基于光纤陀螺颤振探测的图像复原技术研究
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摘要
不论是在日常摄影还是在高分辨率遥感对地观测中,照明条件不佳都将意味着曝光时间的增长,随之而来的问题便是曝光过程中由于手抖动或平台颤振造成的图像模糊,大大损失了图像包含的信息。在数学上,图像模糊可以表述为清晰图像与点扩散函数(PSF)的卷积,再叠加一定噪声的结果,其逆过程称为图像复原或图像反卷积,是一个典型的病态问题,结果极易受到噪声放大和振铃等负面效应的影响,而正则化算法则能在一定程度上克服这些负面效应,提高复原图像的质量。图像复原算法有着极高的应用价值,尤其是在高分辨率遥感对地观测中,可以有效的避免由于设计制造大口径、长焦距成像系统以及相应的稳像设备而带来的成本急剧上升。为此,本文将图像复原算法作为研究重点,详细讨论了与其相关的若干关键问题,概括如下。
首先是PSF的获取。PSF在图像复原问题中扮演着至关重要的角色,传统的获取PSF的方法多种多样,比较经典的有点光源法和刃边法,以及S.K. Navar和M. Ben—Ezra提出的基于运动轨迹的PSF重构方法。针对颤振运动的特点,本文提出了一种基于光纤陀螺颤振探测的PSF重构方法。光纤陀螺是一种角速度敏感器件,具有结构紧凑,探测精度高的特点,将两个敏感轴互相垂直的光纤陀螺与相机光轴进行刚性连接,就能获取相机在曝光时间内的颤振角位置数据,进而根据物像关系得到像面上像的运动轨迹,重构出PSF。此外,本文还对传统的基于运动轨迹的PSF重构方法做了改进,利用设置较高采样频率的方法,将复杂的几何和插值运算转化为简单的统计运算,有效提高了运行效率。
按照PSF是否已知,可将图像复原算法分为非盲复原算法和盲复原算法两大类,本文在前人工作的基础上提出了三种正则化的非盲复原算法,它们分别是分段局部正则化的Richardson—Lucy(RL)算法,基于自然图像梯度先验分布的正则化RL算法和基于混合高斯型马尔可夫专家场(GSM FoE)的非盲复原算法。前两种算法都基于泊松噪声模型,是对标准RL算法的改进。在分段局部正则化的RL算法中,本文设计了一种基于高斯马尔可夫随机场的正则项,并通过一个分段幂函数,对其平滑强度加以调整,从而达到了抑制复原图像中的噪声放大和振铃效应的目的。与其相似,基于自然图像梯度先验分布的正则化RL算法是将自然图像梯度先验分布模型与泊松噪声模型相结合,由于自然图像梯度先验分布模型很好的符合了真实自然图像梯度的稀疏分布规律,因此该算法能够有效的改善标准RL算法的表现,得到高质量的复原图像。GSM FoE是在马尔可夫专家场(FoE)基础上提出的一种新型自然图像概率模型,与传统模型相比,其优势在于构成它的全部滤波器都是通过特殊的最优化方法,采用自然图像库训练得到的,因此它能够对自然图像进行更加准确的建模。本文将其引入非盲复原算法,并采用了Split Bregman算法对问题进行求解,实验结果表明,它是一种优秀的图像复原算法,达到或超过了目前一些主流复原算法的水平。
在盲复原算法方面,本文同样提出了三种方法,它们是基于马尔可夫专家场(FoE)的单幅图像盲复原算法,基于自然图像梯度先验分布的单幅图像盲复原算法和基于多幅图像的盲复原算法。其中,基于马尔可夫专家场的单幅图像盲复原算法的创新主要有两点,首先是将FoE模型引入盲复原算法,与GSM FoE相似,构成它的全部参数和滤波器都是由训练得到的,因此该模型的准确度很高。同时,还采用了基于Student-t函数的概率模型对PSF进行建模。其次,在问题求解上,本文改进了传统的轮换迭代算法,在每次迭代中,都将上次迭代所得的结果作为约束条件,因此克服了传统方法容易收敛到模糊解的缺点,得到了高质量的复原图像。基于自然图像梯度先验分布的单幅图像盲复原算法建立在基于自然图像梯度先验分布的正则化RL算法基础上,并采用了传统的轮换迭代算法求解,其不同之处在于对PSF进行优化时,用高斯概率模型对泊松概率模型做了近似,因而提高了运算速度和结果的准确度。最后,本文还提出了一种基于多幅图像的盲复原算法,它分别采用了自然图像梯度先验分布模型和基于L1范数的概率模型对清晰图像和PSF进行建模,由于多幅模糊图像包含了更多的信息,因此该算法能够得到高质量的复原图像和较为准确的PSF。
最后,本文还搭建了相应的实验系统对上述PSF重构方法和各种复原算法进行了验证,实验结果表明本文提出的基于光纤陀螺颤振探测的图像复原方法具有很强鲁棒性,能够对模糊图像实现有效复原,显著提高图像质量。同时,本文提出的几种图像复原算法也有较好的表现,其中基于混合高斯型马尔可夫专家场的非盲复原算法和基于马尔可夫专家场盲复原算法达到了或超过了目前一些主流图像复原算法的水平。
No matter in daily photography or high-resolution remote sensing, bad lighting condition means the increase of exposure time, the accompanied problem is, during the exposure time, the hand shake or platform vibration results in blurred images, which will greatly reduce the amount of information contained in the images. In mathematics, image blurring is modeled by convolving the clear image with a point spread function (PSF) plus some noise. Its inverse process is called image deconvolution, which is a typical ill-posed problem, the result is usually contaminated by amplified noise and ringing artifacts. However, regularization methods can be used to improve the performance of image deconvolution algorithm to achieve result of high quality. Image deconvolution algorithm is very useful, especially in the application of high-resolution remote sensing, which can effectively avoid the sharp rise of the cost caused by the design and manufacture of imaging systems with large aperture, long focal length and the corresponding stabilization equipments. Therefore, the thesis focuses on the image deconvolution algorithm and detailed discusses some key problems about it, which are summarized as follows.
The first is about how to obtain the PSF. PSF plays a very important role in image deconvolution. There are various methods which can be adopted to achieve it, such as the point lighting source method, the knife edge method and the method based on motion trajectory which is proposed by S.K.Nayar and M.Ben-Ezra. According to the characteristics of vibration, we propose a PSF reconstruction method using the fiber optic gyroscope. The fiber optic gyroscope is a kind of angular velocity sensing device, which has the advantages of compact structure and high detection accuracy. We rigidly connect two fiber optic gyroscopes whose sensitive axes are perpendicular to each other to the optical axis of the camera, such that we can get the angle position of the vibration in two directions during the exposure time, then according to the relationship between the object and the image, we can obtain the motion trajectory of the image and reconstruct the PSF. In addition, we also improve the traditional PSF reconstruction method based on motion trajectory. In the improved version, with the method of setting a high sampling frequency, the complicated geometric and interpolation calculations are converted into a simple statistical calculation, and thus enhance the efficiency.
According to whether the PSF is known, image deconvolution algorithms can be divided into two kinds, i.e., non-blind and blind image deconvolution. The thesis propose three non-blind image deconvolution algorithms, they are the piecewise local regularized Richardson-Lucy (RL) algorithm, the regularized RL algorithm based on natural image gradient prior and the algorithm based on Gaussian Scale Mixture Fields of Experts (GSM FoE) prior. The first two are derived from the model of Poisson noise, which are all improved versions of standard RL algorithm. In the piecewise local regularized RL algorithm, we design a regularization term based on the Gaussian Markov random field, and adopt a piecewise power function to adjust the smoothing strength to suppress the amplified noise and ringing artifacts in the restored image. Similarly, in the regularized RL algorithm based on natural image gradient prior, the model of Poisson noise is combined with the prior of image gradient, because the prior is in good agreement with the sparse probabilistic distribution of the gradient of nature images, the algorithm can efficiently improve the performance of standard RL algorithm and reach result of high quality. GSM FoE which is derived from Fields of Experts (FoE) is a very effective probabilistic model for natural image, in contrast to traditional priors, its advantage is that all the filters used to construct the GSM FoE prior are trained with a database, thus it can seize the characteristics of natural images more accurately. The thesis introduces this prior into non-blind image deconvolution and adopts the Split Bregman method to solve the resulted cost function. Experimental results show that its performance meets or exceeds some state of the art methods.
The thesis also proposes three blind image deconvolution algorithms, i.e., the single image deconvolution algorithm based on Fields of Experts (FoE) prior, the single image deconvolution algorithm based on natural image gradient prior and the deconvolution algorithm with multiple blurred images. There are two innovations in the single image deconvolution algorithm based on FoE prior. Firstly, we introduce the FoE prior into blind image deconvolution. similar to the GSM FoE prior, all its parameters and filters are trained from natural images, thus it is of high accuracy. Meanwhile, a prior based on Student-t function is also used to regularize the PSF.
Secondly, we improve the traditional alternating minimization (AM) algorithm which is usually used to solve the problem of blind image deconvolution. In each iteration of the improved algorithm, the mid-restored image obtained from the former iteration is used as a constraint, and thus it will not converge to the unwanted "blurry" result. The single image deconvolution algorithm based on natural image gradient prior adopts the proposed regularized RL algorithm with natural image gradient prior. The result is reached by the traditional AM algorithm. The innovation is that the Gaussian noise model is used to approximate the Poisson noise model to estimate the PSF, so the computation speed and accuracy are enhanced. We also propose a blind image deconvolution algorithm adopting multiple blurred images, the natural image gradient prior and a L1norm based prior is used to regularize the clear image and the PSF respectively. Since multiple frames contain more information about the clear image, it can achieve results of high quality.
Finally, we also set up experimental system to verify the effectiveness of the proposed PSF reconstruction method and the image deconvolution algorithms. The results show that the image deconvolution method based on vibration detection using fiber optic gyroscope is robust, it can effectively enhance the quality of the obtained image. Meanwhile, the performances of the deconvolution algorithms proposed in this thesis are also good. Especially, the blind image deconvolution algorithm based on the FoE prior and the non-blind image deconvolution algorithm based on the GSM FoE prior are comparable with some state of the art methods.
首先是PSF的获取。PSF在图像复原问题中扮演着至关重要的角色,传统的获取PSF的方法多种多样,比较经典的有点光源法和刃边法,以及S.K. Navar和M. Ben—Ezra提出的基于运动轨迹的PSF重构方法。针对颤振运动的特点,本文提出了一种基于光纤陀螺颤振探测的PSF重构方法。光纤陀螺是一种角速度敏感器件,具有结构紧凑,探测精度高的特点,将两个敏感轴互相垂直的光纤陀螺与相机光轴进行刚性连接,就能获取相机在曝光时间内的颤振角位置数据,进而根据物像关系得到像面上像的运动轨迹,重构出PSF。此外,本文还对传统的基于运动轨迹的PSF重构方法做了改进,利用设置较高采样频率的方法,将复杂的几何和插值运算转化为简单的统计运算,有效提高了运行效率。
按照PSF是否已知,可将图像复原算法分为非盲复原算法和盲复原算法两大类,本文在前人工作的基础上提出了三种正则化的非盲复原算法,它们分别是分段局部正则化的Richardson—Lucy(RL)算法,基于自然图像梯度先验分布的正则化RL算法和基于混合高斯型马尔可夫专家场(GSM FoE)的非盲复原算法。前两种算法都基于泊松噪声模型,是对标准RL算法的改进。在分段局部正则化的RL算法中,本文设计了一种基于高斯马尔可夫随机场的正则项,并通过一个分段幂函数,对其平滑强度加以调整,从而达到了抑制复原图像中的噪声放大和振铃效应的目的。与其相似,基于自然图像梯度先验分布的正则化RL算法是将自然图像梯度先验分布模型与泊松噪声模型相结合,由于自然图像梯度先验分布模型很好的符合了真实自然图像梯度的稀疏分布规律,因此该算法能够有效的改善标准RL算法的表现,得到高质量的复原图像。GSM FoE是在马尔可夫专家场(FoE)基础上提出的一种新型自然图像概率模型,与传统模型相比,其优势在于构成它的全部滤波器都是通过特殊的最优化方法,采用自然图像库训练得到的,因此它能够对自然图像进行更加准确的建模。本文将其引入非盲复原算法,并采用了Split Bregman算法对问题进行求解,实验结果表明,它是一种优秀的图像复原算法,达到或超过了目前一些主流复原算法的水平。
在盲复原算法方面,本文同样提出了三种方法,它们是基于马尔可夫专家场(FoE)的单幅图像盲复原算法,基于自然图像梯度先验分布的单幅图像盲复原算法和基于多幅图像的盲复原算法。其中,基于马尔可夫专家场的单幅图像盲复原算法的创新主要有两点,首先是将FoE模型引入盲复原算法,与GSM FoE相似,构成它的全部参数和滤波器都是由训练得到的,因此该模型的准确度很高。同时,还采用了基于Student-t函数的概率模型对PSF进行建模。其次,在问题求解上,本文改进了传统的轮换迭代算法,在每次迭代中,都将上次迭代所得的结果作为约束条件,因此克服了传统方法容易收敛到模糊解的缺点,得到了高质量的复原图像。基于自然图像梯度先验分布的单幅图像盲复原算法建立在基于自然图像梯度先验分布的正则化RL算法基础上,并采用了传统的轮换迭代算法求解,其不同之处在于对PSF进行优化时,用高斯概率模型对泊松概率模型做了近似,因而提高了运算速度和结果的准确度。最后,本文还提出了一种基于多幅图像的盲复原算法,它分别采用了自然图像梯度先验分布模型和基于L1范数的概率模型对清晰图像和PSF进行建模,由于多幅模糊图像包含了更多的信息,因此该算法能够得到高质量的复原图像和较为准确的PSF。
最后,本文还搭建了相应的实验系统对上述PSF重构方法和各种复原算法进行了验证,实验结果表明本文提出的基于光纤陀螺颤振探测的图像复原方法具有很强鲁棒性,能够对模糊图像实现有效复原,显著提高图像质量。同时,本文提出的几种图像复原算法也有较好的表现,其中基于混合高斯型马尔可夫专家场的非盲复原算法和基于马尔可夫专家场盲复原算法达到了或超过了目前一些主流图像复原算法的水平。
No matter in daily photography or high-resolution remote sensing, bad lighting condition means the increase of exposure time, the accompanied problem is, during the exposure time, the hand shake or platform vibration results in blurred images, which will greatly reduce the amount of information contained in the images. In mathematics, image blurring is modeled by convolving the clear image with a point spread function (PSF) plus some noise. Its inverse process is called image deconvolution, which is a typical ill-posed problem, the result is usually contaminated by amplified noise and ringing artifacts. However, regularization methods can be used to improve the performance of image deconvolution algorithm to achieve result of high quality. Image deconvolution algorithm is very useful, especially in the application of high-resolution remote sensing, which can effectively avoid the sharp rise of the cost caused by the design and manufacture of imaging systems with large aperture, long focal length and the corresponding stabilization equipments. Therefore, the thesis focuses on the image deconvolution algorithm and detailed discusses some key problems about it, which are summarized as follows.
The first is about how to obtain the PSF. PSF plays a very important role in image deconvolution. There are various methods which can be adopted to achieve it, such as the point lighting source method, the knife edge method and the method based on motion trajectory which is proposed by S.K.Nayar and M.Ben-Ezra. According to the characteristics of vibration, we propose a PSF reconstruction method using the fiber optic gyroscope. The fiber optic gyroscope is a kind of angular velocity sensing device, which has the advantages of compact structure and high detection accuracy. We rigidly connect two fiber optic gyroscopes whose sensitive axes are perpendicular to each other to the optical axis of the camera, such that we can get the angle position of the vibration in two directions during the exposure time, then according to the relationship between the object and the image, we can obtain the motion trajectory of the image and reconstruct the PSF. In addition, we also improve the traditional PSF reconstruction method based on motion trajectory. In the improved version, with the method of setting a high sampling frequency, the complicated geometric and interpolation calculations are converted into a simple statistical calculation, and thus enhance the efficiency.
According to whether the PSF is known, image deconvolution algorithms can be divided into two kinds, i.e., non-blind and blind image deconvolution. The thesis propose three non-blind image deconvolution algorithms, they are the piecewise local regularized Richardson-Lucy (RL) algorithm, the regularized RL algorithm based on natural image gradient prior and the algorithm based on Gaussian Scale Mixture Fields of Experts (GSM FoE) prior. The first two are derived from the model of Poisson noise, which are all improved versions of standard RL algorithm. In the piecewise local regularized RL algorithm, we design a regularization term based on the Gaussian Markov random field, and adopt a piecewise power function to adjust the smoothing strength to suppress the amplified noise and ringing artifacts in the restored image. Similarly, in the regularized RL algorithm based on natural image gradient prior, the model of Poisson noise is combined with the prior of image gradient, because the prior is in good agreement with the sparse probabilistic distribution of the gradient of nature images, the algorithm can efficiently improve the performance of standard RL algorithm and reach result of high quality. GSM FoE which is derived from Fields of Experts (FoE) is a very effective probabilistic model for natural image, in contrast to traditional priors, its advantage is that all the filters used to construct the GSM FoE prior are trained with a database, thus it can seize the characteristics of natural images more accurately. The thesis introduces this prior into non-blind image deconvolution and adopts the Split Bregman method to solve the resulted cost function. Experimental results show that its performance meets or exceeds some state of the art methods.
The thesis also proposes three blind image deconvolution algorithms, i.e., the single image deconvolution algorithm based on Fields of Experts (FoE) prior, the single image deconvolution algorithm based on natural image gradient prior and the deconvolution algorithm with multiple blurred images. There are two innovations in the single image deconvolution algorithm based on FoE prior. Firstly, we introduce the FoE prior into blind image deconvolution. similar to the GSM FoE prior, all its parameters and filters are trained from natural images, thus it is of high accuracy. Meanwhile, a prior based on Student-t function is also used to regularize the PSF.
Secondly, we improve the traditional alternating minimization (AM) algorithm which is usually used to solve the problem of blind image deconvolution. In each iteration of the improved algorithm, the mid-restored image obtained from the former iteration is used as a constraint, and thus it will not converge to the unwanted "blurry" result. The single image deconvolution algorithm based on natural image gradient prior adopts the proposed regularized RL algorithm with natural image gradient prior. The result is reached by the traditional AM algorithm. The innovation is that the Gaussian noise model is used to approximate the Poisson noise model to estimate the PSF, so the computation speed and accuracy are enhanced. We also propose a blind image deconvolution algorithm adopting multiple blurred images, the natural image gradient prior and a L1norm based prior is used to regularize the clear image and the PSF respectively. Since multiple frames contain more information about the clear image, it can achieve results of high quality.
Finally, we also set up experimental system to verify the effectiveness of the proposed PSF reconstruction method and the image deconvolution algorithms. The results show that the image deconvolution method based on vibration detection using fiber optic gyroscope is robust, it can effectively enhance the quality of the obtained image. Meanwhile, the performances of the deconvolution algorithms proposed in this thesis are also good. Especially, the blind image deconvolution algorithm based on the FoE prior and the non-blind image deconvolution algorithm based on the GSM FoE prior are comparable with some state of the art methods.
引文
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