(Physica D. 1992)
Definition 1.1. is the subspace of functions in such that the following quantity is finite:
Remark: if , then
In the ROF model, one seeks to minimize:
Chambolle's model: A. Chambolle has proposed a projection algorithm to minimize the total variation (MIA 2002).
Proposition 1.1. The solution of (1.2) is given by:
Meyer's model :
Y. Meyer (2001) has proposed the following model:
The Banach space contains signals signals with strong oscillations, and thus in particular textures and noise.
Definition 1.2. is the Banach space composed of the distributions which can be written
|textured image||1 000 000||9 500||360|
|geometric image||64 600||9 500||2000|
Lemma 1.1. and are dual (in the sens of the Legendre-Fenchel duality).
Proposition 1.2. In the discrete case, the space identifies with the following subspace: