On the stability of the PPH nonlinear multiresolution

This letter is devoted to the stability of the so-called piecewise polynomial harmonic (PPH) multiresolution transform that belongs to the class of data dependent nonlinear multiresolution algorithms. The presentation of the PPH multiresolution as some specific perturbation of a linear multiresolution allows to establish a two step contraction property that leads first to a convergence result and finally to the stability.