Nonlinear cell-average multiscale signal representations: Application to signal denoising

In this paper, we present a new class of nonlinear cell-average multiscale signal representations. After having introduced the general multiscale framework, we recall convergence and stability results for such multiscale representations and then build a particular example which appears to be relevant for piecewise smooth functions denoising.

► This paper presents a new type of nonlinear multiscale representations adapted for signals containing jump singularities.
► We provide a convergence and stability analysis for this type of representations.
► We finally give some illustrations of the practical interest of these representations for signal denoising.