Total Variation image restoration with local constraints

L. Rudin, S. Osher and E. Fatemi proposed a method for image restoration based on the minimization of the Total Variation submitted to the constraints given by the image acquisition model. To ensure the satisfaction of the constraints, a Lagrange multiplier λ has to be estimated. We observe that if λ is global, the constraints are also globally satisfied, but not locally. We discuss the problem of imposing local constraints with a finite number of Lagrange multipliers associated to a partition of the image and we display some experimental results obtained with this model.