退化图像的复原改进算法研究与实现
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摘要
退化图像根据对图像造成的视觉效果的不同，可分为两大类，即模糊图像和畸变图像。针对这两类退化图像的复原算法一直是图像处理领域的研究热点，本文也针对此进行了大量的实验研究。
模糊图像复原的关键是获得退化图像的点扩展函数或者其傅立叶变换的先验知识。经典复原算法都是以系统的点扩展函数已知为前提的，它具有复原效果好，复原速度快等优点，但在实际应用中由于系统的点扩展函数往往未知，使其受到实际应用的限制。盲复原算法可以在未知系统点扩展函数的情况下，通过模糊图像来估计系统点扩展函数进而复原原始图像，因此在实际应用中更具价值。但是目前的盲复原方法存在点扩展函数估计误差大、运算复杂等缺陷，影响了模糊图像的复原效果和复原速度。
本文通过对已有模糊图像复原算法的深入研究，针对上述两类复原算法目前存在的不足，提出了一种新型的自适应盲复原算法。该算法依据不同的降质方法会造成图像频谱中不同频率成份丢失的特点，通过有效的频谱变换和特征提取，实现了运动模糊、散焦模糊、高斯模糊以及其他模糊的自动分类，并对三种常见模糊通过相应的模糊参数辨识方法自动给出点扩展函数的精确估计，利用经典复原算法—维纳滤波实现了退化图像的复原；对于其他模糊系统自动采用改进的NAS-RIF盲复原算法进行复原。该算法最大的优点是兼顾了盲复原的广泛实用性和经典复原的良好复原性能，具有复原效果好、计算量小、复原适应性强等优点。
同时在运动模糊图像的模糊参数辨识中，通过对运动模糊图像的运动方向估计方法的深入研究，提出了有效的改进方法。首先将运动模糊图像进行3×3方向微分运算，然后将微分图像灰度值通过灰度线性变换，求取和值中的极大值来自动且有效地识别出运动方向。实验结果表明，改进的方法提高了计算精度并扩大了算法适用范围。
畸变图像的校正尤其是非线性畸变图像由于其非线性的复杂度，到目前为止仍未能得到很好的解决。传统的非线性畸变图像校正方法，需要建立畸变数学模型，不仅求解畸变参数复杂，计算量大，且存在很大的数值计算误差等问题。
本文通过对非线性光学畸变退化图像深入研究，利用人工神经网络通过学习训练畸变图像的输入输出数据来建立畸变图像与非畸变图像的映射关系，从而较好地实现了基于人工神经网络的图像畸变矫正，且实现方法简单。
Basing on the difference of vision influence brought, degraded image can be divided into two species: blur image and distortion image, so the restoration algorithm aiming at these images is a hotpot of the digital signal process and the paper also does many researches about this field.
The key of the image restoration problem is to obtain the prior knowledge of point spread function (PSF) or its Fourier Transform. If the estimate of PSF is inaccurate, the restoration image will be much worse. The original restoration methods are all based on the knowledge of PSF, they have the advantages of high restoration quality and fast computation. But the actual PSF of the system cannot be obtained usually which restricts the application of these methods. In the situation of unknown the knowledge of PSF, blind image restoration methods can restoration the blur image by estimating the PSF. But they have some false, such as large calculation、the large estimating error of PSF which influence the restoration quantity and speed.
In order to overcome these problems, an adaptive blind image restoration method is proposed. According to the feature that the certain blur may lead to the specific frequency component distortion of the image Fourier spectrum, we can automaticly classify the types of motion blur、defocus blur、gaussian blur and others by spectrum conversion and feature extraction. And then, we estimate the usual types of PSF with corresponding method and restore it with the typical method, while for others, we use an improved NAS-RIF blind restoration algorithm. The new method combines the typical methods and blind methods of image restoration, not only reduces the calculation quantity, but also has strong effectivity and good adaptivity.
Based on the research of the methods of identification of motion blur direction from motion blurred image, an improved method is proposed. First, convoluting with 3x3 direction derivation matrix, the motion blur image is derivatived, and then gray level transformation is applied to the values of the pixels of directional derivative of the image. Finally, motion direction is identified automatically by measuring the direction where the summation of the absolute transformed values of the pixels of the image derivative. The experimental results show that the improved method can not only improve the calculate precision, but also expand the application of the method.
The distorted images especially non-line distorted images have not been done well for the complexity of non-line. The normal distortion correction method for distorted images which obtains distortion coefficients by setting up a distortion model, but as the calculation is complicated and numerical error becomes a big problem.
The image of nonlinear distortion was researched through the research of non-line distorted. The relationship of the distortion image and the normal image had been built via the input-output data gained by the trained neural networks. And the nonlinear distorted image correction based on neural was reached.
模糊图像复原的关键是获得退化图像的点扩展函数或者其傅立叶变换的先验知识。经典复原算法都是以系统的点扩展函数已知为前提的，它具有复原效果好，复原速度快等优点，但在实际应用中由于系统的点扩展函数往往未知，使其受到实际应用的限制。盲复原算法可以在未知系统点扩展函数的情况下，通过模糊图像来估计系统点扩展函数进而复原原始图像，因此在实际应用中更具价值。但是目前的盲复原方法存在点扩展函数估计误差大、运算复杂等缺陷，影响了模糊图像的复原效果和复原速度。
本文通过对已有模糊图像复原算法的深入研究，针对上述两类复原算法目前存在的不足，提出了一种新型的自适应盲复原算法。该算法依据不同的降质方法会造成图像频谱中不同频率成份丢失的特点，通过有效的频谱变换和特征提取，实现了运动模糊、散焦模糊、高斯模糊以及其他模糊的自动分类，并对三种常见模糊通过相应的模糊参数辨识方法自动给出点扩展函数的精确估计，利用经典复原算法—维纳滤波实现了退化图像的复原；对于其他模糊系统自动采用改进的NAS-RIF盲复原算法进行复原。该算法最大的优点是兼顾了盲复原的广泛实用性和经典复原的良好复原性能，具有复原效果好、计算量小、复原适应性强等优点。
同时在运动模糊图像的模糊参数辨识中，通过对运动模糊图像的运动方向估计方法的深入研究，提出了有效的改进方法。首先将运动模糊图像进行3×3方向微分运算，然后将微分图像灰度值通过灰度线性变换，求取和值中的极大值来自动且有效地识别出运动方向。实验结果表明，改进的方法提高了计算精度并扩大了算法适用范围。
畸变图像的校正尤其是非线性畸变图像由于其非线性的复杂度，到目前为止仍未能得到很好的解决。传统的非线性畸变图像校正方法，需要建立畸变数学模型，不仅求解畸变参数复杂，计算量大，且存在很大的数值计算误差等问题。
本文通过对非线性光学畸变退化图像深入研究，利用人工神经网络通过学习训练畸变图像的输入输出数据来建立畸变图像与非畸变图像的映射关系，从而较好地实现了基于人工神经网络的图像畸变矫正，且实现方法简单。
Basing on the difference of vision influence brought, degraded image can be divided into two species: blur image and distortion image, so the restoration algorithm aiming at these images is a hotpot of the digital signal process and the paper also does many researches about this field.
The key of the image restoration problem is to obtain the prior knowledge of point spread function (PSF) or its Fourier Transform. If the estimate of PSF is inaccurate, the restoration image will be much worse. The original restoration methods are all based on the knowledge of PSF, they have the advantages of high restoration quality and fast computation. But the actual PSF of the system cannot be obtained usually which restricts the application of these methods. In the situation of unknown the knowledge of PSF, blind image restoration methods can restoration the blur image by estimating the PSF. But they have some false, such as large calculation、the large estimating error of PSF which influence the restoration quantity and speed.
In order to overcome these problems, an adaptive blind image restoration method is proposed. According to the feature that the certain blur may lead to the specific frequency component distortion of the image Fourier spectrum, we can automaticly classify the types of motion blur、defocus blur、gaussian blur and others by spectrum conversion and feature extraction. And then, we estimate the usual types of PSF with corresponding method and restore it with the typical method, while for others, we use an improved NAS-RIF blind restoration algorithm. The new method combines the typical methods and blind methods of image restoration, not only reduces the calculation quantity, but also has strong effectivity and good adaptivity.
Based on the research of the methods of identification of motion blur direction from motion blurred image, an improved method is proposed. First, convoluting with 3x3 direction derivation matrix, the motion blur image is derivatived, and then gray level transformation is applied to the values of the pixels of directional derivative of the image. Finally, motion direction is identified automatically by measuring the direction where the summation of the absolute transformed values of the pixels of the image derivative. The experimental results show that the improved method can not only improve the calculate precision, but also expand the application of the method.
The distorted images especially non-line distorted images have not been done well for the complexity of non-line. The normal distortion correction method for distorted images which obtains distortion coefficients by setting up a distortion model, but as the calculation is complicated and numerical error becomes a big problem.
The image of nonlinear distortion was researched through the research of non-line distorted. The relationship of the distortion image and the normal image had been built via the input-output data gained by the trained neural networks. And the nonlinear distorted image correction based on neural was reached.
引文
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[2] J L Harris. Image Evaluation and Restoration. J. Opt. Soc. Amen. 1966, 56(6): 569-574P
[3] B L McGlamery. Restoration of Turbulence Degraded Images. J. Opt. Soc. Amen. 1967, 57(3):293- 297P
[4] C W Helstrom. Image Restoration by the Method of Least Squares. J. Opt. Soc. Amen. 1967, 57(3):297-303P
[5] D Slepian. Linear Least-Squares Filtering of Distorted Images. J. Opt. Soc. Amen. 1967, 57(7):918-922P
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[7] A Habibi.Fast Suboptimal Wiener Filtering of Markov Processes. University of Southern California, USCIPI Report 530, Los Angeles. 1974(3): 75-80P
[8] T M Cannon.Digital Image Debluming by Nonlinear Homomorphic Filtering. Ph. D. Thesis, Computer Science Department, University of Utah, Salt Lake City. 1974,25-30P
[9] H C Andrews And B R Hunt. Digital Image Restoration. Prentice-Hall Inc. Englewood Cliffs, NJ. 1977,123-125P
[10] B R Hunt. A Matrix Theory Proof of the Discrete Convolution Theorem. IEEE. Trans. 1971,AU-19(4):285-288P
[11] B R Hunt. The Application of Constrained Least Estimation to Image Restoration by Digital Computer. IEEE Trans, 1973, C-22(9):805-812P
[12] G M Robbins, T S Huang. Inverse Filtering for Linear Shift-Variant Imaging. Systems.Proc. IEEE. 1972, 60(7):862- 872P
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[14] Y T Zhou, R Chellappa. Image restoration using a neural network. IEEE Trans. Speech, Signal Processing. 1988, 36(7):1141-1151P
[15] J K Paik,A K Katsaggelos. Image restoration using a modified Hopfield network. IEEE Trans. Image Processing. 1992,1(1):49-63P
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[18] R G Lane, R H Bates. Automatic multidimensional deconvolution. J. Opt. Soc. 1987, 4(1):180-188P
[19] D Kundur, D Hatzinakos. A novel blind deconvolution scheme for image restoration using recursive filtering. IEEE TRANS. On signal processing. 1998,46(2): 375-389P
[20] N P Galatsanos, V Z Mesarovic. Bayesian Image Restoration from Partially Known Blurs. IEEE Trans. Image. Processing. Oct 2000, 9(10): 1784-1797P
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[24] 戴或虹，袁亚湘．非线性共轭梯度法．上海：上海科学技术出版社，2000，10：121-124页
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[26] M M Chang,A M Tekalp,A T Erdem.Blur identification using the bispectrum. IEEE Trans. Signal Processing. 1991, 39(10):2323-2325P
[27] B Chalmond. PSF estimation for image deblurring. CVGIP:Graphical Models and Image Processing. 1991, 53(4):364-372P
[28] R Fabian,D Malah. Robust identification of motion and out-of-focus blur parameters from blurred and noisy images. CVGIP:Graphical Models and Image Processing. 1991, 53(5):403-412P
[29] M M Chang,A M Tekalp. Blur identification using the bispectrum.IEEE Trans. Signal Processing. 1991, 39(10):2323-2325P
[30] R Fabian, D Malah. Robust identification of motion and out-of-focus blur parameters from blurred and noisy images. CVGIP:Graphical Models and Image Processing.1991, 53(5):403-421P
[31] R G Lane, R H Bates, Automatic multidimensional deconvolution. Opt. Soc. Am. 1987,4(1):180-188P
[32] Chin Ann ong,A Joanthon.An enhanced NAS-RIF algorithm for blind image deconvolution.IEEE Trans. On signal processing.1997,8(7): 988-992P
[33] M Matsuyama, Y tanji.Enhancing the ability of NAS-RIF algorithm for blind image deconvolution.ISCAS 2000-IEEE international symposium on circults and systems.2005,5:553-556P
[34] T W Chow, Li xiao-dong.Improve blind image restoration using recurrent filtering.Vision,image and signal processing.IEEE Procedings.2000,147(1): 23-28P
[35] 谷口庆治．数字图像处理-基础篇．北京：科学出版社，2002：136-138页
[36] 阮秋琦．数字图像处理学．北京电子工业出版社，2001，7页
[37] J G Schave maker. Image sharpening by morphclogical filtering.Pattern Recognition. 2000,33:997-1012P
[38] 冯国进，顾国华，陈钱．基于形态学的红外图像边缘增强．激光与红外，2003，33(6)：453-454页
[39] 董立菊．图像阈值化技术的综述、分类及评价．沈阳大学学报．2004，16(4)：8-11页
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[41] M K Hu. Visual pattern recognition by moment invariant. IEEE Trans. on Information Theory. 1962,28:179-187P
[42] M Cannon.Blind deconvolution of spatially invariant image blurs width phase. IEEE Trans. Acoust. Speech Signal process. 1986P
[43] 王晓红，赵荣椿．匀速直线运动模糊的PSF之估计．计算机应用．2001，21(9)：40-41页
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[2] J L Harris. Image Evaluation and Restoration. J. Opt. Soc. Amen. 1966, 56(6): 569-574P
[3] B L McGlamery. Restoration of Turbulence Degraded Images. J. Opt. Soc. Amen. 1967, 57(3):293- 297P
[4] C W Helstrom. Image Restoration by the Method of Least Squares. J. Opt. Soc. Amen. 1967, 57(3):297-303P
[5] D Slepian. Linear Least-Squares Filtering of Distorted Images. J. Opt. Soc. Amen. 1967, 57(7):918-922P
[6] W K Pratt.Generalized Wiener Filter Computation Techniques. IEEE Trans, Computers. 1972(7): 636-641P
[7] A Habibi.Fast Suboptimal Wiener Filtering of Markov Processes. University of Southern California, USCIPI Report 530, Los Angeles. 1974(3): 75-80P
[8] T M Cannon.Digital Image Debluming by Nonlinear Homomorphic Filtering. Ph. D. Thesis, Computer Science Department, University of Utah, Salt Lake City. 1974,25-30P
[9] H C Andrews And B R Hunt. Digital Image Restoration. Prentice-Hall Inc. Englewood Cliffs, NJ. 1977,123-125P
[10] B R Hunt. A Matrix Theory Proof of the Discrete Convolution Theorem. IEEE. Trans. 1971,AU-19(4):285-288P
[11] B R Hunt. The Application of Constrained Least Estimation to Image Restoration by Digital Computer. IEEE Trans, 1973, C-22(9):805-812P
[12] G M Robbins, T S Huang. Inverse Filtering for Linear Shift-Variant Imaging. Systems.Proc. IEEE. 1972, 60(7):862- 872P
[13] A P Dempster, N M Laird and D B Rubin. Maximum likelihood from. incomplete data via the EM algorithm. J Royal Statiscal Ser. B. 1977, 39(1): 1-38P
[14] Y T Zhou, R Chellappa. Image restoration using a neural network. IEEE Trans. Speech, Signal Processing. 1988, 36(7):1141-1151P
[15] J K Paik,A K Katsaggelos. Image restoration using a modified Hopfield network. IEEE Trans. Image Processing. 1992,1(1):49-63P
[16] G R Ayers, J C Dainty. Iterative blind deconvolution method and its applications. Optics Letters. 1998,13(7):547-549P
[17] B C Macallum. Blind decovolution by simulated annealing. Optics Communications. 1990, 75(2):101-105P
[18] R G Lane, R H Bates. Automatic multidimensional deconvolution. J. Opt. Soc. 1987, 4(1):180-188P
[19] D Kundur, D Hatzinakos. A novel blind deconvolution scheme for image restoration using recursive filtering. IEEE TRANS. On signal processing. 1998,46(2): 375-389P
[20] N P Galatsanos, V Z Mesarovic. Bayesian Image Restoration from Partially Known Blurs. IEEE Trans. Image. Processing. Oct 2000, 9(10): 1784-1797P
[21] W Faig.Calibration of close-range photogrammetric systems mathematical form ulation.Photogrammetic engineering & Remote Sensing.1975,41: 1479～1486P
[22] 姜大志，郁倩，王冰洋等．计算机视觉成像的非线性畸变研究与综述．计算机工程．2001，27(12)：108-110页
[23] 廖士中，高培焕，苏艺等．一种光学镜头摄影机图像几何畸变的修正方法．中国图象图形学报．2000，5(7)：593～595页
[24] 戴或虹，袁亚湘．非线性共轭梯度法．上海：上海科学技术出版社，2000，10：121-124页
[25] M Cannon. Blind deconvolution of spatially invariant image blurs with phase.IEEE Trans. Acoust. Speech Signal Process. 1976, 24(1):58-63P
[26] M M Chang,A M Tekalp,A T Erdem.Blur identification using the bispectrum. IEEE Trans. Signal Processing. 1991, 39(10):2323-2325P
[27] B Chalmond. PSF estimation for image deblurring. CVGIP:Graphical Models and Image Processing. 1991, 53(4):364-372P
[28] R Fabian,D Malah. Robust identification of motion and out-of-focus blur parameters from blurred and noisy images. CVGIP:Graphical Models and Image Processing. 1991, 53(5):403-412P
[29] M M Chang,A M Tekalp. Blur identification using the bispectrum.IEEE Trans. Signal Processing. 1991, 39(10):2323-2325P
[30] R Fabian, D Malah. Robust identification of motion and out-of-focus blur parameters from blurred and noisy images. CVGIP:Graphical Models and Image Processing.1991, 53(5):403-421P
[31] R G Lane, R H Bates, Automatic multidimensional deconvolution. Opt. Soc. Am. 1987,4(1):180-188P
[32] Chin Ann ong,A Joanthon.An enhanced NAS-RIF algorithm for blind image deconvolution.IEEE Trans. On signal processing.1997,8(7): 988-992P
[33] M Matsuyama, Y tanji.Enhancing the ability of NAS-RIF algorithm for blind image deconvolution.ISCAS 2000-IEEE international symposium on circults and systems.2005,5:553-556P
[34] T W Chow, Li xiao-dong.Improve blind image restoration using recurrent filtering.Vision,image and signal processing.IEEE Procedings.2000,147(1): 23-28P
[35] 谷口庆治．数字图像处理-基础篇．北京：科学出版社，2002：136-138页
[36] 阮秋琦．数字图像处理学．北京电子工业出版社，2001，7页
[37] J G Schave maker. Image sharpening by morphclogical filtering.Pattern Recognition. 2000,33:997-1012P
[38] 冯国进，顾国华，陈钱．基于形态学的红外图像边缘增强．激光与红外，2003，33(6)：453-454页
[39] 董立菊．图像阈值化技术的综述、分类及评价．沈阳大学学报．2004，16(4)：8-11页
[40] M W Roth. Survey of neural network technology for automatic target recognition. IEEE Trans. on Neural Networks. 1990,1(1):28-43P
[41] M K Hu. Visual pattern recognition by moment invariant. IEEE Trans. on Information Theory. 1962,28:179-187P
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