Chambolle's Projection Algorithm for Total Variation Denoising

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 + �, andis supposed to be at each pixel inde- pendently 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 bound- aries of the objects. This paper focuses on the simple description of the theory and on the implementation of Cham- bolle's projection algorithm for minimizing the total variation of a grayscale image. Further- more, we adapt the algorithm to the vectorial total variation for color images. The implementa- tion is described in detail and its parameters are analyzed and varied to come up with a reliable implementation.

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