A cell-average non-separable progressive multivariate WENO method for image processing applications

Accurate and efficient reconstruction techniques are essential in multiresolution analysis and image compression, particularly when the data are represented as cell averages. In this work, we present a non-separable progressive multivariate Weighted Essentially Non-Oscillatory (WENO) scheme specifically designed for cell-average data, with applications to digital image processing. The proposed method extends Harten’s multiresolution framework through a non-linear WENO reconstruction adapted to the cell-average context. In contrast to classical WENO schemes, the progressive strategy allows the recursive recovery of high-order accuracy even when the largest stencil is affected by a discontinuity. The method achieves high-order accuracy in smooth regions together with stable, non-oscillatory behavior near discontinuities. We also establish theoretical results regarding the consistency and approximation properties of the method. Finally, several numerical experiments on piecewise smooth functions and digital images are presented to demonstrate its performance and validate its effectiveness against the linear Lagrange reconstruction of the same order of accuracy.