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1、华中科技大学博士学位论文 I摘摘 要要 目标通过大气湍流的成像是工作在湍流大气环境中机/弹载光学成像传感器系统必然会遇到的问题。在光线进入成像传感器窗口之前，大气湍流随机地干扰来自目标的辐射的传播，使成像焦平面产生像点强度分布扩散、峰值降低、图像模糊和位置偏移等气动光学效应，给目标识别带来了很大的困难。气动光学效应湍流退化图像的复原是一个世界性难题，它的研究富有挑战性。湍流退化图像复原的困难之处在于其点扩展函数是未知的和随机变化的，且难以用数学解析式表述。本文针对气动光学效应湍流退化图像的复原问题开展了研究，主要涉及湍流退化图像复原算法研究，同时对机/弹载成像平台旋转运动所引起的空间可变模糊图
2、像的复原问题进行了研究，主要工作包括： 1. 在湍流退化图像复原问题中，湍流随机点扩展函数值的正确估计是其核心部分。本文提出了一种基于估计湍流点扩展函数离散值的湍流退化图像复原算法，采用两帧短曝光湍流退化图像来建立关于湍流点扩展函数离散值计算的数学模型。对所建立的数学模型即线性方程组的稳定性与其条件数的关系进行了扰动理论分析，制定了一些行之有效的挑选方程的规则。为克服噪声对点扩展函数值估计的干扰，在点扩展函数值非负和空间相关性的约束条件下，将计算问题转化为基于非负最小二乘的约束优化估计问题，给出了一种基于非负和空间相关性约束的点扩展函数离散值的优化估计方法。将约束优化理论应用到湍流退化图像复原
3、中，为湍流退化图像的恢复提供了一种新途径。 2. 在有噪声的情况下，为了从两帧湍流退化图像中有效地估计出与真实情况接近的湍流点扩展函数离散值，提出了一种基于各向异性和非线性正则化的湍流退化图像复原新算法。在点扩展函数离散值的优化估计过程中合理地融合了有关湍流点扩展函数的一些先验知识，首先将点扩展函数的非负性和光滑性约束转化为数学上可表达的惩罚项，加入到目标函数中，同时针对湍流点扩展函数的衰减性质，建立了一个具有非线性和各向异性的正则化函数，使其在估计点扩展函数值时能自适应地进行梯度平滑。通过迭代极小化目标函数估计湍流点扩展函数值，进而恢复图像。 华中科技大学博士学位论文 II3. 从信号空间分
4、解出发，建立了湍流退化图像的小波多分辨率矩阵表达式，给出了一种基于小波分解的湍流退化图像的多分辨率复原新方法。主要思路是通过小波的多尺度空间分解，利用湍流退化图像在大尺度空间上的逼近信息，估计出其在低分辨率上的点扩展函数值，在低频子频段去模糊，在高频子频段抑制噪声和保边缘信息，然后通过小波逆变换重建目标原图像。将小波变换与分解的多分辨特性和时频局部化特性应用在湍流退化图像的盲目复原中，降低了算法的计算复杂性并提高了其抗噪能力。 4. 为了从序列多帧湍流退化图像中将目标图像有效地恢复出来，给出了一种新颖的基于图像随机场模型的交替迭代复原算法。根据图像Poisson随机场概率模型假定,建立了多帧图
5、像的联合对数似然函数,推导和建立了目标图像及各帧点扩展函数的交替迭代求解公式。通过迭代寻找最相似于序列退化图像的各帧点扩展函数和目标的估计，从而保证在概率意义上极大程度地恢复出目标图像。为了提高计算效率，给出了一种整体数据输入、分块计算复原的并行处理方案。 5. 对极大似然估计复原算法的正则化技术进行了研究。为了平滑噪声同时保存图像细节以及避免无价值的解，对极大似然估计复原方法进行一些改进，将基于保细节的平滑准则及辅助惩罚项加入到对数似然函数中，给出了一种基于正则化技术的极大似然估计图像复原的算法。通过引用EM算法来有效地极大化带有平滑项的对数似然函数，推导出了点扩展函数和目标图像的迭代求解公
6、式。 6. 针对成像平台随弹体/机体作旋转运动时所形成的空间可变模糊图像的复原问题，提出了一种沿模糊路径去卷积的快速复原算法。该方法避免了传统的费时的几何坐标转换，将旋转运动空间可变模糊沿模糊路径分解为一系列的空不变模糊，沿模糊路径去除模糊。同时，为了恢复矩形图像角点处的灰度信息，提出了一种基于邻域知识引导的最小代价复原算法，且避开了迭代计算。另外，为了确定旋转运动模糊参数，给出了一种基于互相关的旋转模糊参数识别方法。 关键词关键词：气动光学，图像复原，湍流退化图像，点扩展函数，约束优化估计，盲目去卷积，正则化，小波分解，极大似然估计，旋转空变模糊 华中科技大学博士学位论文 IIIAbstra
7、ct The imaging of objects through atmospheric turbulence is an inevitable problem encountered by optical imaging sensors mounted in missiles or machines working in the turbulence atmospheric environment. Owing to the existence of the atmosphere, before light-rays enter the window of the imaging sens
8、ors, the atmospheric turbulence will randomly interfere with the transmission of the light waves came from the objects, causing the distribution of image intensity values on the focal plane to diffuse, the peak value to decrease, the image to get blurred, and the pixels to deviate, and making object
9、 identification very difficult. Owing to the fact that the point spread function of turbulence is unknown, changable with time, and hard to be described by mathematics models, the restoration of turbulence-degraded images is much more difficult and challenging in the world. This paper concerns the r
10、estoration of turbulence-degraded images, focusing the research on the new restoration algorithms. Meanwhile, the restoration algorithm of images blurred by the high rotational motion of the imaging platform mounted in a missile or a machine is also investigated in this paper. The main contributions
11、 of this paper are given below. 1. For the problem of restoration of turbulence-degraded images, it is of utmost importance to make a correct estimation of the turbulence s stochastic point spread function (PSF). A new method is proposed for estimating the discrete values of the turbulence PSFs, in
12、which two short-exposure images are used as the inputs and a series of equations for calculating the discrete values of the PSFs are developed. The relationship of the stability of the solution for a system of equations and the conditional number of its coefficient matrix has been analyzed. On the b
13、asis of theoretical investigation, some effective rules for selecting equations have been worked out to ensure a reliable solution for the PSFs. In order to overcome the interference of noise, the principle of constraint optimization has been applied in the algorithm, in which the problem of calcula
14、ting the PSF values has been boiled down to the least-squares optimum estimation under the constraint of the PSF values being non-negative and spatial smoothing. Thus, a restoration algorithm based on the optimum estimation of the PSF values is proposed, which provides a new method for the restorati
15、on of turbulence-degraded images. 华中科技大学博士学位论文 IV2. A new restoration algorithm based on anisotropic and nonlinear regularization is presented for restoring the turbulence-degraded images, in which, in order to estimate the PSF values that are close to the true ones in noisy cases, some a priori kno
16、wledge about turbulence PSFs are incorporated properly in the process of optimum estimation. Firstly, the constraints of the PSF values being non-negative and spatial smoothing are transformed mathematically into the penalty terms and added them to the objective function. Secondly, to match the decay nature of turbulence PSFs, an anisotropic and nonlinear regularization function is suggested to regulate the PSF values adequately in the process of rebuilding PSF. The PSF values can be esti
