Image super-resolution by TV-regularization and Bregman iteration. (English) Zbl 1203.94014
Summary: We formulate a new time dependent convolutional model for super-resolution based on a constrained variational model that uses the total variation of the signal as a regularizing functional. We propose an iterative refinement procedure based on Bregman iteration to improve spatial resolution. The model uses a dataset of low resolution images and incorporates a downsampling operator to relate the high resolution scale to the low resolution one. We present an algorithm for the model and we perform a series of numerical experiments to show evidence of the good behavior of the numerical scheme and quality of the results.
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 94A20 | Sampling theory in information and communication theory |
| 44A35 | Convolution as an integral transform |
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
| 65R10 | Numerical methods for integral transforms |
Keywords:
super-resolution; total variation restoration; Bregman iteration; downsampling; edge preservingReferences:
| [1] | Bregman, L.: The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming. USSR Comput. Math. Math. Phys. 7, 200–217 (1967) · Zbl 0186.23807 · doi:10.1016/0041-5553(67)90040-7 |
| [2] | Burger, M., Gilboa, G., Osher, S., Xu, J.: Nonlinear inverse scale space methods. Commun. Math. Sci. 4(1), 179–212 (2006) · Zbl 1106.68117 |
| [3] | Candela, V.F., Marquina, A., Serna, S.: A local spectral inversion of a linearized TV model for denoising and deblurring. IEEE Trans. Image Process. 12(7), 808–816 (2003) · doi:10.1109/TIP.2003.812760 |
| [4] | Chan, T.F., Ng, M.K., Yau, A.C., Yip, A.M.: Superresolution image reconstruction using fast inpainting algorithms. Appl. Comput. Harmon. Anal. 23, 3–24 (2007) · Zbl 1116.94002 · doi:10.1016/j.acha.2006.09.005 |
| [5] | Chaudhuri, S.: Super-Resolution Imaging. Kluwer Academic, Dordrecht (2001) |
| [6] | Gopinath, R.A., Burrus, C.S.: On upsampling, downsampling and rational sampling rate filter banks. IEEE Trans. Signal Process. 42, 812–824 (1994) · doi:10.1109/78.285645 |
| [7] | He, L., Marquina, A., Osher, S.J.: Blind deconvolution using TV regularization and Bregman iteration. Int. J. Imaging Syst. Technol. 15, 74–83 (2005) · doi:10.1002/ima.20040 |
| [8] | Irani, M., Peleg, S.: Motion analysis for image enhancement: resolution, occlusion and transparency. J. Vis. Commun. Image Represent. 4, 324–335 (1993) · doi:10.1006/jvci.1993.1030 |
| [9] | Malgouyres, F.: Total Variation Based oversampling of noisy images. Lect. Notes Comput. Sci. 2106, 111–122 (2001) · Zbl 0991.68098 · doi:10.1007/3-540-47778-0_10 |
| [10] | Malgouyres, F., Guichard, F.: Edge direction preserving image zooming: a mathematical and numerical analysis. SIAM J. Numer. Anal. 39, 1–37 (2001) · Zbl 1001.68174 · doi:10.1137/S0036142999362286 |
| [11] | Marquina, A.: Inverse scale space methods for blind deconvolution. UCLA CAM Report 06-36 (2006) |
| [12] | Marquina, A., Osher, S.: Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal. SIAM J. Sci. Comput. 22(2), 387–405 (2000) · Zbl 0969.65081 · doi:10.1137/S1064827599351751 |
| [13] | Osher, S.J., Burger, M., Goldfarb, D., Xu, J., Jin, W.: An Iterative regularization method for total variation based image restoration. Multiscale Model Simul. 4, 460–489 (2005) · Zbl 1090.94003 · doi:10.1137/040605412 |
| [14] | Peeters, R.R., Kornprobst, P., Nikolova, M., Sumert, S., Vieville, T., Malandain, G., Derich, R., Faugeras, O., Ng, M., Van Hecke, P.: The use of super-resolution techniques to reduce slice thickness. Int. J. Imaging Syst. Technol. 14, 131–138 (2004) · doi:10.1002/ima.20016 |
| [15] | Rudin, L., Osher, S.J.: Total variation based image restoration with free local constraints. In Proc. of the IEEE ICIP-94, vol. 1, pp. 31–35, Austin, TX (1994) |
| [16] | Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992) · Zbl 0780.49028 · doi:10.1016/0167-2789(92)90242-F |
| [17] | Scherzer, O., Groetsch, C.: Inverse scale space theory for inverse problems. In: Kerckhove, M. (ed.) Scale-Space and Morphology in Computer Vision. Lecture Notes in Computer Science, vol. 2106, pp. 317–325. Springer, New York (2001) · Zbl 0991.68132 |
| [18] | Unser, M., Aldrouli, A., Eden, M.: Enlargement or reduction of digital image with minimum loss of information. IEEE Trans. Image Process. 4, 247–258 (1995) · doi:10.1109/83.366474 |
| [19] | Vogel, C.R., Oman, M.E.: Fast, robust total variation-based reconstruction of noisy, blurred images. IEEE Trans. Image Process. 7(6), 813–824 (1998) · Zbl 0993.94519 · doi:10.1109/83.679423 |
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.
