Chambolle's Projection Algorithm for Total Variation Denoising
Joan Duran, Bartomeu Coll, Catalina Sbert
→ BibTeX
    title   = {{Chambolle's Projection Algorithm for Total Variation Denoising}},
    author  = {Duran, Joan and Coll, Bartomeu and Sbert, Catalina},
    journal = {{Image Processing On Line}},
    volume  = {3},
    pages   = {311--331},
    year    = {2013},
    doi     = {10.5201/ipol.2013.61},
% if your bibliography style doesn't support doi fields:
    note    = {\url{}}
Joan Duran, Bartomeu Coll, and Catalina Sbert, Chambolle's Projection Algorithm for Total Variation Denoising, Image Processing On Line, 3 (2013), pp. 311–331.

Communicated by Antonin Chambolle
Demo edited by José-Luis Lisani


Denoising is the problem of removing the inherent noise from an image. The standard noise model is additive white Gaussian noise, where the observed image f is related to the underlying true image u by the degradation model f=u+n, and n is supposed to be at each pixel independently and identically distributed as a zero-mean Gaussian random variable. Since this is an ill-posed problem, Rudin, Osher and Fatemi introduced the total variation as a regularizing term. It has proved to be quite efficient for regularizing images without smoothing the boundaries of the objects.

This paper focuses on the simple description of the theory and on the implementation of Chambolle's projection algorithm for minimizing the total variation of a grayscale image. Furthermore, we adapt the algorithm to the vectorial total variation for color images. The implementation is described in detail and its parameters are analyzed and varied to come up with a reliable implementation.