超分辨率图像重建过程就是对同一目标进行多次观测,获取多幅低分辨率影像,利用低分辨率影像求取目标的真实影像,即求取高分辨率影像的过程。这一过程与测绘领域中对同一对象进行观测,用测量平差求取对象最佳值的过程类似。本文尝试用测量平差的方法来解决超分辨率重建的问题。文中首先建立了超分辨率重建的积分型非线性平差模型,提出了用二次函数将平差模型中的积分函数参数化,用最小二乘平差方法求解。基于所提出的平差方法,制定了图像重建的具体策略。该方法可以定量分析成果的好坏,可以成功避免出现病态问题等。试验结果表明,相对于传统的超分辨率重建方法获得重建图像的视觉效果有较大的提高,而且其峰值信噪比及结构相似性指数也有很大的提高,因此方法可靠且可行。
The process of super resolution image reconstruction is such a process that multiple observations are taken on the same target to obtain low resolution images, then the low resolution images are used to reconstruct the real image of the target, namely high resolution image. This process is similar to that in the field of surveying and mapping, in which the same target is observed repeatedly and the optimal values is calculated with surveying adjustment methods. In this paper, the method of surveying adjustment is applied into super resolution image reconstruction. A integral nonlinear adjustment model for super resolution image reconstruction is proposed at first. And then the model is parameterized with a quadratic function. Finally the model is solved with the least squares adjustment method. Based on the proposed adjustment method, the specific strategy of image reconstruction is presented. This method for super resolution image reconstruction can make quantitative analysis of the results, and avoid successfully ill-condition problem, etc. The results show that, compared to the traditional method of super resolution image reconstruction, this method has greatly improved the visual effects, and the PSNR and SSIM has also greatly improved, so the method is reliable and feasible.
[1] SHEN Huanfeng, LI Pingxiang, ZHANG Liangpei, et al. Overview on Super Resolution Image Reconstruction[J]. Optical Technique, 2009, 35(2): 194-199. (沈焕锋, 李平湘, 张良培, 等. 图像超分辨率重建技术与方法综述[J]. 光学技术, 2009, 35(2): 194-199.)
[2] TSAI R Y, HUANG T S. Multiframe Image Restoration and Registration[J]. Advances in Computer Vision and Image Processing, 1984(1): 101-106.
[3] TEKALP A M, OZKAN M K, SEZAN M I. High Resolution Image Reconstruction from Lower Resolution Image Sequences and Spacevarying Image Restoration[C]//The IEEE International Conference on Acoustics, Speech and Signal Processing.San Francisco, CA: IEEE, 1992: 169-172.
[4] DAVILA C E. An Efficient Recursive Total Least Squares Algorithms for FIR Adaptive Filtering[J]. IEEE Transactions on Signal Processing, 1994, 42(2): 268-280.
[5] KALTENBACHER E, HARDIE R C. Highresolution Infrared Image Reconstruction Using Multiple, Low Resolution, Aliased Frames[C]//Proceedings of the IEEE 1996 National Aerospace Electronics Conference.Dayton, OH: IEEE, 1996: 702-709.
[6] CLARK J J, PALMER M R, LAURENCE P D. A Transformation Method for the Reconstruction of Functions from Nonuniformly Spaced Samples[J]. IEEE Transactions on Acoustics, Speech and Signal Processing, 1985, 33(4): 1151-1165.
[7] IRANI M, PELEG S. Improving Resolution by Image Registration[J]. Graphical Models and Image Processing, 1991, 53(3): 231-239.
[8] STARK H, OSKOUI P. High-resolution Image Recovery from Image-plane Arrays, Using Convex Projections[J]. Journal of the Optical Society of America A, 1989, 6(11): 1715-1726.
[9] SCHUULZ R R, STEVENSON R L. Extraction of High Resolution Frames from Video Sequences[J]. IEEE Transactions on Image Processing, 1996, 5(6): 996-1011.
[10] ELAD M, FEUER A. Super Resolution Restoration of an Image Sequence: Adaptive Filtering Approach[J]. IEEE Transactions on Image Processing, 1999, 8(3): 387-395.
[11] ZHANG Xinming, SHEN Lansun. The Development of Super-resolution Restoration from Image Sequences[J]. Measurement & Control Technology,2002,21(5): 33-35. (张新明, 沈兰荪. 超分辨率复原技术的发展[J]. 测控技术,2002,21(5): 33-35.)
[12] FAN Chong, GONG Jianya, ZHU Jianjun. POCS Super-resolution Sequence Image Reconstruction Based on Image Registration Excluded Aliased Frequency Domain[J]. Acta Geodaetica et Cartographica Sinica,2006,35(4): 358-363. (范冲, 龚健雅, 朱建军. 一种基于去混叠影像配准方法的POCS超分辨率序列图像重建[J]. 测绘学报,2006,35(4): 358-363.)
[13] SHEN Huanfeng, ZHANG Liangpei, HUANG Bo, et al. A Map Approach for Joint Motion Estimation, Segmentation, and Super Resolution[J]. IEEE Transactions on Image Processing, 2007, 16(2): 479-490.
[14] RUDIN L I, OSHER S, FATEMI E. Nonlinear Total Variation Based Noise Removal Algorithms[J]. Physica D: Nonlinear Phenomena, 1992, 60(1-4): 259-268.
[15] FARSIU S, Robinson M D. Fast and Robust Multi-frame Super Resolution[J]. IEEE Transactions on Image Processing, 2004, 13(10): 1327-1344.
[16] ZHANG Liangpei, SHEN Huanfeng, ZHANG Hongyan, et al. Super Resolution Image Reconstruction[M]. Beijing: Science Press,2012. (张良培, 沈焕锋, 张洪艳, 等. 图像超分辨率重建[M]. 北京:科学出版社,2012.)
[17] FAN Donghao, ZHU Jianjun, ZHOU Cui, et al. Designing and Implementation of the Simulation System of the Image Degradation[J]. Geotechnical Investigation & Surveying,2014,42(5): 75-79.(樊东昊, 朱建军, 周璀, 等. 图像退化仿真系统的设计与实现[J]. 工程勘察,2014,42(5): 75-79.)
[18] KANG Yanni, HUANG Huan, ZHU Yuyan, et al. Super-resolution Image Registration Based on SIFT and Its Realization with Matlab[J]. Computer Knowledge and Technology,2009,5(28): 8031-8033. (康燕妮, 黄欢, 朱玉艳, 等. 基于SIFT的超分辨率图像配准及Matlab实现[J]. 电脑知识与技术,2009,5(28): 8031-8033.)
[19] SHEN Huanfeng, LI Pingxiang, ZHANG Liangpei. Adaptive Regularized MAP Super-resolution Reconstruction Method[J]. Geomatics and Information Science of Wuhan University, 2006, 31(11): 949-952. (沈焕锋, 李平湘, 张良培. 一种自适应正则化MAP超分辨率重建方法[J]. 武汉大学学报:信息科学版,2006, 31(11): 949-952.)
[20] SHEN Huangfeng, NGM K, LI Pingxiang, et al. Super-resolution Reconstruction Algorithm to MODIS Remote Sensing Images[J]. The Computer Journal, 2007, 52(1): 90-100.
[21] PURKAIT P, CHANDA B. Morphologic Gain-controlled Regularization for Edge-preserving Super-resolution Image Reconstruction[J]. Signal, Image and Video Processing,2013,7(5): 925-938.
[22] SHI Wenzhong, TIAN Yan, LIU Jian. A Fast Super-resolution Reconstruction from Image Sequence[J]. Wuhan University of Natural Sciences,2006,11(2): 399-404.
[23] MA Jun, JING Weili, FAN Chong. Papoulis-gerchberg Super-resolution Reconstruction Based on Improvement Approach of Keren Registration Method[J]. Bulletin of Surveying and Mapping,2007(12): 14-17(马俊, 景维立, 范冲. 一种基于改进Keren空域配准方法的Papoulis-gerchberg超分辨率重建[J]. 测绘通报,2007(12): 14-17.)
[24] WU Yan. One Improved Super-reconstruction Algorithm Based on IBP Theory[J]. Infrared,2009,30(12): 11-15. (吴艳. 一种改进的IBP超分辨率重构算法[J]. 红外,2009,30(12): 11-15.)
[25] LUCCHESEL, CORTELAZZO GM. A Noise-robust Frequency Domain Technique for Estimating Planar Roto-translations[J]. IEEE Transactions on Signal Processing, 2000,48(6): 1769-1786.
