G. Aubert and P. Kornprobst, Mathematical problems in image processing, 2006.

A. Beck and M. Teboulle, Smoothing and First Order Methods: A Unified Framework, SIAM Journal on Optimization, vol.22, issue.2, pp.557-580, 2012.
DOI : 10.1137/100818327

J. F. Bonnans, J. Gilbert, C. Lemaréchal, and C. A. Sagastizábal, Numerical Optimization (Theoretical and Practical Aspects, 2003.

P. L. Combettes, J. Pesquet, H. H. Bauschke, R. S. Burachik, and P. , Proximal Splitting Methods in Signal Processing Fixed-Point Algorithms for Inverse Problems in Science and Engineering, pp.185-212, 2011.

T. Chan and S. Esedoglu, Function Approximation, SIAM Journal on Applied Mathematics, vol.65, issue.5, pp.1817-1837, 2005.
DOI : 10.1137/040604297

T. Chan and P. Mulet, On the Convergence of the Lagged Diffusivity Fixed Point Method in Total Variation Image Restoration, SIAM Journal on Numerical Analysis, vol.36, issue.2, pp.354-367, 1999.
DOI : 10.1137/S0036142997327075

D. Coltuc and P. Bolon, Exact histogram specification, IEEE Transactions on Image Processing, vol.15, issue.5, pp.1143-1152, 2006.
DOI : 10.1109/TIP.2005.864170

URL : https://hal.archives-ouvertes.fr/hal-00023386

D. Geman and G. Reynolds, Constrained restoration and the recovery of discontinuities, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.3, pp.14-367, 1992.
DOI : 10.1109/34.120331

S. Mallat, A Wavelet Tour of Signal Processing, 2009.

M. Nikolova, Analytical bounds on the minimizers of least squares, Inverse Problems in Imaging, vol.1, issue.4, pp.661-677, 2007.

M. Nikolova, Y. Wen, and R. Chan, Exact histogram specifcation for digital images using a variational approach, Journal of Mathematical Imaging and Vision, 2012.

Y. Wan and D. Shi, Joint Exact Histogram Specification and Image Enhancement Through the Wavelet Transform, IEEE Transactions on Image Processing, vol.16, issue.9, pp.2245-2250, 2007.
DOI : 10.1109/TIP.2007.902332

E. Weiszfeld, Sur le point pour lequel la somme des distances de n points donnés est minimum, Tôhoku Mathematics Journal, vol.43, pp.355-386, 1937.

M. Nikolova and C. Ens-cachan, CNRS 61 av. du President Wilson 94235 Cachan Cedex France nikolova@cmla.ens-cachan, p.31

K. Germany-steidl@mathematik, uni-kl.de The work of M. Nikolova was supported in part by the " FMJH Program Gaspard Monge in optimization and operation research