Iterative Total Variation Regularization with Non-Quadratic Fidelity
- 122 Downloads
A generalized iterative regularization procedure based on the total variation penalization is introduced for image denoising models with non-quadratic convex fidelity terms. By using a suitable sequence of penalty parameters we solve the issue of solvability of minimization problems arising in each step of the iterative procedure, which has been encountered in a recently developed iterative total variation procedure Furthermore, we obtain rigorous convergence results for exact and noisy data.
We test the behaviour of the algorithm on real images in several numerical experiments using L 1 and L 2 fitting terms. Moreover, we compare the results with other state-of-the art multiscale techniques for total variation based image restoration.
Keywordsiterative regularization total variation methods image denoising multiscale methods Bregman distances
Unable to display preview. Download preview PDF.
- 1.J.F. Aujol, G. Aubert, L. Blanc-Feraud, and A. Chambolle, “Decomposing an image: Application to textured images and SAR images,” J. Math. Imaging Vision, 2005.Google Scholar
- 4.T.F. Chan and S. Esedoglu, Aspects of total variation regularized L 1 function approximation, CAM-Report 04-07, UCLA, Los Angeles, CA, CAM-Report 04-07, 2004.Google Scholar
- 6.D. Goldfarb and W. Yin, Second order cone programming methods for total variation-based image restoration, CORC Report TR-2004-05, Columbia University, New York, 2004.Google Scholar
- 8.H. Lin, A. Marquina and S. Osher, “Blind deconvolution using TV regularization and bregman iteration,” UCLA CAM report, pp. 04–51, 2004.Google Scholar
- 9.Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. AMS, Providence, RI, 2001.Google Scholar
- 10.S. Osher, M. Burger, D. Goldfarb, J. Xu and W. Yin, “An iterative regularization method for total variation based image restoration,” Multiscale Modeling and Simulation. to appear 2005.Google Scholar
- 13.O. Scherzer and C. Groetsch, Inverse Scale Space Theory for Inverse Problems. Springer-Verlag, New York, 2001.Google Scholar
- 14.O. Scherzer and C. Groetsch, “Inverse scale space theory for inverse problems,” In M. Kerckhove (Ed.), Scale-Space and Morphology in Computer Vision, Lecture Notes in Comput. Sci. 2106, Springer, New York, 2001, pp. 317–325.Google Scholar