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In this paper we translate to the cell-average setting the algorithm for thepoint-value discretization presented in S. Amat, J. Ruiz, C.-W. Shu, D. F.Y\'a\~nez, A new WENO-2r algorithm with progressive order of accuracy close todiscontinuities, submitted to SIAM J. Numer. Anal.. This new strategy tries toimprove the results of WENO-($2r-1$) algorithm close to the singularities,resulting in an optimal order of accuracy at these zones. The main idea is tomodify the optimal weights so that they have a nonlinear expression thatdepends on the position of the discontinuities. In this paper we study theapplication of the new algorithm to signal processing using Harten'smultiresolution. Several numerical experiments are performed in order toconfirm the theoretical results obtained.

Cell-average WENO with progressive order of accuracy close to discontinuities with applications to signal processing