Image Decomposition into a Bounded Variation Component and an Oscillating Component
- 747 Downloads
We construct an algorithm to split an image into a sum u + v of a bounded variation component and a component containing the textures and the noise. This decomposition is inspired from a recent work of Y. Meyer. We find this decomposition by minimizing a convex functional which depends on the two variables u and v, alternately in each variable. Each minimization is based on a projection algorithm to minimize the total variation. We carry out the mathematical study of our method. We present some numerical results. In particular, we show how the u component can be used in nontextured SAR image restoration.
Keywordstotal variation minimization BV texture restoration SAR images speckle
Unable to display preview. Download preview PDF.
- 1.L. Alvarez, Y. Gousseau, and J.M. Morel, “Scales in natural images and a consequence on their bounded variation norm,” in Scale-Space ‘99, volume 1682 of Lecture Notes in Computer Science, 1999.Google Scholar
- 2.J.F. Aujol, G. Aubert, L. Blanc-Féraud, and Antonin Chambolle, “Decomposing an image: Application to textured images and sar images,” 2003. INRIA Research Report 4704.Google Scholar
- 3.A. Chambolle, “An algorithm for total variation minimization and applications,” JMIV, Vol. 20, p. 89, 2004.Google Scholar
- 4.A. Chambolle and P.L. Lions, “Image recovery via total variation minimization and related problems,” Numerische Mathematik, Vol. 76, No. 3, pp. 167–188, 1997.Google Scholar
- 5.I. Ekeland and R. Temam, “Analyse convexe et problemes variationnels,” Grundlehren der mathematischen Wissenschaften, 2nd edn, Dunod, Vol. 224, 1983.Google Scholar
- 6.J.B. Hiriart-Urruty and C. Lemarechal, “Convex analysis ans minimisation algorithms I,” Grundlehren der mathematischen Wissenschaften, Springer-Verlag, Vol. 305, 1993.Google Scholar
- 7.Henderson Lewis, “Principle and applications of Imaging Radar,” Manual of Remote Sensing, 3rd edn., J. Wiley and Sons, Vol. 2, 1998.Google Scholar
- 8.Yves Meyer, “Oscillating patterns in image processing and in some nonlinear evolution equations,” The Fifteenth Dean Jacquelines B. Lewis Memorial Lectures, March 2001.Google Scholar
- 9.S.J. Osher, A. Sole, and L.A. Vese, “Image decomposition and restoration using total variation minimization and the H−1 norm,” SIAM Journal on Multiscale Modeling and Simulation, Vol. 1, No. 3, pp. 349–370, 2002.Google Scholar
- 10.T. Rockafellar, “Convex analysis,” Etudes Mathematiques Princeton University Press, 1974.Google Scholar
- 12.Luminita A. Vese and Stanley J. Osher, “Modeling textures with total variation minimization and oscillating patterns in image processing,” Journal of Scientific Computing, Vol. 15, pp. 553–572, 2003.Google Scholar