TV-L1 Image Denoising Algorithm

Image denoising using the TV-L1 model optimized with a primal-dual algorithm.
The function minimizes the following denoising model wrt I:
sum(sqrt(Ix^2 + Iy^2)) + lambda*||I - g||
where I is the denoised image, Ix, Iy its gradient, g is the observed image and lambda
is the regularization coefficient. Smaller values for lambda result in more aggressive
denoising. For more details, see
* A. Mordvintsev: ROF and TV-L1 denoising with Primal-Dual algorithm,
http://znah.net/rof-and-tv-l1-denoising-with-primal-dual-algorithm.html
also archived as http://www.webcitation.org/6rEjLnF1F
* Chambolle et al. An introduction to Total Variation for Image Analysis, 2009. <hal-00437581>
https://hal.archives-ouvertes.fr/hal-00437581/document