波前编码成像系统解码算法理论研究及其应用
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摘要
波前编码光数混合系统是一种光学编码和数字解码的两步成像系统,通过在光学系统的光瞳面上引入一块相位板,在像面上得到一幅对景深不敏感的中间模糊像,再利用数字图像复原算法进行图像复原,最终得到清晰的输出像。通过这种技术可以获得超大的景深,提高系统的成像质量。目前制约该技术的主要是解码算法存在着边界效应,图像的细节丢失严重,图像不自然等缺点。
本文首先从空间域成像卷积过程入手,讨论了光学系统成像的物理原理,在数学上将其归结为一个空间域线性方程组求解的问题,进一步讨论了边界处理后的线性方程组中线性模糊矩阵的构建方法,利用直积近似的原理将线性方程组的求解问题归结为矩阵方程的求解问题,完成了成像卷积的空间域数学模型的搭建。在此基础上,分析了克雷洛夫子空间在线性方程组求解方面的优势,开发出了两大类图像去卷积空间域迭代算法,即基于广义极小残差法和无转置准极小残差法的图像去卷积复原算法,两类算法都有着优秀的去卷积效果,第一类算法构建了完全正交基,能够给出更加精确的近似解,第二类算法计算存储量小,计算时间少,是第一类算法有益的补充。针对第一类算法,成功的将其与Tikhonov规整化算法及反镜边界条件结合,研究出了一套有效的去卷积抑噪图像空间域迭代复原算法,利用三通道处理原理,给出了最终的彩色图像空间域迭代复原算法,实验结果证明该算法能够给出细腻、自然的复原图像。
其次,首次提出了空间域边界处理和频域快速图像复原算法,利用空间域边界条件的原理,首先将待复原图像进行边界扩展处理,然后再进行频域滤波复原,分析了图像进行边界扩展处理后的频谱特性及其对复原图像边界的影响,实验证明该算法在镜像和反镜像边界处理下,不仅计算速度快,而且有着优秀的去卷积抑噪效果,同时还能有效的减少复原图像的边界振铃效应。
第三,在现有国产普通显微物镜的基础上设计了10X、40X波前编码显微成像物镜,利用我们给出的空间域迭代算法和空域边界处理频域快速复原算法分别进行了图像解码,都取得了很好的效果。尽管由于国产普通显微物镜的光学性能比较差,导致波前编码系统的点扩散函数和调制传递函数有一定的偏差,但是借助我们的算法仍然给出令人满意的结果。
最后,首次提出了利用波前编码系统进行水下成像的应用,利用波前编码系统的大像差特性对水体本身和水下散射进行调制,再利用我们给出的空间域迭代算法进行复原,可以消除水体本身和水下散射对成像的影响。从实验中得到的复原图像对比度明显增强,细节更加丰富,证明了该思路的可行性。
Wavefront coding hybrid optical-digital system is a two-step imaging system. A cubic phase mask is positioned on the pupil plane, in the image plane a defocus-insensitive but blurred intermediate image is acquired, the final sharp image can be given by using the digital image restoration algorithms. This technology can give large depth of field and improve the imaging quality. At present, the deblurring algorithms restrict the development of the technology. The restored image has serious boundary effect, loses more details and does not look natural.
Firstly, we consider the process of the image convolution, and discuss the theory of the optical imaging, then take the process to the solution procedure of the linear equations in mathematics, further we analyze the building method of the linear blurring matrix on different boundary conditions, by using the Kronecker production, finally a matrix equations can be given which stands for the process of the image convolution. Then the Krylov subspace method is discussed and used to solve the matrix equations. Two kinds of domain iterative image deconvolution space algorithms based on the Krylov subspace are given such as generalized minimal residual method (GMRES), and transpose-free quasi-minimal residual algorithm. Both of them have excellent deconvolution effect, the first method constructs complete orthogonal basis and can give exact approximate solution; the second method needs less storage and less computation time than the GMRES method, which is a useful supplement of the first one. Then we combine the Tikhonov reguralization and anti-reflective-boundary conditons, and a space domain iterative algorithm with excellent deconvolution and noise suppression effect is given. Finally by using the three channel principle the space domain iterative color image algorithm is acquired, the experiment shows that the new algorithm can give smooth and natural restored image.
Secondly, a novel image restoration algorithm based on boundary pre-processing in the space domain and fast computing in the frequency domain is proposed for the first time. By using the theory of the boundary conditions, we can get the image which is enlarged by the different boundary hypothesis, then the frequency filtering is used to find the restored result. The frequency property of the enlarged image and the effect to the boundary of the restored image are analyzed. Effectiveness and speediness of the proposed method was demonstrated by experiment results, which can give excellent deconvolution and noise suppression restored image and reduce the boundary ringing effect under the reflective and antireflective boundary condtions.
Thirdly, the 10X and 40X wavefront coding microscopy based on the classical domestic micro objective are designed, which give excellent results by using proposed two algorithms. Although the optical performance of the classical domestic micro objective is poor, and the wavefront coding system could not give exactly similar PSF and MTF, but our proposed image restoration algorithms can still give satisfactory results.
Finaly, we proposed to underwater imaging by using the wavefront coding system for the first time. The water's aberration and scattering can be modulated by the large aberrations introduced by the cubic phase mask, which can be eliminated by using the image restoration algorithm. The experiment showes that the contrast enhanced and more details restored image can be given. It is a validity and feasibility method.
本文首先从空间域成像卷积过程入手,讨论了光学系统成像的物理原理,在数学上将其归结为一个空间域线性方程组求解的问题,进一步讨论了边界处理后的线性方程组中线性模糊矩阵的构建方法,利用直积近似的原理将线性方程组的求解问题归结为矩阵方程的求解问题,完成了成像卷积的空间域数学模型的搭建。在此基础上,分析了克雷洛夫子空间在线性方程组求解方面的优势,开发出了两大类图像去卷积空间域迭代算法,即基于广义极小残差法和无转置准极小残差法的图像去卷积复原算法,两类算法都有着优秀的去卷积效果,第一类算法构建了完全正交基,能够给出更加精确的近似解,第二类算法计算存储量小,计算时间少,是第一类算法有益的补充。针对第一类算法,成功的将其与Tikhonov规整化算法及反镜边界条件结合,研究出了一套有效的去卷积抑噪图像空间域迭代复原算法,利用三通道处理原理,给出了最终的彩色图像空间域迭代复原算法,实验结果证明该算法能够给出细腻、自然的复原图像。
其次,首次提出了空间域边界处理和频域快速图像复原算法,利用空间域边界条件的原理,首先将待复原图像进行边界扩展处理,然后再进行频域滤波复原,分析了图像进行边界扩展处理后的频谱特性及其对复原图像边界的影响,实验证明该算法在镜像和反镜像边界处理下,不仅计算速度快,而且有着优秀的去卷积抑噪效果,同时还能有效的减少复原图像的边界振铃效应。
第三,在现有国产普通显微物镜的基础上设计了10X、40X波前编码显微成像物镜,利用我们给出的空间域迭代算法和空域边界处理频域快速复原算法分别进行了图像解码,都取得了很好的效果。尽管由于国产普通显微物镜的光学性能比较差,导致波前编码系统的点扩散函数和调制传递函数有一定的偏差,但是借助我们的算法仍然给出令人满意的结果。
最后,首次提出了利用波前编码系统进行水下成像的应用,利用波前编码系统的大像差特性对水体本身和水下散射进行调制,再利用我们给出的空间域迭代算法进行复原,可以消除水体本身和水下散射对成像的影响。从实验中得到的复原图像对比度明显增强,细节更加丰富,证明了该思路的可行性。
Wavefront coding hybrid optical-digital system is a two-step imaging system. A cubic phase mask is positioned on the pupil plane, in the image plane a defocus-insensitive but blurred intermediate image is acquired, the final sharp image can be given by using the digital image restoration algorithms. This technology can give large depth of field and improve the imaging quality. At present, the deblurring algorithms restrict the development of the technology. The restored image has serious boundary effect, loses more details and does not look natural.
Firstly, we consider the process of the image convolution, and discuss the theory of the optical imaging, then take the process to the solution procedure of the linear equations in mathematics, further we analyze the building method of the linear blurring matrix on different boundary conditions, by using the Kronecker production, finally a matrix equations can be given which stands for the process of the image convolution. Then the Krylov subspace method is discussed and used to solve the matrix equations. Two kinds of domain iterative image deconvolution space algorithms based on the Krylov subspace are given such as generalized minimal residual method (GMRES), and transpose-free quasi-minimal residual algorithm. Both of them have excellent deconvolution effect, the first method constructs complete orthogonal basis and can give exact approximate solution; the second method needs less storage and less computation time than the GMRES method, which is a useful supplement of the first one. Then we combine the Tikhonov reguralization and anti-reflective-boundary conditons, and a space domain iterative algorithm with excellent deconvolution and noise suppression effect is given. Finally by using the three channel principle the space domain iterative color image algorithm is acquired, the experiment shows that the new algorithm can give smooth and natural restored image.
Secondly, a novel image restoration algorithm based on boundary pre-processing in the space domain and fast computing in the frequency domain is proposed for the first time. By using the theory of the boundary conditions, we can get the image which is enlarged by the different boundary hypothesis, then the frequency filtering is used to find the restored result. The frequency property of the enlarged image and the effect to the boundary of the restored image are analyzed. Effectiveness and speediness of the proposed method was demonstrated by experiment results, which can give excellent deconvolution and noise suppression restored image and reduce the boundary ringing effect under the reflective and antireflective boundary condtions.
Thirdly, the 10X and 40X wavefront coding microscopy based on the classical domestic micro objective are designed, which give excellent results by using proposed two algorithms. Although the optical performance of the classical domestic micro objective is poor, and the wavefront coding system could not give exactly similar PSF and MTF, but our proposed image restoration algorithms can still give satisfactory results.
Finaly, we proposed to underwater imaging by using the wavefront coding system for the first time. The water's aberration and scattering can be modulated by the large aberrations introduced by the cubic phase mask, which can be eliminated by using the image restoration algorithm. The experiment showes that the contrast enhanced and more details restored image can be given. It is a validity and feasibility method.
引文
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[2]赵廷玉,张文字,叶子,刘玉玲,余飞鸿,基于波前编码的光数混合景深延拓技术的研究,光学仪器,2006,28(6),43-47
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