×

Blind motion deblurring using multiple images. (English) Zbl 1167.94307

Summary: Recovery of degraded images due to motion blurring is a challenging problem in digital imaging. Most existing techniques on blind deblurring are not capable of removing complex motion blurring from the blurred images of complex structures. One promising approach is to recover the clear image using multiple images captured for the scene. However, in practice it is observed that such a multi-frame approach can recover a high-quality clear image of the scene only after multiple blurred image frames are accurately aligned during pre-processing, which is a very challenging task even with user interactions. In this paper, by exploring the sparsity of the motion blur kernel and the clear image under certain domains, we propose an alternative iteration approach to simultaneously identify the blur kernels of given blurred images and restore a clear image. Our proposed approach is not only robust to image formation noises, but is also robust to the alignment errors among multiple images. A modified version of linearized Bregman iteration is then developed to efficiently solve the resulting minimization problem. Experiments show that our proposed algorithm is capable of accurately estimating the blur kernels of complex camera motions with minimal requirements on the accuracy of image alignment. As a result, our method is capable of automatically recovering a high-quality clear image from multiple blurred images.

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Andrews, H. C.; Hunt, B. R., Digital Image Restoration (1977), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0379.62098
[2] J. Bergen, P. Anandan, K. Hanna, R. Hingorani, Hierarchical model-based motion estimation, in: ECCV, 1992.; J. Bergen, P. Anandan, K. Hanna, R. Hingorani, Hierarchical model-based motion estimation, in: ECCV, 1992.
[3] Ben-Ezra, M.; Nayar, S. K., Motion-based motion deblurring, IEEE Trans. Pattern Anal. Machine Intell., 26, 6, 689-698 (2004)
[4] J.-F. Cai, H. Ji, C. Liu, Z. Shen, High-quality curvelet based motion deblurring using an image pair, in: CVPR, 2009.; J.-F. Cai, H. Ji, C. Liu, Z. Shen, High-quality curvelet based motion deblurring using an image pair, in: CVPR, 2009.
[5] J.-F. Cai, H. Ji, C. Liu, Z. Shen, Blind motion deblurring from a single image using sparse approximation, in: CVPR, 2009.; J.-F. Cai, H. Ji, C. Liu, Z. Shen, Blind motion deblurring from a single image using sparse approximation, in: CVPR, 2009.
[6] Cai, J.-F.; Osher, S.; Shen, Z., Linearized Bregman iterations for compressed sensing, Math. Comput., 78, 1515-1536 (2009) · Zbl 1198.65102
[7] Cai, J.-F.; Osher, S.; Shen, Z., Linearized Bregman iterations for frame-based image deblurring, SIAM J. Imaging Sci., 2, 1, 226-252 (2009) · Zbl 1175.94010
[8] J.-F. Cai, S. Osher, Z. Shen, Convergence of the linearized Bregman iteration for \(ℓ_1\); J.-F. Cai, S. Osher, Z. Shen, Convergence of the linearized Bregman iteration for \(ℓ_1\) · Zbl 1198.65103
[9] Chai, A.; Shen, Z., Deconvlolution: a wavelet frame approach, Numer. Math., 106, 529-587 (2007) · Zbl 1120.65134
[10] T.F. Chan, J. Shen, Image Processing and Analysis, Variational, PDE, Wavelet, and Stochastic Methods, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2005.; T.F. Chan, J. Shen, Image Processing and Analysis, Variational, PDE, Wavelet, and Stochastic Methods, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2005.
[11] Chan, T. F.; Wong, C. K., Total variation blind deconvolution, IEEE Trans. Image Process., 7, 3, 370-375 (1998)
[12] Chang, M. M.; Tekalp, A. M.; Erdem, A. T., Blur identification using the bispectrum, IEEE Trans. Signal Process., 39, 2323-2325 (1991)
[13] J. Darbon, S. Osher, Fast discrete optimization for sparse approximations and deconvolutions, in: preprint, 2007.; J. Darbon, S. Osher, Fast discrete optimization for sparse approximations and deconvolutions, in: preprint, 2007.
[14] Daubechies, I.; Han, B.; Ron, A.; Shen, Z., Framelets: MRA-based constructions of wavelet frames, Appl. Comput. Harmon. Anal., 14, 1-46 (2003) · Zbl 1035.42031
[15] Dobson, D. C.; Santosa, F., Recovery of blocky images from noisy and blurred data, SIAM J. Appl. Math., 56, 1181-1198 (1996) · Zbl 0858.68121
[16] Fergus, R.; Singh, B.; Hertzmann, A.; Roweis, S. T.; Freeman, W. T., Removing camera shake from a single photograph, Siggraph, 25, 783-794 (2006) · Zbl 1371.94125
[17] T. Goldstein, S. Osher, The split Bregman algorithm for l1 regularized problems, UCLA CAM Reports (08-29).; T. Goldstein, S. Osher, The split Bregman algorithm for l1 regularized problems, UCLA CAM Reports (08-29).
[18] He, L.; Marquina, A.; Osher, S. J., Blind deconvolution using TV regularization and Bregman iteration, Int. J. Imaging Syst. Technol., 15, 74-83 (2005)
[19] H. Ji, C.Q. Liu, Motion blur identification from image gradients, in: CVPR, 2008.; H. Ji, C.Q. Liu, Motion blur identification from image gradients, in: CVPR, 2008.
[20] Y. Lou, X. Zhang, S. Osher, A. Bertozzi, Image recovery via nonlocal operators, UCLA CAM Reports (08-35).; Y. Lou, X. Zhang, S. Osher, A. Bertozzi, Image recovery via nonlocal operators, UCLA CAM Reports (08-35). · Zbl 1203.65088
[21] Y. Lu, J. Sun, L. Quan, H. Shum, Blurred/non-blurred image alignment using kernel sparseness prior, IEEE Int. Conf. Comp. Vision (2007).; Y. Lu, J. Sun, L. Quan, H. Shum, Blurred/non-blurred image alignment using kernel sparseness prior, IEEE Int. Conf. Comp. Vision (2007).
[22] A. Marquina, Inverse scale space methods for blind deconvolution, UCLA CAM Reports (06-36).; A. Marquina, Inverse scale space methods for blind deconvolution, UCLA CAM Reports (06-36).
[23] Mayntz, C.; Aach, T., Blur identification using a spectral inertia tensor and spectral zeros, Proc. IEEE Int. Conf. Image Proc., 885-889 (1999)
[24] Ng, M. K.; Chan, R. H.; Tang, W., A fast algorithm for deblurring models with neumann boundary condition, SIAM J. Sci. Comput., 21, 3, 851-866 (2000) · Zbl 0951.65038
[25] Nikolova, M., Local strong homogeneity of a regularized estimator, SIAM J. Appl. Math., 61, 633-658 (2000) · Zbl 0991.94015
[26] Osher, S.; Burger, M.; Goldfarb, D.; Xu, J.; Yin, W., An iterative regularization method for total variation-based image restoration, Multiscale Model. Simul., 4, 460-489 (2005) · Zbl 1090.94003
[27] S. Osher, Y. Mao, B. Dong, W. Yin, Fast linearized Bregman iteration for compressed sensing and sparse denoising, UCLA CAM Reprots (08-37).; S. Osher, Y. Mao, B. Dong, W. Yin, Fast linearized Bregman iteration for compressed sensing and sparse denoising, UCLA CAM Reprots (08-37). · Zbl 1190.49040
[28] Rav-Acha, A.; Peleg, S., Two motion blurred images are better than one, Pattern Recogn. Lett., 26, 311-317 (2005)
[29] Raskar, R.; Tubmlin, J.; Mohan, A.; Agrawal, A.; Li, Y., Computational photography, Eurographics (2006)
[30] Raskar, R.; Agrawal, A.; Tumblin, J., Coded exposure photography: motion deblurring via fluttered shutter, Siggraph, 25, 795-804 (2006)
[31] Rekleitis, I. M., Steerable filters and cepstral analysis for optical flow calculation from a single blurred image, Vision Interface, 1, 159-166 (1996)
[32] Ron, A.; Shen, Z., Affine system in \(l_2(r^d)\): the analysis of the analysis operator, J. Funct. Anal., 148, 408-447 (1997) · Zbl 0891.42018
[33] Xu, J.; Osher, S. J., Iterative regularization and nonlinear inverse scale space applied to wavelet-based denoising, IEEE Trans. Image Process., 16, 534-544 (2007)
[34] Yin, W.; Osher, S.; Goldfarb, D.; Darbon, J., Bregman iterative algorithms for \(ℓ_1\)-minimization with applications to compressed sensing, SIAM J. Imaging Sci., 1, 143-168 (2008) · Zbl 1203.90153
[35] Zitova, B.; Flusser, J., Image registration methods: a survey, Image Vision Comput., 21, 11, 977-1000 (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.