Abstract
We present a theoretical analysis and a new algorithm for the problem of super-resolution imaging: the reconstruction of HR (high-resolution) images from a sequence of LR (low-resolution) images. Super-resolution imaging entails solutions to two problems. One is the alignment of image frames. The other is the reconstruction of a HR image from multiple aligned LR images. Our analysis of the latter problem reveals insights into the theoretical limits of super-resolution reconstruction. We find that at best we can reconstruct a HR image blurred by a specific low-pass filter. Based on the analysis we present a new wavelet-based iterative reconstruction algorithm which is very robust to noise. Furthermore, it has a computationally efficient built-in denoising scheme with a nearly optimal risk bound. Roughly speaking, our method could be described as a better-conditioned iterative back-projection scheme with a fast and optimal regularization criteria in each iteration step. Experiments with both simulated and real data demonstrate that our approach has significantly better performance than existing super-resolution methods. It has the ability to remove even large amounts of mixed noise without creating smoothing artifacts.
Chapter PDF
Similar content being viewed by others
Keywords
- Iterative Reconstruction
- Tikhonov Regularization
- Total Variation Regularization
- Wavelet Denoising
- Mixed Noise
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Irani, M., Peleg, F.: Motion analysis for image enhancement: Resolution, occlusion and transparency. Journal of Visual Comm. and Image Repr. 4, 324–335 (1993)
Eland, M., Feuer, A.: Restoration of a signal super-resolution image from several blurred, noisy and undersampled measured images. IEEE Transaction on Image Processing, 1646–1658 (1997)
Bascle, B., Blake, A., Zisserman, A.: Motion deblurring and super-resolution from an image sequence. In: Buxton, B.F., Cipolla, R. (eds.) ECCV 1996. LNCS, vol. 1065, pp. 573–582. Springer, Heidelberg (1996)
Zhao, W., Sawhney, H.S.: Is super-resolution with optical flow feasible? In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2350, pp. 599–613. Springer, Heidelberg (2002)
Tekalp, A., Ozkan, M., Sezan, M.: High-resolution image reconstruction from low-resolution image sequences and space-varying image restoration. In: ICASSP, pp. 169–172 (1992)
Farsiu, S., Robinson, D., Elad, M., Milanfar, P.: Robust shift and add approach to super-resolution. In: SPIE (2003)
Chambolle, A., Devore, R., Lee, N., Lucier, B.: Nonlinear wavelet image processing: variational problems, compression and noise removal through wavelets. IEEE Trans. Image Processing 7 (1998)
Youla, C.: Generalized image restoration by the method of alternating orthogonal projections IEEE Trans. Circuits Syst. 25 (1978)
Chan, R., Chan, T., Shen, L., Shen, Z.: Wavelet deblurring algorithms for spatially varying blur from high-resolution image reconstruction. Linear algebra and its applications 366, 139–155 (2003)
Nguyen, N., Milanfar, N.P.: An wavelet-based interpolation-restoration method for superresolution. Circuits, Systems and Signal Processing 19, 321–338 (2002)
Baker, S., Kanade, T.: Limits on super-resolution and how to break them. In: CVPR, pp. 372–379 (2000)
Mallat, S.: A wavelet tour of signal processing. Academic Press, London (1999)
Weickert, J.: Anisotropic Diffusion in Image Processing. ECMI Series, Teubner, Stuttgart (1998)
Mrazek, P., Weickert, J., Steidl, G.: Correspondences between wavelet shrinkage and nonlinear diffusion. In: Scale-Space, pp. 101–116 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ji, H., Fermüller, C. (2006). Wavelet-Based Super-Resolution Reconstruction: Theory and Algorithm. In: Leonardis, A., Bischof, H., Pinz, A. (eds) Computer Vision – ECCV 2006. ECCV 2006. Lecture Notes in Computer Science, vol 3954. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11744085_23
Download citation
DOI: https://doi.org/10.1007/11744085_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33838-3
Online ISBN: 978-3-540-33839-0
eBook Packages: Computer ScienceComputer Science (R0)