Orthogonal projection algorithm for first and second order total variation denoising

Idriss El Mourabit (1) , Mohammed El Rhabi (2) , Abdelilah Hakim (1)

1 UCA - Université Cadi Ayyad [Marrakech]
2 ENPC - École des Ponts ParisTech

The denoising problem is the process of removing the noise from a degraded image. As we know, the Rodin Osher Fatemi (ROF) denoising model based on total variation is a robust approach for solving the ill-posed problem. To avoid the staircasing effects caused by the first order total variation, the second order one is proposed. In this work, we present an orthogonal projection algorithm for solving the ROF model with first and second order total variation. The efficiency and robustness against noise of the proposed model are illustrated and compared with the classical methods through numerical simulations.

Mots clés: second order total variation; Projection algorithm; Total variation; Denoising; Partial Differential Equation; Partial differential equations

Domaines: Analyse numérique [math.NA]; Traitement des images [eess.IV]

Idriss El Mourabit, Mohammed El Rhabi, Abdelilah Hakim. Orthogonal projection algorithm for first and second order total variation denoising. Annals of the University of Craiova. Mathematics and Computer Science series, 2015, 42 (1), pp.148-157. ⟨hal-01811732⟩