been restored by Lucy-Richardson (RL), total variation (TV) and sparse deconvolution (SD), respectively. Finally, we assessed the restoration results by gray mean gradients (GMG), large entropy (LE), Laplacian summation (LS) and modulation transfer function area (MTFA), respectively.
At last, we analyze the degradation of an optical system with an obscuration aperture, and derive OTF of the system in both on-axis and off-axis fields. Then we design and fabricate an imaging system, which is composed of a digital camera and an optical system with an obscuration aperture. MTF under different levels of obscuration (10.56%,20% and 30%) have been computed. Then, degraded images have been restored by four restoration algorithms and evaluated by three objective image quality metrics, respectively. Similar processes have been applied to MTF calculation under different levels of contrast (0.27,0.47 and 0.70).
引文
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