by Triet M. Le and Luke Rogers
In image decompositions, one is interested in decomposing f into u+v where u and v have different features. In a variational approach, such a decomposition is achieved by solving the following variational problem
\inf_{(u,v)∈X1×X2} \{ tF_1(u) + F_2(v) : f = u + v\},
where F_1 and F_2 are positive functionals defined on some function spaces X1 and X2 respectively. Often the scale parameter t is fixed a prior. In this paper, we address the problem of selecting the scale parameter t in a multiscale fashion, and introduce the notion of interpolating scales that are stable with respect to the functional or energy being minimized. The motivation comes from Peetre’s K-functional in interpolation theory.