运动模糊图像恢复方法
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摘要
运动模糊图像恢复一直是图像恢复领域的热点问题,无论在工业、军事、医疗等领域还是在日常生活中都有非常广泛的应用。近年来,多种图像去运动模糊方法被相继提出,但其中绝大部分算法具有计算复杂、速度缓慢、不能处理较大的运动模糊核、需要多幅图像甚至辅助的硬件设备、恢复的图像带有严重的振铃效应等缺点,距离实际应用都相差甚远。本文提出了一种快速、鲁棒的基于反盲卷积的单幅运动模糊图像恢复算法,该算法通过冲击滤波器预测清晰图像的强边缘,该预测使得我们可以使用简单而易于优化的高斯分布先验知识来约束自然图像的梯度和运动模糊核,并能够在频域中快速、准确地计算出运动模糊核;之后我们通过基于自然图像梯度大尾巴分布的稀疏反非盲卷积算法恢复清晰图像,该算法能够恢复出图像清晰的边缘和纹理,并能够显著地抑制振铃效应以及图像的噪声。在计算运动模糊核的过程中,我们使用共轭梯度法来优化能量方程,并利用图像一阶和二阶导数比图像像素值本身具有更小的条件数的良好结构使得算法能够快速收敛。此外,本文提出的约束运动模糊核的磁滞阈值方法可以显著地抑制运动模糊核的噪声;本文提出的运动模糊核中心定位的方法极大地提高了计算较大运动模糊核的鲁棒性。实验结果表明,本文提出的算法可以快速、稳定地从单幅运动模糊图像恢复出具有清晰边缘和纹理、极少振铃和噪声的高质量的清晰图像。
Image motion deblurring is a research hot spot in image restoration, and applied abroad in industry, military affairs, medical treatment and daily life. In recent years, lots of algorithms about image motion deblurring have been proposed, however, most of them have limitations such as heavy computation, slow speed, small motion kernel assumption, multi-images, additional hardware, or severe artifacts such as ringing, and all of them make it far from practical use. In this paper, we introduce a fast, robust blind deconvolution based single image motion deblurring algorithm. We use shock filter to predict strong edges of latent image, and with this we can constrain image gradients and motion kernel with simple and easily optimized Gaussian prior, and estimate motion kernel in frequency domain fast and robustly. After that, we use a heavy-tailed distribution of natural images based sparse non-blind deconvolution algorithm to restore the latent image, which can restore the salient edges and texture as well as suppresses ringing and noise. In the motion kernel estimation part, we use conjugate gradient method to optimize the energy function, and use well conditioned image first and second derivatives with small condition number only and exclude pixel value with large condition number to make the algorithm converge fast. Besides, we introduce a hysteresis thresholding to suppress the noise of motion kernel significantly, and use a re-center method to improve the robustness of large motion kernel estimation. The experimental results show that our algorithm can restore high quality latent images with clear edge and texture, little ringing or noise from a single motion blurred image fast and robustly.
Image motion deblurring is a research hot spot in image restoration, and applied abroad in industry, military affairs, medical treatment and daily life. In recent years, lots of algorithms about image motion deblurring have been proposed, however, most of them have limitations such as heavy computation, slow speed, small motion kernel assumption, multi-images, additional hardware, or severe artifacts such as ringing, and all of them make it far from practical use. In this paper, we introduce a fast, robust blind deconvolution based single image motion deblurring algorithm. We use shock filter to predict strong edges of latent image, and with this we can constrain image gradients and motion kernel with simple and easily optimized Gaussian prior, and estimate motion kernel in frequency domain fast and robustly. After that, we use a heavy-tailed distribution of natural images based sparse non-blind deconvolution algorithm to restore the latent image, which can restore the salient edges and texture as well as suppresses ringing and noise. In the motion kernel estimation part, we use conjugate gradient method to optimize the energy function, and use well conditioned image first and second derivatives with small condition number only and exclude pixel value with large condition number to make the algorithm converge fast. Besides, we introduce a hysteresis thresholding to suppress the noise of motion kernel significantly, and use a re-center method to improve the robustness of large motion kernel estimation. The experimental results show that our algorithm can restore high quality latent images with clear edge and texture, little ringing or noise from a single motion blurred image fast and robustly.
引文
[1] A.C. Likas, N.P. Galatsanos. A Variational Approach for Bayesian Blind Image Deconvolution. IEEE Transactions on Signal Processing, 2004, 52:2222-2233
[2] A.K. Katsaggelos, K.T. Lay. Maximum Likelihood Blur Identification and Image Restoration Using the EM Algorithm. IEEE Transactions on Signal Processing, 1991, 39(3):729-733
[3] A. Levin, A. Zomet, Y Weiss. Learning How to Inpaint from Global Image Statistics. Proceedings of IEEE International Conference on Computer Vision, 2003, 2:305
[4] A. Levin, P. Sand, T.S. Cho, F.Durand, W.T.Freeman. Motion-Invariant Photography. ACM Transactions on Graphics, 2008, 27(3)
[5] A. Levin, R. Fergus, F. Durand, W.T. Freeman. Image and Depth From a Conventional Camera with a Coded Aperture. ACM Transactions on Graphics, 2007, 26(3)
[6] A. Levin, Y. Weiss, F. Durand, W.T. Freeman. Understanding and Evaluating Blind Deconvolution Algorithms. Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2009
[7] A. Levin, Y. Weiss, F. Durand, W.T. Freeman. Understanding and evaluating blind econvolution algorithms. Technical report, MIT-CSAIL-TR-2009-014, 2009
[8] A. Levin. Blind motion deblurring using image statistics. Neural Information Processing Systems, 2006
[9] A. Rav-Acha, S. Peleg. Two Motion-Blurred Images are Better Than One. Pattern Recognition Letters, 2005, 26(3):311-317
[10] B. Bascle, A. Blake, A. Zisserman. Motion Deblurring and Super-resolution from an Image Sequence. Proceedings of European Conference on Computer Vision, 1996, 2:573-582
[11] B. Weiss. Fast Median and Bilateral Filtering. ACM Transactions of Graphics, 2006, 25(3):519-526
[12] C. Tomasi, R. Manduchi. Bilateral Filtering for Gray and Color Images. Proceedings of IEEE International Conference on Computer Vision, 1998
[13] D. Kundur, D. Hatzinakos. Blind image deconvolution. IEEE Signal Processing Magazine, 1996
[14] E. Thiebaut, J.-M. Conan. Strict a Priori Constraints for Maximum-Likelihood Blind Deconvolution. Journal of the Optical Society of America A: Optics, Image Science, and Vision, 1995, 12(3):485-492
[15] G.R. Ayers, J.C. Dainty. Interative Blind Deconvolution Method and Its Applications. Optics Letters, 1988, 13(7):547-549
[16] J. Canny. A Computational Approach to Edge Detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1986, 8(6):679-698
[17] J.H. Money, S.H. Kang. Total Variation Minimizing Blind Deconvolution with Shock Filter Reference. Image and Vision Computing, 2008, 26(2):302-314
[18] J. Jia. Single Image Motion Deblurring Using Transparency. Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2007
[19] J. Portilla, V. Strela, M. Wainwright, E.P. Simoncelli. Image Denoising Using Scale Mixtures of Gaussians in the Wavelet Domain. IEEE Transactions on Image Processing, 2003, 12(11):1338-1351
[20] J.W. Miskin ,D.J.C. MacKay. Ensemble Learning for Blind Image Separation and Deconvolution. Independent Component Analysis, 2000
[21] L. Lucy. An Iterative Technique for the Rectification of Observed Distributions. Astronomical Journal, 1974, 79(6):745-754
[22] L. Yuan, J. Sun, L. Quan, H.-Y. Shum. Blurred/Non-Blurred Image Alignment Using an Image Sequence. ACM Transactions on Graphics, 2007
[23] L. Yuan, J. Sun, L. Quan, H.-Y. Shum. Image Deblurring with Blurred/Noisy Image Pairs. ACM Transactions on Graphics, 2007, 26(3)
[24] L. Yuan, J. Sun, L. Quan, H.-Y. Shum. Progressive Inter-Scale and Intra-Scale Non-Blind Image Deconvolution. ACM Transactions on Graphics, 2008, 27(3)
[25] M. Ben-Ezra, S.K. Nayar. Motion Deblurring Using Hybrid Imaging. Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003, 1:657-664
[26] M. Ben-Ezra, S.K. Nayar. Motion-Based Motion Deblurring. IEEE Transactions on Pattern Analysis Machine Intelligence, 2004, 26(6):689-698
[27] M. Donatelli, C. Estatico, A. Martinelli, S. Serra-Capizzano. Improved Image Deblurring with Antireflective Boundary Conditions and Re-Blurring. Inverse Problems, 2006, 22(6):2035-2053
[28] M.F. Tappen, B.C. Russell, W.T. Freeman. Exploiting the Sparse Derivative Prior for Super-Resolution and Image Demosaicing. IEEE Workshop on Statistical and Computational Theories of Vision, 2003
[29] M.K. Simon. Probability Distributions Involving Gaussian Random Variables: A Handbook for Engineers, Scientists and Mathematicians. Springer, 2002
[30] N. Joshi, R. Szeliski, D. Kreigman. PSF Estimation Using Sharp Edge Prediction. Proceeding of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2008
[31] N. Wiener. Extrapolation, Interpolation, and Smoothing of Stationary Time Series. MIT Press, 1964
[32] Q. Hou, K. Zhou, B. Guo. BSGP: Bulksynchronous GPU Programming. ACM Transactions on Graphics, 2008, 27(3)
[33] Q. Shan, J. Jia, A. Agarwala. High-Quality Motion Deblurring from a Single Image. ACM Transactions on Graphics, 2008, 27(3):73
[34] Q. Shan, W. Xiong, J. Jia. Rotational Motion Deblurring of a Rigid Object from a Single Image. Proceeding of IEEE International Conference on Computer Vision, 2007
[35] R.N. Bracewell. The Fourier Transform and Its Applications. McGraw-Hill, 1999
[36] R.C. Gonzalez, R.E. Woods. Digital Image Processing. Prentice Hall, 2002
[37] R. Fergus, B. Singh, A. Hertzmann, S.T. Roweis, W.T. Freeman. Removing Camera Shake From a Single Photograph. ACM Transactions on Graphics, 2006, 25:783-794
[38] R. Liu, J. Jia. Reducing Boundary Artifacts in Image Deconvolution. International Conference on Image Processing, 2008
[39] R. Molina, A.K. Katsaggelos, J. Abad, J. Mateos. A Bayesian Approach to Blind Deconvolution Based on Dirichlet Distributions. International Conference on Acoustics, Speech, and Signal Processing, 1997
[40] S. Cho, S. Lee. Fast Motion Deblurring. ACM Transactions on Graphics(SIGGRAPH ASIA), 2009, 28(5): 145
[41] S. Cho, Y. Matsushita, S. Lee. Removing Non-Uniform Motion Blur from Images. Proceedings of the IEEE International Conference on Computer Vision 2007
[42] S.H. Lim, D.A. Silverstein. Method for deblurring an image. US Patent Application, Pub. No. US2006/0187308 A1, 2006
[43] S.-J. Kim, K. Koh, M. Lustig, S. Boyd. An Efficient Method for Compressed Sensing. Proceedings of International Conference on Image Processing, 2007
[44] S. Osher, L.I. Rudin. Feature-Oriented Image Enhancement using Shock Filters. SIAM Journal on Numerical Analysis, 1990, 27(4):919-940
[45] S. Roth, M.J. Black. Fields of Experts: A Framework for Learning Image Priors. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005, 2:860-867
[46] T.W. Gamelin. Complex Analysis. Springer, 2003
[47] Y.-W. Tai, H. Du, M.S. Brown, S. Lin. Image/Video Deblurring Using a Hybrid Camera. Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2008
[48] Y. Weiss, W.T. Freeman. What Makes a Good Model of Natural Images? Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2007
[2] A.K. Katsaggelos, K.T. Lay. Maximum Likelihood Blur Identification and Image Restoration Using the EM Algorithm. IEEE Transactions on Signal Processing, 1991, 39(3):729-733
[3] A. Levin, A. Zomet, Y Weiss. Learning How to Inpaint from Global Image Statistics. Proceedings of IEEE International Conference on Computer Vision, 2003, 2:305
[4] A. Levin, P. Sand, T.S. Cho, F.Durand, W.T.Freeman. Motion-Invariant Photography. ACM Transactions on Graphics, 2008, 27(3)
[5] A. Levin, R. Fergus, F. Durand, W.T. Freeman. Image and Depth From a Conventional Camera with a Coded Aperture. ACM Transactions on Graphics, 2007, 26(3)
[6] A. Levin, Y. Weiss, F. Durand, W.T. Freeman. Understanding and Evaluating Blind Deconvolution Algorithms. Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2009
[7] A. Levin, Y. Weiss, F. Durand, W.T. Freeman. Understanding and evaluating blind econvolution algorithms. Technical report, MIT-CSAIL-TR-2009-014, 2009
[8] A. Levin. Blind motion deblurring using image statistics. Neural Information Processing Systems, 2006
[9] A. Rav-Acha, S. Peleg. Two Motion-Blurred Images are Better Than One. Pattern Recognition Letters, 2005, 26(3):311-317
[10] B. Bascle, A. Blake, A. Zisserman. Motion Deblurring and Super-resolution from an Image Sequence. Proceedings of European Conference on Computer Vision, 1996, 2:573-582
[11] B. Weiss. Fast Median and Bilateral Filtering. ACM Transactions of Graphics, 2006, 25(3):519-526
[12] C. Tomasi, R. Manduchi. Bilateral Filtering for Gray and Color Images. Proceedings of IEEE International Conference on Computer Vision, 1998
[13] D. Kundur, D. Hatzinakos. Blind image deconvolution. IEEE Signal Processing Magazine, 1996
[14] E. Thiebaut, J.-M. Conan. Strict a Priori Constraints for Maximum-Likelihood Blind Deconvolution. Journal of the Optical Society of America A: Optics, Image Science, and Vision, 1995, 12(3):485-492
[15] G.R. Ayers, J.C. Dainty. Interative Blind Deconvolution Method and Its Applications. Optics Letters, 1988, 13(7):547-549
[16] J. Canny. A Computational Approach to Edge Detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1986, 8(6):679-698
[17] J.H. Money, S.H. Kang. Total Variation Minimizing Blind Deconvolution with Shock Filter Reference. Image and Vision Computing, 2008, 26(2):302-314
[18] J. Jia. Single Image Motion Deblurring Using Transparency. Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2007
[19] J. Portilla, V. Strela, M. Wainwright, E.P. Simoncelli. Image Denoising Using Scale Mixtures of Gaussians in the Wavelet Domain. IEEE Transactions on Image Processing, 2003, 12(11):1338-1351
[20] J.W. Miskin ,D.J.C. MacKay. Ensemble Learning for Blind Image Separation and Deconvolution. Independent Component Analysis, 2000
[21] L. Lucy. An Iterative Technique for the Rectification of Observed Distributions. Astronomical Journal, 1974, 79(6):745-754
[22] L. Yuan, J. Sun, L. Quan, H.-Y. Shum. Blurred/Non-Blurred Image Alignment Using an Image Sequence. ACM Transactions on Graphics, 2007
[23] L. Yuan, J. Sun, L. Quan, H.-Y. Shum. Image Deblurring with Blurred/Noisy Image Pairs. ACM Transactions on Graphics, 2007, 26(3)
[24] L. Yuan, J. Sun, L. Quan, H.-Y. Shum. Progressive Inter-Scale and Intra-Scale Non-Blind Image Deconvolution. ACM Transactions on Graphics, 2008, 27(3)
[25] M. Ben-Ezra, S.K. Nayar. Motion Deblurring Using Hybrid Imaging. Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003, 1:657-664
[26] M. Ben-Ezra, S.K. Nayar. Motion-Based Motion Deblurring. IEEE Transactions on Pattern Analysis Machine Intelligence, 2004, 26(6):689-698
[27] M. Donatelli, C. Estatico, A. Martinelli, S. Serra-Capizzano. Improved Image Deblurring with Antireflective Boundary Conditions and Re-Blurring. Inverse Problems, 2006, 22(6):2035-2053
[28] M.F. Tappen, B.C. Russell, W.T. Freeman. Exploiting the Sparse Derivative Prior for Super-Resolution and Image Demosaicing. IEEE Workshop on Statistical and Computational Theories of Vision, 2003
[29] M.K. Simon. Probability Distributions Involving Gaussian Random Variables: A Handbook for Engineers, Scientists and Mathematicians. Springer, 2002
[30] N. Joshi, R. Szeliski, D. Kreigman. PSF Estimation Using Sharp Edge Prediction. Proceeding of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2008
[31] N. Wiener. Extrapolation, Interpolation, and Smoothing of Stationary Time Series. MIT Press, 1964
[32] Q. Hou, K. Zhou, B. Guo. BSGP: Bulksynchronous GPU Programming. ACM Transactions on Graphics, 2008, 27(3)
[33] Q. Shan, J. Jia, A. Agarwala. High-Quality Motion Deblurring from a Single Image. ACM Transactions on Graphics, 2008, 27(3):73
[34] Q. Shan, W. Xiong, J. Jia. Rotational Motion Deblurring of a Rigid Object from a Single Image. Proceeding of IEEE International Conference on Computer Vision, 2007
[35] R.N. Bracewell. The Fourier Transform and Its Applications. McGraw-Hill, 1999
[36] R.C. Gonzalez, R.E. Woods. Digital Image Processing. Prentice Hall, 2002
[37] R. Fergus, B. Singh, A. Hertzmann, S.T. Roweis, W.T. Freeman. Removing Camera Shake From a Single Photograph. ACM Transactions on Graphics, 2006, 25:783-794
[38] R. Liu, J. Jia. Reducing Boundary Artifacts in Image Deconvolution. International Conference on Image Processing, 2008
[39] R. Molina, A.K. Katsaggelos, J. Abad, J. Mateos. A Bayesian Approach to Blind Deconvolution Based on Dirichlet Distributions. International Conference on Acoustics, Speech, and Signal Processing, 1997
[40] S. Cho, S. Lee. Fast Motion Deblurring. ACM Transactions on Graphics(SIGGRAPH ASIA), 2009, 28(5): 145
[41] S. Cho, Y. Matsushita, S. Lee. Removing Non-Uniform Motion Blur from Images. Proceedings of the IEEE International Conference on Computer Vision 2007
[42] S.H. Lim, D.A. Silverstein. Method for deblurring an image. US Patent Application, Pub. No. US2006/0187308 A1, 2006
[43] S.-J. Kim, K. Koh, M. Lustig, S. Boyd. An Efficient Method for Compressed Sensing. Proceedings of International Conference on Image Processing, 2007
[44] S. Osher, L.I. Rudin. Feature-Oriented Image Enhancement using Shock Filters. SIAM Journal on Numerical Analysis, 1990, 27(4):919-940
[45] S. Roth, M.J. Black. Fields of Experts: A Framework for Learning Image Priors. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005, 2:860-867
[46] T.W. Gamelin. Complex Analysis. Springer, 2003
[47] Y.-W. Tai, H. Du, M.S. Brown, S. Lin. Image/Video Deblurring Using a Hybrid Camera. Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2008
[48] Y. Weiss, W.T. Freeman. What Makes a Good Model of Natural Images? Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2007