基于正则化的超分辨率图像序列重建技术研究
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摘要
在当前数字图像应用领域,由于受成像系统物理条件和气候条件等因素的影响,在成像过程中常常存在光学模糊和运动模糊、降采样和噪声等退化过程,这使得实际获取的图像发生降质,导致图像的分辨率达不到应用的要求。超分辨率图像序列重建技术的思想是利用低分辨率图像序列获得高分辨率图像,这恰能解决当前数字图像应用领域所存在的问题,然而超分辨率图像序列重建函数具有病态性,在实际应用中存在缺陷。
正则化方法是解决病态问题的有效方法,为了解决上述诸类问题,本文针对超分辨率图像序列重建方法中的正则化方法进行了较为全面的分析与研究,主要内容包括:
第一,设计了一种新的自适应正则化超分辨率图像序列重建方法。传统的方法都是假定配准参数的估计结果是准确的,然而在实际应用中,运动估计的结果存在一定程度的误差。本文在传统的最大后验概率估计的超分辨率图像重建模型基础上,充分考虑配准参数的估计误差对重建的影响,利用自适应技术选择正则化参数,设计出综合多个模型优点的正则化目标函数,对正则化超分辨率图像序列重建模型进行了改进。仿真实验结果显示,新方法使得重建后的图像在整体上具有更好的视觉效果。
第二,改进了L2范数总变分正则化超分辨率图像序列重建算法。传统的正则化超分辨率图像序列重建算法都是假设每幅低分辨率图像对重建的相对贡献量是相等的,这将影响重建结果。本文充分考虑每幅低分辨率对重建的相对贡献量,并且把总变分正则化方法用在对超分辨率图像序列重建中,利用总变分正则化克服重建问题的病态性,有效地保持图像的边缘。仿真实验结果显示改进后的算法不仅提高了图像的边缘保持能力,而且更有效地抑制了噪声,使得重建后的图像更清晰。
第三,设计了一种快速的总变分正则化超分辨率图像序列重建算法。传统的总变分正则化目标函数中的数据项是L2范数的形式,然而L2范数的数学形式较为复杂。本文利用L1范数代替L2范数对传统的总变分正则化目标函数进行改进,仿真实验结果显示改进后的算法重建速度比传统算法的重建速度要快,而重建结果与传统算法相当,甚至要好。
In the current field of application for digital image, there often exists the optical blur, motion blur, down-sampling and noise in the process of imaging due to being affected by these factors like the physical conditions of imaging systems, climatic conditions and so on. It makes the image actually obtained be degraded, and leads to resolution of the image not to meet the application requirements. The idea of technology of super resolution reconstruction for image sequence is to use low resolution image sequence to reconstruct a high resolution image, which can exactly resolve the problem of existing in current field of application for digital image. However, the function of super resolution reconstruction for image sequence is ill-posed, and still exist defects in practical applications.
Since regularization approach is an effective way to solve ill-posed problem, this paper completely analyzed and researched the regularization method based on super resolution reconstruction for image sequence in order to resolve the problems mentioned above. The main research works are as follows:
First, a new adaptive regularization based on super resolution reconstruction for image sequence was proposed. The registration parameters estimated were assumed accurate in traditional methods, but in practice, error existed in motion estimation to a certain extent. On the basis of traditional maximum a posteriori estimation model of super resolution reconstruction for image, the impact of estimation error on reconstruction were fully considered. Regularization parameters were selected by using adaptive technique. The objective function integrated the advantages of several models was designed, and the model of super resolution reconstruction for image sequence based on regularization was improved. The simulation experiment showed that the proposed method made the reconstructed image take on better visual effect.
Second, the algorithm of super resolution reconstruction for image sequence based on L2 norm of total variation regularization was improved. The relative contributions of each frame low resolution image to reconstruction were assumed equal in the traditional algorithm of super resolution reconstruction for image sequence based on regularization, which made the result of reconstruction be influenced. The relative contributions of each frame low resolution image to reconstruction were fully considered, and total variation regularization method was used in the super resolution reconstruction for image sequence; it was used to overcome the ill-posed problem of image reconstruction, and the edge of image was effectively preserved. The simulation experiment showed that the improved algorithm not only enhanced the ability of preserving image edge, but also effectively restrained the noise, which made the reconstructed image clearer.
Third, the algorithm of fast super resolution reconstruction for image sequence based on total variation regularization was proposed. The data term in traditional objective function of total variation regularization was in the form of L2 norm, but L2 norm was more complicated. The traditional objective function of total variation regularization was improved by using L1 norm instead of L2 norm. The simulation experiment showed that the speed of reconstruction for the proposed algorithm comparing to the traditional algorithm was faster, and the result of reconstruction was similar, or even better.
正则化方法是解决病态问题的有效方法,为了解决上述诸类问题,本文针对超分辨率图像序列重建方法中的正则化方法进行了较为全面的分析与研究,主要内容包括:
第一,设计了一种新的自适应正则化超分辨率图像序列重建方法。传统的方法都是假定配准参数的估计结果是准确的,然而在实际应用中,运动估计的结果存在一定程度的误差。本文在传统的最大后验概率估计的超分辨率图像重建模型基础上,充分考虑配准参数的估计误差对重建的影响,利用自适应技术选择正则化参数,设计出综合多个模型优点的正则化目标函数,对正则化超分辨率图像序列重建模型进行了改进。仿真实验结果显示,新方法使得重建后的图像在整体上具有更好的视觉效果。
第二,改进了L2范数总变分正则化超分辨率图像序列重建算法。传统的正则化超分辨率图像序列重建算法都是假设每幅低分辨率图像对重建的相对贡献量是相等的,这将影响重建结果。本文充分考虑每幅低分辨率对重建的相对贡献量,并且把总变分正则化方法用在对超分辨率图像序列重建中,利用总变分正则化克服重建问题的病态性,有效地保持图像的边缘。仿真实验结果显示改进后的算法不仅提高了图像的边缘保持能力,而且更有效地抑制了噪声,使得重建后的图像更清晰。
第三,设计了一种快速的总变分正则化超分辨率图像序列重建算法。传统的总变分正则化目标函数中的数据项是L2范数的形式,然而L2范数的数学形式较为复杂。本文利用L1范数代替L2范数对传统的总变分正则化目标函数进行改进,仿真实验结果显示改进后的算法重建速度比传统算法的重建速度要快,而重建结果与传统算法相当,甚至要好。
In the current field of application for digital image, there often exists the optical blur, motion blur, down-sampling and noise in the process of imaging due to being affected by these factors like the physical conditions of imaging systems, climatic conditions and so on. It makes the image actually obtained be degraded, and leads to resolution of the image not to meet the application requirements. The idea of technology of super resolution reconstruction for image sequence is to use low resolution image sequence to reconstruct a high resolution image, which can exactly resolve the problem of existing in current field of application for digital image. However, the function of super resolution reconstruction for image sequence is ill-posed, and still exist defects in practical applications.
Since regularization approach is an effective way to solve ill-posed problem, this paper completely analyzed and researched the regularization method based on super resolution reconstruction for image sequence in order to resolve the problems mentioned above. The main research works are as follows:
First, a new adaptive regularization based on super resolution reconstruction for image sequence was proposed. The registration parameters estimated were assumed accurate in traditional methods, but in practice, error existed in motion estimation to a certain extent. On the basis of traditional maximum a posteriori estimation model of super resolution reconstruction for image, the impact of estimation error on reconstruction were fully considered. Regularization parameters were selected by using adaptive technique. The objective function integrated the advantages of several models was designed, and the model of super resolution reconstruction for image sequence based on regularization was improved. The simulation experiment showed that the proposed method made the reconstructed image take on better visual effect.
Second, the algorithm of super resolution reconstruction for image sequence based on L2 norm of total variation regularization was improved. The relative contributions of each frame low resolution image to reconstruction were assumed equal in the traditional algorithm of super resolution reconstruction for image sequence based on regularization, which made the result of reconstruction be influenced. The relative contributions of each frame low resolution image to reconstruction were fully considered, and total variation regularization method was used in the super resolution reconstruction for image sequence; it was used to overcome the ill-posed problem of image reconstruction, and the edge of image was effectively preserved. The simulation experiment showed that the improved algorithm not only enhanced the ability of preserving image edge, but also effectively restrained the noise, which made the reconstructed image clearer.
Third, the algorithm of fast super resolution reconstruction for image sequence based on total variation regularization was proposed. The data term in traditional objective function of total variation regularization was in the form of L2 norm, but L2 norm was more complicated. The traditional objective function of total variation regularization was improved by using L1 norm instead of L2 norm. The simulation experiment showed that the speed of reconstruction for the proposed algorithm comparing to the traditional algorithm was faster, and the result of reconstruction was similar, or even better.
引文
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[2] T. Komatsu, K. Aizawa, T. Lgarashi, et al. Signal-processing Based Method for Acquiring Very High Resolution Image with Multiple Cameras and Its Theoretical Analysis[J]. IEEE Proceedings, Communications Speech and Vision, 1993, 140(1): 19-24.
[3]袁小华,欧阳晓丽,夏德深.超分辨率图像恢复研究综述[J].地理与地理信息科学,2006, 22(3):43-47.
[4] R. Y. Tsai, T. S. Huang. Multiframe Image Restoration and Registration[M]. Greenwich, Conn.: JAI Press Inc. 1984, 317-739.
[5] A. M. Tekalp, M. K. Ozkan, M. I. Sezan. High Resolution Image Reconstruction from Lower Resolution Image Sequences and Space Varying Image Restoration[C]. ICASSP, San Francisco, CA, USA, 1992. New York: IEEE, 1992, 3: 169-172.
[6] E. Kaltenbacher, R. C. Hardie. High Resolution Infrared Image Reconstruction Using Multiple Low Resolution Aliased Frames[C]. NAECON, Dayton, OH, USA, 1996. New York: IEEE, 1996, 2: 702-709.
[7] N. K. Bose, H. C. Kim, H. M. Valenzuela. Recursive Implementation of Total Least Squares Algorithm for Image Reconstruction from Noisy, under sampled Multiframe[C]. ICASSP, Minneapolis, MN, 1993. New York: IEEE, 1993, 5: 269-272.
[8] N. K. Bose, H. C. Kim, H. M. Valenzuela. Recursive Total Least Squares Algorithm for Image Reconstruction from Noisy,Under sampled Frames[J]. Multidimensional Systems and Signal Processing, 1993, 4(3): 253-268.
[9] A. Gilman, D. G. Bailey, S. Marsland. Least-Squares Optimal Interpolation for fast Image Super-Resolution[C]. DELTA, Vietnam, 2010. New York: IEEE, 2010: 29-35.
[10] N. Nguyen, P. Milanfar. An Efficient Wavelet-Based Algorithm for Image Super Resolution[C]. ICIP, Canada, 2000. New York: IEEE, 2000, 2: 351-354.
[11]吴艳.一种改进的IBP超分辨率重构算法[J].红外,2009,30(12):11-16.
[12] M. Irani, S. peleg. Motion Analysis for Image Enhancement Resolution, Occlusion and Transparency [J]. Visual Common Image Represent, 1993, 4: 324-335.
[13]肖创柏,段娟,禹晶.序列图像的POCS超分辨率重建方法[J].北京工业大学学报,2009, 35(1):108-114.
[14] R. C. Hardie, K. J, Barnard, E. E. Armstrong. Joint MAP Registration and High Resolution ImageEstimation Using a Sequence of under sampled Images [J]. IEEE Transaction on Image Processing, 1997, 6(12): 1620-1632.
[15]张冬明,潘炜,陈怀新.基于MAP框架的时空联合自适应视频序列超分辨率重建[J].自动化学报,2009,35(5):484-490.
[16] M. Elad, A. Feuer. Restoration of a Single Super Resolution Image from Several Blurred, Noisy and under sampled Measured Images [J]. IEEE Transactions on Image Processing, 1997, 6(12): 1646-1658.
[17] M. G. Kang, A. K. Katsaggelos. General Choice of the Regularization Functional in Regularized Image Restoration [J]. IEEE Transactions on Image Processing, 1995, 4(5): 594-602.
[18] E. S. Lee, M. G. Kang. Regularized Adaptive High-Resolution Image Reconstruction Considering Inaccurate Sub-Pixel Registration [J]. IEEE Transactions on Image Processing, 2003, 9(10): 1784-1797.
[19] M. Elad, A. Feuer. Super Resolution Restoration of an Image Sequence: Adaptive Filtering Approach[J]. IEEE Transactions on Image Processing, 1999, 8: 387-395.
[20] K. X. Zhang, Y. H. Chan, W. C. Siu. An Improved Adaptive Wiener Filtering Algorithm for Super Resolution[C]. APSIPA ASC, Sapporo Japan, 2009. Japan: Hokkaido, 2009: 821-824.
[21] W. T. Freeman, T. R. Fones, E. C. Pasztor. Example-Based Super Resolution [J]. IEEE Computer Graphics and Applications, 2002, 22(2): 56-65.
[22] M. Christopher, M. Bishop, B. Andrew. Super Resolution Enhancement of Video[C]. AI & Statistics, Florida, 2003. Florida: key West, 2003.
[23] H. Chang, D. Y. Yeung, Y. Xiong. Super Resolution through Neighbor Embedding[C]. CVPR, Washington, DC, 2004. New York: IEEE, 2004: 275-282.
[24] A. T. Murat. Digital Video Processing[M]. London: Prentice Hall. 1995.
[25] H. Hu, P. K. Lisimachos. An Image Super Resolution Algorithm for Different Error Levels per Frame [J]. IEEE Transactions on Image Processing. 2006, 15(3): 592-603.
[26]苏秉华,金伟其,牛丽红等.超分辨率图像复原及其进展[J].光学技术,2001,27(1): 6-10.
[27] M. Elad, Y. Helor. A Fast Super-Resolution Reconstruction Algorithm for Pure TranslationalMotion and Common Space-Invariant Blur[J]. IEEE Transactions on Image Processing, 2001, 10(8): 1187-1193.
[28] S. Farsiu, M. D. Robinson. Fast and Robust Multiframe Super Resolution[J]. IEEE Transactions on Image Processing, 2004, 13(10): 1327-1344.
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