图像超分辨率重建和插值算法研究
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摘要
图像超分辨率重建(Super-resolution Reconstruction, SRR)是指从降质低分辨率图像序列中构造出高分辨率图像的分辨率增强技术。本文对图像超分辨率重建算法以及关键插值算法问题进行了研究。
随着对高分辨率的需求,低成本获取装置产生的图像需要通过信号和图像处理技术来提高质量,因此超分辨率重建已成为图像研究领域热点之一。其中,高精度的运动配准算法、盲重建算法、稳定的高效算法一直是超分辨率重建研究领域的重难点。
首先,本文介绍了超分辨率重建的数学模型,对几种经典超分辨率重建算法做了讨论。重建算法主要分为两类:频域法和空域法。现今广泛应用的图像超分辨率重建算法如:贝叶斯法、凸集投影法、混合MAP-POCS法、迭代反投影法等。其次,低分辨率图像必须插值到高分辨率图像网格,所以本文研究了图像插值理论。多项式内插:最近邻插值、线性插值、双三次插值具有固有的局限性,因此引进了样条插值和核回归插值。最后,仿真实验的图像结果展示了各算法的重建质量。
本文引进正则化项解决超分辨率重建反问题的病态性。利用现今广泛采用2阶范数作为正则化的基础上,在经典核回归方法重建图像中,提出的新型权重函数与取样窗范围内随机像素点位置有关。然后引入局部方向信息,利用可控核回归法,进一步提高重建图像的质量。仿真结果表明,改进后核回归的方法不仅提高了图像的质量,而且降低了重建图像的均方误差。
Image super-resolution reconstruction (SRR) refers to a resolution enhancement technology, which produce the image of high-resolution (HR) image from a set of degraded low-resolution (LR) images. This dissertation investigates image SRR algorithm and the key issues of interpolation algorithm.
With the demand of HR, the images produced from low cost acquisition system need the signal and image processing technology to improve the quality, so SRR has become one of the hot areas of the research on image. Among this, the high-precision movement registration algorithm, the blind reconstruction algorithms, and stable of fast and the effective algorithm are the focus of the difficulties of SRR.
In this paper, Firstly, the mathematical model of SRR is introduced, and several classical SRR algorithms are discussed. Frequency algorithms and spatial algorithms are the two main reconstruction technique. Now, Bayesian approach, projections onto convex sets (POCS) Approach, MAP-POCS hybrid approach and iterative back projection (IBP) approach are wide used in SRR algorithms. Secondly, LR image must be inserted into the HR image grid, so image interpolation theory is investigated. Polynomial interpolation, as nearest neighbor interpolation, bi1inear interpolation, cubic interpolation, has the inherent drawbacks, so we adopt spline Interpolation, kernel regression interpolation. Finally, simulation results of the HR image show the quality of there algorithm.
We adopt the regularization term to solve the ill-posed inverse problem of SRR. With the current wide spread use of norm 2 as the regularization, classical kernel regression (CKR) method was utilized for image reconstruction. We propose the novel weight function related to the position of the random pixels in the scale of the sample window. Then steering kernel regression (SKR) method contained local orientation was used to improve the quality of the reconstruction image. Simulation results demonstrated the improvement of image quality and the reduction of root mean square error (RMSE).
随着对高分辨率的需求,低成本获取装置产生的图像需要通过信号和图像处理技术来提高质量,因此超分辨率重建已成为图像研究领域热点之一。其中,高精度的运动配准算法、盲重建算法、稳定的高效算法一直是超分辨率重建研究领域的重难点。
首先,本文介绍了超分辨率重建的数学模型,对几种经典超分辨率重建算法做了讨论。重建算法主要分为两类:频域法和空域法。现今广泛应用的图像超分辨率重建算法如:贝叶斯法、凸集投影法、混合MAP-POCS法、迭代反投影法等。其次,低分辨率图像必须插值到高分辨率图像网格,所以本文研究了图像插值理论。多项式内插:最近邻插值、线性插值、双三次插值具有固有的局限性,因此引进了样条插值和核回归插值。最后,仿真实验的图像结果展示了各算法的重建质量。
本文引进正则化项解决超分辨率重建反问题的病态性。利用现今广泛采用2阶范数作为正则化的基础上,在经典核回归方法重建图像中,提出的新型权重函数与取样窗范围内随机像素点位置有关。然后引入局部方向信息,利用可控核回归法,进一步提高重建图像的质量。仿真结果表明,改进后核回归的方法不仅提高了图像的质量,而且降低了重建图像的均方误差。
Image super-resolution reconstruction (SRR) refers to a resolution enhancement technology, which produce the image of high-resolution (HR) image from a set of degraded low-resolution (LR) images. This dissertation investigates image SRR algorithm and the key issues of interpolation algorithm.
With the demand of HR, the images produced from low cost acquisition system need the signal and image processing technology to improve the quality, so SRR has become one of the hot areas of the research on image. Among this, the high-precision movement registration algorithm, the blind reconstruction algorithms, and stable of fast and the effective algorithm are the focus of the difficulties of SRR.
In this paper, Firstly, the mathematical model of SRR is introduced, and several classical SRR algorithms are discussed. Frequency algorithms and spatial algorithms are the two main reconstruction technique. Now, Bayesian approach, projections onto convex sets (POCS) Approach, MAP-POCS hybrid approach and iterative back projection (IBP) approach are wide used in SRR algorithms. Secondly, LR image must be inserted into the HR image grid, so image interpolation theory is investigated. Polynomial interpolation, as nearest neighbor interpolation, bi1inear interpolation, cubic interpolation, has the inherent drawbacks, so we adopt spline Interpolation, kernel regression interpolation. Finally, simulation results of the HR image show the quality of there algorithm.
We adopt the regularization term to solve the ill-posed inverse problem of SRR. With the current wide spread use of norm 2 as the regularization, classical kernel regression (CKR) method was utilized for image reconstruction. We propose the novel weight function related to the position of the random pixels in the scale of the sample window. Then steering kernel regression (SKR) method contained local orientation was used to improve the quality of the reconstruction image. Simulation results demonstrated the improvement of image quality and the reduction of root mean square error (RMSE).
引文
[1] T Komatsu, K Aizawa, T Igarashi, et al. Signal processing based method for acquiring very high resolution image with multiple cameras and its theoretical analysis[J]. Proc. Inst. Elec. Eng. , 1993,140(1):19-25.
[2] S C Park, M K Park, M G Kang. Super resolution image reconstruction: a technical review[J]. IEEE Signal Processing Magazine, 2003,5:21-35.
[3]苏秉华.超分辨率图像复原研究[D].北京:北京理工大学,2002.
[4] Tsai, T Huang. Multiframes Image Resolution and Registration[J]. Advances in Computer Vision and Image Processing, 1984,1:101-106.
[5] B R Hunt. Super-Resolution of Images: Algorithms, Principles, Performance[J]. International Journal of Imaging Systems and Technology,1995,6:297 -304.
[6] P Vandewalle. Super-Resolution from Unregistered Aliased Images[D]. Switzerland:Ecole Polytechnique Federale de Lausanne (EPFL), 2006:54-55.
[7] H Ur, D Gross. Improved resolution from sub-pixel shifted pictures[J]. CVGIP:Graphical Models and Image Processing,1992,54:181-186.
[8] H Stark, P Oskoui. High resolution image recovery from image-plane arrays, using convex projections[J]. J. Opt. Soc. Am. A, 1989, 6:1715-1726.
[9] E S Lee, M G Kang. Regularized adaptive high-resolution image reconstruction considering inaccurate sub-pixel registration[J]. IEEE trans. On Image Proc. ,2003,12(7):826-837.
[10] M ELAD, A FEUER. Super-Resolution Reconstruction of Continuous Image Sequences[C]. International Conference on Image Processing-ICIP 1999, Kobe, Japan,1999(3):459-463.
[11] S Farsiu , M D Robinson , M Elad , et al. Fast and robust multiframe super resolution[J]. IEEE Trans. on Image Proc. , 2004,13(10):1327-1344.
[12] R C Hardie, K J Barnard, J G Bognar,.et al. High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system[J]. Opt. Eng. , 1998,37(1):247-260.
[13] M. Elad, A Feuer. Restoration of a single super-resolution image from several blurred, noise, and undersampled measured images[J]. IEEE Trans. on Image Proc. , 1997, 6(8):1646-1658.
[14] G K Chantas, N P. Galatsanos, N A Woods.Super-Resolution Based on Fast Registration and Maximum a Posteriori Reconstruction[J].IEEE Trans. on Image Proc.,2007,16(7):1821-1829.
[15] N K Bose, M K Ng, A. C. Yau. A Fast Algorithm for Image Super-Resolution from Blurred Observations[J]. EURASIP Journal on Applied Signal Processing. 2006:1-14.
[16] S Farsiu, D Robinson. M Elad, et al. Fast and robust multiframe super-resolution[J]. IEEE Trans. on Image Proc.,2004:1327–1344.
[17] T F Chan, C K Wong. Muhichannel Image Deconvolution by Total Variation Regularization[C]. SPIE, San Diego, 1997:358—366.
[18] J Nagy, N Bose. Mathematical analysis of super resolution methodology[J]. IEEE Signal Processing Magazine, 2003,20(3):62-74.
[19] S Wood, D Rajan, M Christensen, et a1. Resolution improvement for compound eye images through diversity[C]. Proceedings of DSP Workshop. New Mexico,2004.
[20] H W Kim, J H Jang, K S Hong. Edge-enhancing super-resolution using anisotropic diffusion[C]. IEEE Int. Conf. mage Proc. Thessaloniki, Greece, 2001:130-133.
[21]田兵兵.超分辨率图像重建算法研究[D].合肥:中国科学技术大学,2009:8-13.
[22] Z Z Wang, F H Qi. On ambiguities in super-resolution modeling[J]. IEEE Signal Processing Letters, 2004, (11),:678-681.
[23] S Borman, R Stevenson. Spatial resolution enhancement of low-resolution image sequences: a comprehensive review with directions for future research[R]. Indian Laboratory for Image and Signal Analysis(LISA),University of Notre Dame:1998.
[24] Tekalp, M Ozkan, M. Sezan. High-resolution image reconstruction from lower-resolution image sequences and space-varying image restoration[J]. In Proc. ICASSP. 1992,3:169-172.
[25] S P Kim, W Su. Recursive high-resolution reconstruction of blurred multiframe images [J]. IEEE Trans. Image Proc. , 1993,2:534-539.
[26]程燕.图像超分辨率重建关键技术的研究[D].上海:上海交通大学,2007 :12-15.
[27] U Hanoch, G Daniel. Improved resolution from subpixel shifted pictures[J]. CVGIP:Graph. Models Image Process. ,1992,54(2):181-186.
[28] Q P Tuan, J V Lucas, S Klamer. Robust fusion of irregularly sampled data using adaptive normalized convolution[J]. EURASIP Journal on Applied Signal Processing,2006,:1-12.
[29] N Nguyen, P Milanfar, G Golub. A computationally efficient superresolution image reconstruction algorithm[J]. IEEE Trans. Image Processing, 2001,4:573-583.
[30] P. Cheeseman, B Kanefsky, R Kraft, et al. Super-resolved surface reconstruction from multiple images[R]. NASA Ames Research Center,Moffett Field:CA,1994.
[31] R R Schultz , R L Stevenson. Extraction of high-resolution frames from video sequences[J]. IEEE Trans. Image Processing, 1996, 5(6):996-1011.
[32] R C Hardie, K J Barnard, E E Armstrong. Joint MAP registration and high-resolution image estimation using a sequence of undersampled images[J]. IEEE Transactions on Image Processing, 1997, 12(6):1621-1633.
[33] B C Tom, A K Katsaggelos. Reconstruction of a high-resolution image by simultaneous registration, restoration, and interpolation of low-resolution images[J]. IEEE Int. Conf. Image Processing, 1995, 10(2):539-542.
[34]韩玉兵,吴乐南.基于自适应滤波的视频序列超分辨率重建.计算机学报,2006,29:642-647.
[35] A J Patti,M I Sezan,A M Tekalp. Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time[J]. IEEE Trans. Image Proc. , 1997, 8(6):1064-1076.
[36] P E Eren, M I Sezan, A M Tekalp. Robust, object-based high-resolution image reconstruction from low-resolution video[J]. IEEE Trans. Image Proc. , 1997, 10(6): 1446-1451.
[37] M Irani, S Peleg. Super resolution from image sequences[A]. In Proceedings of International Conference on Pattern Recognition[C]. Piscataway, NJ, USA.1990:115-120.
[38] M Irani, S Peleg. Improving resolution by image registration[J]. Graph.Models Image Process, 1991, 5(53):231-239.
[39] M Irani, S Peleg. Motion analysis for image enhancement. Resolution, occlusion, and transparency [J]. J Vis. Commun. Image, 1993, 4(4):324-336.
[40] S Mann, R W Picard. Virtual bellows: Constructing high quality stills from Video[C]. IEEE Int. Conf. Image Proc. Austin, TX,1994:13-16.
[41]乔建苹,刘琚,闫华,孙建德.基于矢量量化的模糊参数辨识及分辨率增强方法.电子与信息学报,2006,28:592-596.
[42] M Vega, R Molina, A K Katsaggelos. A Bayesian uper-resolution approach to demosaicing of blurred images[C]. EURASIP Journal on Applie. Signal Processing. 2006(2006):1–12.
[43]张正贤.正则超分辨率图像复原算法研究[D].西安:西北工业大学.2006:24-31.
[44] M R Charest, M Elad, P Milanfar. A General Iterative Regularization Framework For Image Denoising[C]. Proc. of the 40th Conference on Information Sciences and Systems, Princeton, NJ, March 2006.
[45] T Q Pham, L. J. Vliet, K. Schutte. Robust Fusion of Irregularly Sampled Data Using Adaptive Normalized Convolution[J]. EURASIP JASP, ID83268, 2006(10):1-12.
[46] H Takeda, S Farsiu, P Milanrar. Kernel Regression for Image Processing and Reconstruction[J]. IEEE Transactions on Image Processing, 2007, 16(2):349-366.
[47] C L Nikias, A P Petropulu. Higher-order spectra analysis: a nonlinear signal processing framework[M]. Englewood Cliffs, N.J. : PTR Prentice Hall, c1993.
[48] H Takeda, P Milanfar, M Protter, et al. Super-resolution without Explicit Subpixel Motion Estimation[J]. EDICS: TEC-ISR, doi=10.1.1.141.510.
[49] Z G Zhang, S C Chan, X Zhang, et al. High-resolution Reconstruction of Human Brain MRI Image based on Local Polynomial regression[C]. IEEE/EMBS Conference on NeuralEngineering, April 29 - May 2, 2009. Antalya, Turkey. NER '09:245-248.
[50] B Sch?lkopf, A Smola, K R Müller. Nonlinear Component Analysis as a Kernel Eigenvalue Problem[J]. Neural computation, 1998, 10(5):1299-1319.
[51] H Takeda. Kernel regression for image processing and reconstruction[D]. Santa Cruz: Univ. of California,2006:32-57.
[52] T Q Pham, L J Vliet, K Schutte. Robust Super-Resolution without Regularization[J]. Journal of Physics: Conference Series, 2008,124-143.
[53] S Farsiu, D Robinson, M Elad, et al. Robust shift and add approach to superresolution[J]. Proc. SPIE. 2003, (5203):121-130.
[54] L M Gevrekci. Super resolution and dynamic range enhancement of image sequence[D]. Baton Rouge: Louisiana State University.2009
[55] J A Parker, R V Kenyon, D E Troxel. Comparison of interpolation methods for image resampling[J]. IEEE trans. on medical imaging. 1983, 1(MI-2).
[56] T William, Freeman, R Thouis , et al. Example-Based Super-Resolution[J]. IEEE Computer Graphics and Applications. 2002, pp 56-65.
[57] P Thévenaz,T Blu,ichael Unser.M.Unser. Image interpolation and resampling[M]. Handbook of Medical Imaging, Processing and Analysis. USA, Academic Press, 2000:393-420
[58] R Keys. Cubic convolution interpolation for digital image processing[J]. IEEE Transactions on Acoustics, Speech and Signal Processing. 1981, 29(6):1153-1160.
[59] M Unser,A Aldroubi,M Eden.Fast B-Spline Transforms for Continuous Image Representation and Interpolation[J]. IEEE Trans. Pattern Anal. Mach. Int. , 1991,13(3):277-285.
[60] H Takeda, S Farsiu, P Milanfar. Deblurring Using Regularized Locally Adaptive Kernel Regression[J]. IEEE transactions on image processing, 2008, 4(17).
[61] K I Kim, Y Kwon. Example-Based Learning for Single-Image Super-Resolution[M]. Lecture Notes in Computer Science. Berlin, Heidelberg : Springer, 2008,(5096):456-465.
[2] S C Park, M K Park, M G Kang. Super resolution image reconstruction: a technical review[J]. IEEE Signal Processing Magazine, 2003,5:21-35.
[3]苏秉华.超分辨率图像复原研究[D].北京:北京理工大学,2002.
[4] Tsai, T Huang. Multiframes Image Resolution and Registration[J]. Advances in Computer Vision and Image Processing, 1984,1:101-106.
[5] B R Hunt. Super-Resolution of Images: Algorithms, Principles, Performance[J]. International Journal of Imaging Systems and Technology,1995,6:297 -304.
[6] P Vandewalle. Super-Resolution from Unregistered Aliased Images[D]. Switzerland:Ecole Polytechnique Federale de Lausanne (EPFL), 2006:54-55.
[7] H Ur, D Gross. Improved resolution from sub-pixel shifted pictures[J]. CVGIP:Graphical Models and Image Processing,1992,54:181-186.
[8] H Stark, P Oskoui. High resolution image recovery from image-plane arrays, using convex projections[J]. J. Opt. Soc. Am. A, 1989, 6:1715-1726.
[9] E S Lee, M G Kang. Regularized adaptive high-resolution image reconstruction considering inaccurate sub-pixel registration[J]. IEEE trans. On Image Proc. ,2003,12(7):826-837.
[10] M ELAD, A FEUER. Super-Resolution Reconstruction of Continuous Image Sequences[C]. International Conference on Image Processing-ICIP 1999, Kobe, Japan,1999(3):459-463.
[11] S Farsiu , M D Robinson , M Elad , et al. Fast and robust multiframe super resolution[J]. IEEE Trans. on Image Proc. , 2004,13(10):1327-1344.
[12] R C Hardie, K J Barnard, J G Bognar,.et al. High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system[J]. Opt. Eng. , 1998,37(1):247-260.
[13] M. Elad, A Feuer. Restoration of a single super-resolution image from several blurred, noise, and undersampled measured images[J]. IEEE Trans. on Image Proc. , 1997, 6(8):1646-1658.
[14] G K Chantas, N P. Galatsanos, N A Woods.Super-Resolution Based on Fast Registration and Maximum a Posteriori Reconstruction[J].IEEE Trans. on Image Proc.,2007,16(7):1821-1829.
[15] N K Bose, M K Ng, A. C. Yau. A Fast Algorithm for Image Super-Resolution from Blurred Observations[J]. EURASIP Journal on Applied Signal Processing. 2006:1-14.
[16] S Farsiu, D Robinson. M Elad, et al. Fast and robust multiframe super-resolution[J]. IEEE Trans. on Image Proc.,2004:1327–1344.
[17] T F Chan, C K Wong. Muhichannel Image Deconvolution by Total Variation Regularization[C]. SPIE, San Diego, 1997:358—366.
[18] J Nagy, N Bose. Mathematical analysis of super resolution methodology[J]. IEEE Signal Processing Magazine, 2003,20(3):62-74.
[19] S Wood, D Rajan, M Christensen, et a1. Resolution improvement for compound eye images through diversity[C]. Proceedings of DSP Workshop. New Mexico,2004.
[20] H W Kim, J H Jang, K S Hong. Edge-enhancing super-resolution using anisotropic diffusion[C]. IEEE Int. Conf. mage Proc. Thessaloniki, Greece, 2001:130-133.
[21]田兵兵.超分辨率图像重建算法研究[D].合肥:中国科学技术大学,2009:8-13.
[22] Z Z Wang, F H Qi. On ambiguities in super-resolution modeling[J]. IEEE Signal Processing Letters, 2004, (11),:678-681.
[23] S Borman, R Stevenson. Spatial resolution enhancement of low-resolution image sequences: a comprehensive review with directions for future research[R]. Indian Laboratory for Image and Signal Analysis(LISA),University of Notre Dame:1998.
[24] Tekalp, M Ozkan, M. Sezan. High-resolution image reconstruction from lower-resolution image sequences and space-varying image restoration[J]. In Proc. ICASSP. 1992,3:169-172.
[25] S P Kim, W Su. Recursive high-resolution reconstruction of blurred multiframe images [J]. IEEE Trans. Image Proc. , 1993,2:534-539.
[26]程燕.图像超分辨率重建关键技术的研究[D].上海:上海交通大学,2007 :12-15.
[27] U Hanoch, G Daniel. Improved resolution from subpixel shifted pictures[J]. CVGIP:Graph. Models Image Process. ,1992,54(2):181-186.
[28] Q P Tuan, J V Lucas, S Klamer. Robust fusion of irregularly sampled data using adaptive normalized convolution[J]. EURASIP Journal on Applied Signal Processing,2006,:1-12.
[29] N Nguyen, P Milanfar, G Golub. A computationally efficient superresolution image reconstruction algorithm[J]. IEEE Trans. Image Processing, 2001,4:573-583.
[30] P. Cheeseman, B Kanefsky, R Kraft, et al. Super-resolved surface reconstruction from multiple images[R]. NASA Ames Research Center,Moffett Field:CA,1994.
[31] R R Schultz , R L Stevenson. Extraction of high-resolution frames from video sequences[J]. IEEE Trans. Image Processing, 1996, 5(6):996-1011.
[32] R C Hardie, K J Barnard, E E Armstrong. Joint MAP registration and high-resolution image estimation using a sequence of undersampled images[J]. IEEE Transactions on Image Processing, 1997, 12(6):1621-1633.
[33] B C Tom, A K Katsaggelos. Reconstruction of a high-resolution image by simultaneous registration, restoration, and interpolation of low-resolution images[J]. IEEE Int. Conf. Image Processing, 1995, 10(2):539-542.
[34]韩玉兵,吴乐南.基于自适应滤波的视频序列超分辨率重建.计算机学报,2006,29:642-647.
[35] A J Patti,M I Sezan,A M Tekalp. Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time[J]. IEEE Trans. Image Proc. , 1997, 8(6):1064-1076.
[36] P E Eren, M I Sezan, A M Tekalp. Robust, object-based high-resolution image reconstruction from low-resolution video[J]. IEEE Trans. Image Proc. , 1997, 10(6): 1446-1451.
[37] M Irani, S Peleg. Super resolution from image sequences[A]. In Proceedings of International Conference on Pattern Recognition[C]. Piscataway, NJ, USA.1990:115-120.
[38] M Irani, S Peleg. Improving resolution by image registration[J]. Graph.Models Image Process, 1991, 5(53):231-239.
[39] M Irani, S Peleg. Motion analysis for image enhancement. Resolution, occlusion, and transparency [J]. J Vis. Commun. Image, 1993, 4(4):324-336.
[40] S Mann, R W Picard. Virtual bellows: Constructing high quality stills from Video[C]. IEEE Int. Conf. Image Proc. Austin, TX,1994:13-16.
[41]乔建苹,刘琚,闫华,孙建德.基于矢量量化的模糊参数辨识及分辨率增强方法.电子与信息学报,2006,28:592-596.
[42] M Vega, R Molina, A K Katsaggelos. A Bayesian uper-resolution approach to demosaicing of blurred images[C]. EURASIP Journal on Applie. Signal Processing. 2006(2006):1–12.
[43]张正贤.正则超分辨率图像复原算法研究[D].西安:西北工业大学.2006:24-31.
[44] M R Charest, M Elad, P Milanfar. A General Iterative Regularization Framework For Image Denoising[C]. Proc. of the 40th Conference on Information Sciences and Systems, Princeton, NJ, March 2006.
[45] T Q Pham, L. J. Vliet, K. Schutte. Robust Fusion of Irregularly Sampled Data Using Adaptive Normalized Convolution[J]. EURASIP JASP, ID83268, 2006(10):1-12.
[46] H Takeda, S Farsiu, P Milanrar. Kernel Regression for Image Processing and Reconstruction[J]. IEEE Transactions on Image Processing, 2007, 16(2):349-366.
[47] C L Nikias, A P Petropulu. Higher-order spectra analysis: a nonlinear signal processing framework[M]. Englewood Cliffs, N.J. : PTR Prentice Hall, c1993.
[48] H Takeda, P Milanfar, M Protter, et al. Super-resolution without Explicit Subpixel Motion Estimation[J]. EDICS: TEC-ISR, doi=10.1.1.141.510.
[49] Z G Zhang, S C Chan, X Zhang, et al. High-resolution Reconstruction of Human Brain MRI Image based on Local Polynomial regression[C]. IEEE/EMBS Conference on NeuralEngineering, April 29 - May 2, 2009. Antalya, Turkey. NER '09:245-248.
[50] B Sch?lkopf, A Smola, K R Müller. Nonlinear Component Analysis as a Kernel Eigenvalue Problem[J]. Neural computation, 1998, 10(5):1299-1319.
[51] H Takeda. Kernel regression for image processing and reconstruction[D]. Santa Cruz: Univ. of California,2006:32-57.
[52] T Q Pham, L J Vliet, K Schutte. Robust Super-Resolution without Regularization[J]. Journal of Physics: Conference Series, 2008,124-143.
[53] S Farsiu, D Robinson, M Elad, et al. Robust shift and add approach to superresolution[J]. Proc. SPIE. 2003, (5203):121-130.
[54] L M Gevrekci. Super resolution and dynamic range enhancement of image sequence[D]. Baton Rouge: Louisiana State University.2009
[55] J A Parker, R V Kenyon, D E Troxel. Comparison of interpolation methods for image resampling[J]. IEEE trans. on medical imaging. 1983, 1(MI-2).
[56] T William, Freeman, R Thouis , et al. Example-Based Super-Resolution[J]. IEEE Computer Graphics and Applications. 2002, pp 56-65.
[57] P Thévenaz,T Blu,ichael Unser.M.Unser. Image interpolation and resampling[M]. Handbook of Medical Imaging, Processing and Analysis. USA, Academic Press, 2000:393-420
[58] R Keys. Cubic convolution interpolation for digital image processing[J]. IEEE Transactions on Acoustics, Speech and Signal Processing. 1981, 29(6):1153-1160.
[59] M Unser,A Aldroubi,M Eden.Fast B-Spline Transforms for Continuous Image Representation and Interpolation[J]. IEEE Trans. Pattern Anal. Mach. Int. , 1991,13(3):277-285.
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