Abstract
We introduce a locally adaptive parameter selection method for total variation regularization applied to image denoising. The algorithm iteratively updates the regularization parameter depending on the local smoothness of the outcome of the previous smoothing step. In addition, we propose an anisotropic total variation regularization step for edge enhancement. Test examples demonstrate the capability of our method to deal with varying, unknown noise levels.
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Acar, R., Vogel, C.R.: Analysis of bounded variation penalty methods for ill-posed problems. Inverse Probl. 10(6), 1217–1229 (1994)
Aubert, G., Kornprobst, P.: Mathematical problems in image processing. In: Partial differential equations and the calculus of variations, With a foreword by Olivier Faugeras, 2nd edn. Applied Mathematical Sciences, vol. 147. Springer, New York (2006)
Burger, M., Osher, S.: Convergence rates of convex variational regularization. Inverse Probl. 20(5), 1411–1421 (2004)
Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imaging Vision 20(1–2), 89–97 (2004)
Chambolle, A., Lions, P.-L.: Image recovery via total variation minimization and related problems. Numer. Math. 76(2), 167–188 (1997)
Davies, P.L., Kovac, A.: Local extremes, runs, strings and multiresolution. Ann. Statist. 29(1), 1–65 (2001)
Ekeland, I., Temam, R.: Convex Analysis and Variational Problems. North-Holland, Amsterdam (1976)
Engl, H.W., Hanke, M., Neubauer, A.: Regularization of inverse problems. Mathematics and its Applications, vol. 375. Kluwer Academic Publishers Group, Dordrecht (1996)
Frigaard, I.A., Ngwa, G., Scherzer, O.: On effective stopping time selection for visco-plastic nonlinear BV diffusion filters used in image denoising. SIAM J. Appl. Math. 63(6), 1911–1934 (electronic) (2003)
Frigaard, I.A., Scherzer, O.: Herschel–Bulkley diffusion filtering: non-Newtonian fluid mechanics in image processing. Z. Angew. Math. Mech. 86(6), 474–494 (2006)
Gilboa, G., Sochen, N., Zeevi, Y.Y.: Variational denoising of partly-textured images by spatially varying constraints. IEEE Trans. Image Process. 15(8), 2281–2289 (2006)
Ito, K., Kunisch, K.: Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces. Nonlinear Anal. 41A, 591–616 (2000)
Nashed, M.Z., Scherzer, O.: Least squares and bounded variation regularization with nondifferentiable functional. Numer. Funct. Anal. Optim. 19(7-8), 873–901 (1998)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60(1–4), 259–268 (1992)
Scherzer, O., Grasmair, M., Grossauer, H., Haltmeier, M., Lenzen, F.: Variational Methods in Imaging. Applied Mathematical Sciences, vol. 167. Springer, New York (2008)
Strong, D.M.: Adaptive Total Variation Minimizing Image Restoration. CAM Report 97-38, University of California, Los Angeles (1997)
Strong, D.M., Aujol, J.-F., Chan, T.F.: Scale recognition, regularization parameter selection, and Meyer’s G norm in total variation regularization. Multiscale Model. Simul. 5(1), 273–303 (electronic) (2006)
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Grasmair, M. (2009). Locally Adaptive Total Variation Regularization. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_28
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DOI: https://doi.org/10.1007/978-3-642-02256-2_28
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