Abstract
We examine the problem of finding the optimal weight of the fidelity term in variational denoising. Our aim is to maximize the signal to noise ratio (SNR) of the restored image. A theoretical analysis is carried out and several bounds are established on the performance of the optimal strategy and a widely used method, wherein the variance of the residual part equals the variance of the noise. A necessary condition is set to achieve maximal SNR. We provide a practical method for estimating this condition and show that the results are sufficiently accurate for a large class of images, including piecewise smooth and textured images.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aujol, J.F., Gilboa, G.: Implementation and parameter selection for BV-Hilbert space regularizations, UCLA CAM Report 04-66 (November 2004)
Charbonnier, P., Blanc-Feraud, L., Aubert, G., Barlaud, M.: Two deterministic half-quadratic regularization algorithms for computed imaging. In: Proc. IEEE ICIP 1994, vol. 2, pp. 168–172 (1994)
Deriche, R., Faugeras, O.: Les EDP en traitement des images et vision par ordinateur. Traitement du Signal 13(6) (1996)
Engl, H.W., Gfrerer, H.: A posteriori parameter choice for general regularization methods for solving linear ill-posed problems. Appl. Numer. Math. 4(5), 395–417 (1988)
Gilboa, G., Sochen, N., Zeevi, Y.Y.: Estimation of optimal PDE-based denoising in the SNR sense. In: CCIT report No. 499, Technion (August 2004)
Gilboa, G., Sochen, N., Zeevi, Y.Y.: Texture preserving variational denoising using an adaptive fidelity term. In: Proc. VLSM 2003, Nice, France, pp. 137–144 (2003)
Mrázek, P., Navara, M.: Selection of optimal stopping time for nonlinear diffusion filtering. IJCV 52(2/3), 189–203 (2003)
Meyer, Y.: Oscillatory Patterns in Image Processing and Nonlinear Evolution Equations. University Lecture Series, vol. 22. AMS, Providence (2001)
Pereverzev, S., Schock, E.: Morozov’s discrepancy principle for Tikhonov regularization of severely ill-posed problems in finite-dimensional subspaces. Numer. Funct. Anal. Optim. 21, 901–916 (2000)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. PAMI 12(7), 629–639 (1990)
Rudin, L., Osher, S., Fatemi, E.: Nonlinear Total Variation based noise removal algorithms. Physica D 60, 259–268 (1992)
Vogel, R.V., Oman, M.E.: Iterative methods for total variation denoising. SIAM J. Scientific Computing 17(1), 227–238 (1996)
Weickert, J.: Coherence-enhancing diffusion of colour images. IVC 17, 201–212 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gilboa, G., Sochen, N.A., Zeevi, Y.Y. (2005). Estimation of the Optimal Variational Parameter via SNR Analysis. In: Kimmel, R., Sochen, N.A., Weickert, J. (eds) Scale Space and PDE Methods in Computer Vision. Scale-Space 2005. Lecture Notes in Computer Science, vol 3459. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11408031_20
Download citation
DOI: https://doi.org/10.1007/11408031_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25547-5
Online ISBN: 978-3-540-32012-8
eBook Packages: Computer ScienceComputer Science (R0)