L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, pp.259-268, 1992.
DOI : 10.1016/0167-2789(92)90242-F

A. Chambolle, V. Caselles, D. Cremers, M. Novaga, and T. Pock, An introduction to total variation for image analysis Theoretical foundations and numerical methods for sparse recovery, pp.263-340, 2010.

L. Ambrosio, N. Fusco, and D. Pallara, Free Discontinuity Problems and Special Functions with Bounded Variation, 2000.
DOI : 10.1007/978-3-0348-8974-2_2

A. Chambolle, An algorithm for total variation minimization and applications, J. Math. Imag. Vis, vol.20, issue.12, pp.89-97, 2004.

R. , T. , and T. Methods, The top row shows the full image, whereas close-ups are displayed on the other rows. A clean 465 × 348 image (original author: Heinz Albers, source: wikipedia) was corrupted by a Gaussian additive white noise with standard deviation ? = 10, then denoised with the ROF, TV-LSE and TV-ICE algorithms. The parameters were chosen so that the norm of the estimated noisê u ? u was the same for each algorithm, leading to: ? = 20, ? = 10 for TV-LSE (initial choice, TV-ICE, and ? = 15.6 for ROF. Note the similarity between LSE and ICE, and the staircasing effect clearly visible on the ROF close-ups

P. Weiss, L. Blanc-féraud, and G. Aubert, Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing, SIAM Journal on Scientific Computing, vol.31, issue.3, pp.2047-2080, 2009.
DOI : 10.1137/070696143

URL : https://hal.archives-ouvertes.fr/inria-00166096

D. Dobson and F. Santosa, Recovery of Blocky Images from Noisy and Blurred Data, SIAM Journal on Applied Mathematics, vol.56, issue.4, pp.1181-1198, 1996.
DOI : 10.1137/S003613999427560X

C. Bouman and K. Sauer, A generalized Gaussian image model for edge-preserving MAP estimation, IEEE Transactions on Image Processing, vol.2, issue.3, pp.296-310, 1993.
DOI : 10.1109/83.236536

C. Louchet and L. Moisan, Total variation denoising using posterior expectation, Proc. Eur. Signal Process. Conf, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00258849

C. Louchet and L. Moisan, Posterior Expectation of the Total Variation Model: Properties and Experiments, SIAM Journal on Imaging Sciences, vol.6, issue.4, pp.2640-2684, 2013.
DOI : 10.1137/120902276

URL : https://hal.archives-ouvertes.fr/hal-00764175

S. Geman, K. Manbeck, and D. Mcclure, A comprehensive statistical model for single-photon emission tomography, Markov Random Fields: Theory and Applications, pp.93-130, 1993.

T. Ru?i´ru?i´c, A. Pi?urica, and W. Philips, Neighborhood-consensus message passing as a framework for generalized iterated conditional expectations, Pattern Recognition Letters, vol.33, issue.3, pp.309-318, 2012.
DOI : 10.1016/j.patrec.2011.10.014

H. Quick, S. Banerjee, and B. Carlin, Modeling temporal gradients in regionally aggregated California asthma hospitalization data, The Annals of Applied Statistics, vol.7, issue.1, pp.154-176, 2013.
DOI : 10.1214/12-AOAS600SUPP

M. Nikolova, Weakly Constrained Minimization: Application to the Estimation of Images and Signals Involving Constant Regions, Journal of Mathematical Imaging and Vision, vol.21, issue.2, pp.155-175, 2004.
DOI : 10.1023/B:JMIV.0000035180.40477.bd

K. D. Schmidt, On the covariance of monotone functions of a random variable, 2003.