小波域HMT模型的图像超分辨率插值算法研究
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摘要
随着图像采集传感器技术的发展,虽然已经可以获得较高分辨率的图像,但是由于硬件制作水平的限制,如何利用软件方法提高图像分辨率日益受到关注。
传统的超分辨率插值算法由于实现原理的局限性,没有充分考虑图像数据中的空间梯度信息和统计特征,无法较好地识别图像边缘,从而导致边缘细节模糊或出现阶梯状锯齿现象。
本文研究了一种基于小波变换与隐马尔可夫树(HMT)模型相结合的图像超分辨率插值方法。针对小波系数进行小波域HMT模型建模,使用混合高斯模型描述小波各子带系数的概率统计分布情况,利用树状Markov结构来反映小波系数在尺度间的相关性,对小波系数相对应的隐状态建模。为了实现小波系数与HMT模型匹配,采用期望值最大化(EM)算法来估计HMT模型参数,将图像超分辨率插值问题转化为一个约束优化问题。实验结果显示的效果图与实验数据,验证了本文算法的有效性和实用性。
With the development of sensor technology of image acquisition, though the higher resolution image can be obtained, but the production level due to hardware limitations, and how to use the software methods to improve the image resolution is growing concern.
The conventional super-resolution image interpolation algorithm due to the limitation of principle, not fully consider the space gradient information and the statistics characteristic of image data, it also can not effectively identify image edge, resulting in blurred edge details or stepped aliasing edge.
This paper deals with the super-resolution image interpolation method based on wavelet transform combined with hidden Markov tree (HMT) model. Wavelet coefficients are modeled as the wavelet domain HMT model, using Gaussian mixture model to describe the probability statistical distribution of wavelet coefficients of each sub-band. Use of the tree shape Markov reflected in the structure of the wavelet coefficients across the scales, the wavelet coefficients corresponding to the hidden state modeling. In order to achieve the wavelet coefficients and the HMT model matching using the expectation maximization (EM) algorithm to estimate the HMT model parameters, the super-resolution image interpolation problem is transformed into a constrained optimization problem. The experimental results show that the effect of images with the experimental data, to verify the effectiveness and practicality of the proposed algorithm.
传统的超分辨率插值算法由于实现原理的局限性,没有充分考虑图像数据中的空间梯度信息和统计特征,无法较好地识别图像边缘,从而导致边缘细节模糊或出现阶梯状锯齿现象。
本文研究了一种基于小波变换与隐马尔可夫树(HMT)模型相结合的图像超分辨率插值方法。针对小波系数进行小波域HMT模型建模,使用混合高斯模型描述小波各子带系数的概率统计分布情况,利用树状Markov结构来反映小波系数在尺度间的相关性,对小波系数相对应的隐状态建模。为了实现小波系数与HMT模型匹配,采用期望值最大化(EM)算法来估计HMT模型参数,将图像超分辨率插值问题转化为一个约束优化问题。实验结果显示的效果图与实验数据,验证了本文算法的有效性和实用性。
With the development of sensor technology of image acquisition, though the higher resolution image can be obtained, but the production level due to hardware limitations, and how to use the software methods to improve the image resolution is growing concern.
The conventional super-resolution image interpolation algorithm due to the limitation of principle, not fully consider the space gradient information and the statistics characteristic of image data, it also can not effectively identify image edge, resulting in blurred edge details or stepped aliasing edge.
This paper deals with the super-resolution image interpolation method based on wavelet transform combined with hidden Markov tree (HMT) model. Wavelet coefficients are modeled as the wavelet domain HMT model, using Gaussian mixture model to describe the probability statistical distribution of wavelet coefficients of each sub-band. Use of the tree shape Markov reflected in the structure of the wavelet coefficients across the scales, the wavelet coefficients corresponding to the hidden state modeling. In order to achieve the wavelet coefficients and the HMT model matching using the expectation maximization (EM) algorithm to estimate the HMT model parameters, the super-resolution image interpolation problem is transformed into a constrained optimization problem. The experimental results show that the effect of images with the experimental data, to verify the effectiveness and practicality of the proposed algorithm.
引文
[1]田岩,田金文,柳健,张继贤,林宗坚.超分辨率技术的实现——一种改善的小波插值方法[J].中国图象图形学报.2003(12)：1422-1426.
[2]朱艳亮.实时视频缩放算法研究及FPGA实现[D].中南大学.2009.
[3]Parker J A, Kenyon R V, Troxel D E. Comparison of interpolating methods for image resampling[J]. IEEE Transactions on Medical Imaging,1983,2(1):31-39.
[4]Jain A K. Fundamentals of Digital Image Processing[M]. Englewood Cliffs: prentice-Hall,1989.
[5]Chen T.C., Figueiredo R.J.P.de. Two-dimensional Interpolation by Generalized Spline Filters Based on Partial Differential Equation Image Models [J]. IEEE Transactions on Acoustics, Speech, and Signal Processing,1985,33(3):631-642.
[6]章毓晋.图像处理和分析[M].北京：清华大学出版社,1999.
[7]Yokoya N, Yamamoto K. Fractal-based Analysis and Interpolation of 3D Natural Surface Shapes and Their Application to Terrain Modeling[J]. Computer Vision, Graphics and Image Processing,1989,46(3):284-302.
[8]Ledda.A, Luong.H.Q, Philips.W, De Witte.V, Kerre.E.E. Image interpolation using mathematical morphology[C]. Proceedings of the Second International Conference on Document Image Analysis for Libraries,2006, (4):358-367.
[9]Stanco F., Gallo G, Battiato S. A Locally-Adaptive Zooming Algorithm for Digital Images[J]. Image and Vision Computing Journal,2002,20(11): 805-812.
[10]Dan Su, Philip Willis. Image Interpolation by Pixel-Level Data-Dependent Triangulation[J]. Computer Graphics Forum,2004,23(7):189-201.
[11]刘笑宙,涂国防.小波双线性插值应用于光学遥感图像[J].中国科学院研究生院学报,2003,20(1)：39-43.
[12]屈有山,田维坚,李英才,张薇,达选福.基于小波双三次插值提高光学 遥感图像空间分辨率的研究[J].光子学报,2004,33(5)：604-601.
[13]陈德元,涂国防.小波分形插值医学图像处理[J].电视技术,2001(6)：67-70.
[14]Nhat Nguyen, Peyman Milanfar. A wavelet-based interpolation-restoration method for superresolution (wavelet superresolution) [J]. Circuits, Systems and Signal Process,2000,19(4):321-338.
[15]Yu-Len Huang. Wavelet-based image interpolation using multilayer perceptrons [J]. Neural Computing & Applications,2005,14(1):1-10.
[16]Woo D.H., Eom I.K., Kim Y.S. Image Interpolation based on interscale dependency in wavelet domain[J]. IEEE ICIP,2004,3(10):1687-1690.
[17]郭晓新.超分辨率重建问题的研究[D].吉林大学.2005.
[18]张明.图像超分辨率重建和插值算法研究[D].中国科学技术大学.2010.
[19]Vega M, Molina R, Katsaggelos A.K. A Bayesian super-resolution approach to demosaicing of blurred images [J]. EURASIP Journal on Applied Signal Processing.2006(01):1-12.
[20]彭玉华.小波变换与工程应用[M].北京：科学出版社,1999.
[21]杨福生.小波变换的工程分析与应用[M].北京：科学出版社,1999.
[22]邓堰.转子故障智能诊断中的特征提取与选择技术研究[D].南京航空航天大学.2008.
[23]Daubechies I. Ten Lectures on Wavelet [M]. Capital City Press,1992.
[24]Mallat S G A theory for multiresolution signal decomposition:the wavelet representation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1989,11 (7):674-693.
[25]Mallat S G. Multiresolution approximations and wavelet orthonormal bases of L2(R)[J]. Transactions of the American Mathematical Society,1989,315(1): 69-87.
[26]Saito N, Beylkin G. Multiresolution representations using the autocorrelation functions of compactly supported wavelets[J]. IEEE Transactions on Signal Processing,1993,41(12):3584-3590.
[27]Michael Unser. Splines:A Perfect Fit for Signal and Image Processing[J]. IEEE Transactions on Signal Processing,1999, (11):22-38.
[28]Chulhee Lee, Murray Eden, Michael Unser. High-Quality Image Resizing Using Oblique Projection Operators[J]. IEEE Transactions on Image Processing,1998,7(5):679-692.
[29]Thevenaz P, Blu T, Unser M. Interpolation revisited [medical images application][J]. IEEE Transactions on Medical Imaging,2000,19(7):739-758.
[30]Thomas M. Lehmann, Claudia Gonner, Klaus Spitzer. Survey:Interpolation Methods in Medical Image Processing[J]. IEEE Transactions on Medical Imaging,1999,18(11):1049-1075.
[31]胡迪鹤.随机过程论第二版[M].武汉：武汉大学出版社,2005.
[32]刘河生,高小榕,杨福生.隐马尔可夫模型的原理与实现[J].国外医学生物医学工程分册,2002,25(6)：253-259.
[33]尚丽.RoboCup2D中的多Agent协作技术研究[D].合肥工业大学.2010.
[34]Van Der Merwe R. Sigma-point Kalman filters for probabilistic inference in dynamic state-space models[D]. University of Stellenbosch,2004.
[35]Julier S. J., Uhlmann J.K. Unscented filtering and nonlinear estimation[J]. Proceedings of the IEEE,2004,92(3):401-422.
[36]Van Der Merwe R, Wan E A. The square-root unscented Kalman filter for state and parameter-estimation[C] Acoustics, Speech, and Signal Processing,2001. Proceedings.(ICASSP'01).2001 IEEE International Conference on. IEEE,2001, 6:3461-3464.
[37]汪西莉,刘芳,焦李成.一种小波域HMT模型参数初始化方法[J].计算机科学,2003,30(1)：85-87.
[38]Zhao S, Han H, Peng S. Wavelet-domain HMT-based image super-resolution[C] IEEE International Conference on Image Processing,2003,2(9):14-17.
[39]Woo D.H, Eom I.K, Kim Y.S. Image interpolation based on interscale dependency in wavelet domain[C]. IEEE International Conference on Image Processing,2004,3:1687-1690.
[40]Romberg J K, Choi H, Baraniuk R G Bayesian tree-structured image modeling using wavelet-domain hidden Markov models[J]. IEEE Transactions on Image Processing,2001,10(7):1056-1068.
[41]彭玲.基于小波域隐马尔可夫树模型的遥感图像纹理分类研究[D].中国科学院遥感应用研究所.2005.
[42]Bilmes J A. A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models[J]. International Computer Science Institute,1998,4(510):10-126.
[43]浦利,刘玉树,金伟其.基于非均衡系数小波变换的插值算法研究[J].南京理工大学学报：自然科学版,2007,3：323-326.
[44]龙兴明,周静.基于EM算法的图像小波系数统计研究[J].计算机仿真,2005,22(6)：71-74.
[45]汪西莉,刘芳,焦李成.一种小波域HMT模型参数初始化方法[J].计算机科学,2003,30(1)：85-86.
[46]Elad M, Feuer A. Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images[J]. IEEE Transactions on Image Processing,1997,6(12):1646-1658.
[2]朱艳亮.实时视频缩放算法研究及FPGA实现[D].中南大学.2009.
[3]Parker J A, Kenyon R V, Troxel D E. Comparison of interpolating methods for image resampling[J]. IEEE Transactions on Medical Imaging,1983,2(1):31-39.
[4]Jain A K. Fundamentals of Digital Image Processing[M]. Englewood Cliffs: prentice-Hall,1989.
[5]Chen T.C., Figueiredo R.J.P.de. Two-dimensional Interpolation by Generalized Spline Filters Based on Partial Differential Equation Image Models [J]. IEEE Transactions on Acoustics, Speech, and Signal Processing,1985,33(3):631-642.
[6]章毓晋.图像处理和分析[M].北京：清华大学出版社,1999.
[7]Yokoya N, Yamamoto K. Fractal-based Analysis and Interpolation of 3D Natural Surface Shapes and Their Application to Terrain Modeling[J]. Computer Vision, Graphics and Image Processing,1989,46(3):284-302.
[8]Ledda.A, Luong.H.Q, Philips.W, De Witte.V, Kerre.E.E. Image interpolation using mathematical morphology[C]. Proceedings of the Second International Conference on Document Image Analysis for Libraries,2006, (4):358-367.
[9]Stanco F., Gallo G, Battiato S. A Locally-Adaptive Zooming Algorithm for Digital Images[J]. Image and Vision Computing Journal,2002,20(11): 805-812.
[10]Dan Su, Philip Willis. Image Interpolation by Pixel-Level Data-Dependent Triangulation[J]. Computer Graphics Forum,2004,23(7):189-201.
[11]刘笑宙,涂国防.小波双线性插值应用于光学遥感图像[J].中国科学院研究生院学报,2003,20(1)：39-43.
[12]屈有山,田维坚,李英才,张薇,达选福.基于小波双三次插值提高光学 遥感图像空间分辨率的研究[J].光子学报,2004,33(5)：604-601.
[13]陈德元,涂国防.小波分形插值医学图像处理[J].电视技术,2001(6)：67-70.
[14]Nhat Nguyen, Peyman Milanfar. A wavelet-based interpolation-restoration method for superresolution (wavelet superresolution) [J]. Circuits, Systems and Signal Process,2000,19(4):321-338.
[15]Yu-Len Huang. Wavelet-based image interpolation using multilayer perceptrons [J]. Neural Computing & Applications,2005,14(1):1-10.
[16]Woo D.H., Eom I.K., Kim Y.S. Image Interpolation based on interscale dependency in wavelet domain[J]. IEEE ICIP,2004,3(10):1687-1690.
[17]郭晓新.超分辨率重建问题的研究[D].吉林大学.2005.
[18]张明.图像超分辨率重建和插值算法研究[D].中国科学技术大学.2010.
[19]Vega M, Molina R, Katsaggelos A.K. A Bayesian super-resolution approach to demosaicing of blurred images [J]. EURASIP Journal on Applied Signal Processing.2006(01):1-12.
[20]彭玉华.小波变换与工程应用[M].北京：科学出版社,1999.
[21]杨福生.小波变换的工程分析与应用[M].北京：科学出版社,1999.
[22]邓堰.转子故障智能诊断中的特征提取与选择技术研究[D].南京航空航天大学.2008.
[23]Daubechies I. Ten Lectures on Wavelet [M]. Capital City Press,1992.
[24]Mallat S G A theory for multiresolution signal decomposition:the wavelet representation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1989,11 (7):674-693.
[25]Mallat S G. Multiresolution approximations and wavelet orthonormal bases of L2(R)[J]. Transactions of the American Mathematical Society,1989,315(1): 69-87.
[26]Saito N, Beylkin G. Multiresolution representations using the autocorrelation functions of compactly supported wavelets[J]. IEEE Transactions on Signal Processing,1993,41(12):3584-3590.
[27]Michael Unser. Splines:A Perfect Fit for Signal and Image Processing[J]. IEEE Transactions on Signal Processing,1999, (11):22-38.
[28]Chulhee Lee, Murray Eden, Michael Unser. High-Quality Image Resizing Using Oblique Projection Operators[J]. IEEE Transactions on Image Processing,1998,7(5):679-692.
[29]Thevenaz P, Blu T, Unser M. Interpolation revisited [medical images application][J]. IEEE Transactions on Medical Imaging,2000,19(7):739-758.
[30]Thomas M. Lehmann, Claudia Gonner, Klaus Spitzer. Survey:Interpolation Methods in Medical Image Processing[J]. IEEE Transactions on Medical Imaging,1999,18(11):1049-1075.
[31]胡迪鹤.随机过程论第二版[M].武汉：武汉大学出版社,2005.
[32]刘河生,高小榕,杨福生.隐马尔可夫模型的原理与实现[J].国外医学生物医学工程分册,2002,25(6)：253-259.
[33]尚丽.RoboCup2D中的多Agent协作技术研究[D].合肥工业大学.2010.
[34]Van Der Merwe R. Sigma-point Kalman filters for probabilistic inference in dynamic state-space models[D]. University of Stellenbosch,2004.
[35]Julier S. J., Uhlmann J.K. Unscented filtering and nonlinear estimation[J]. Proceedings of the IEEE,2004,92(3):401-422.
[36]Van Der Merwe R, Wan E A. The square-root unscented Kalman filter for state and parameter-estimation[C] Acoustics, Speech, and Signal Processing,2001. Proceedings.(ICASSP'01).2001 IEEE International Conference on. IEEE,2001, 6:3461-3464.
[37]汪西莉,刘芳,焦李成.一种小波域HMT模型参数初始化方法[J].计算机科学,2003,30(1)：85-87.
[38]Zhao S, Han H, Peng S. Wavelet-domain HMT-based image super-resolution[C] IEEE International Conference on Image Processing,2003,2(9):14-17.
[39]Woo D.H, Eom I.K, Kim Y.S. Image interpolation based on interscale dependency in wavelet domain[C]. IEEE International Conference on Image Processing,2004,3:1687-1690.
[40]Romberg J K, Choi H, Baraniuk R G Bayesian tree-structured image modeling using wavelet-domain hidden Markov models[J]. IEEE Transactions on Image Processing,2001,10(7):1056-1068.
[41]彭玲.基于小波域隐马尔可夫树模型的遥感图像纹理分类研究[D].中国科学院遥感应用研究所.2005.
[42]Bilmes J A. A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models[J]. International Computer Science Institute,1998,4(510):10-126.
[43]浦利,刘玉树,金伟其.基于非均衡系数小波变换的插值算法研究[J].南京理工大学学报：自然科学版,2007,3：323-326.
[44]龙兴明,周静.基于EM算法的图像小波系数统计研究[J].计算机仿真,2005,22(6)：71-74.
[45]汪西莉,刘芳,焦李成.一种小波域HMT模型参数初始化方法[J].计算机科学,2003,30(1)：85-86.
[46]Elad M, Feuer A. Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images[J]. IEEE Transactions on Image Processing,1997,6(12):1646-1658.