Stability in a class of variational methods

The purpose of this work is to investigate the stability property of some models which are currently used in image processing. Following L. Rudin, S.J. Osher and E. Fatemi, we decompose an image f∈L2(R2) as a sum u+v where u belongs to BV(R2) and v belongs to L2(R2). The Banach space BV is aimed at modeling the objects contained in the given image. the optimal decomposition minimizes the energy . We denote this optimal solution. After recalling some properties of that optimal decomposition, we prove the stability of the mapping Φ. Moreover, we generalize the stability result to other models where the Banach space BV is replaced by other functional Banach spaces E.