A Cell-Average Non-Separable Progressive Multivariate WENO Method for Image Processing Applications

TL;DR

This paper introduces a novel non-separable multivariate WENO scheme tailored for cell-average data, enhancing image processing by providing high-order accuracy and stability near discontinuities.

Contribution

It extends multiresolution frameworks with a non-linear WENO reconstruction for improved image processing applications.

Findings

Achieves high-order accuracy in smooth regions

Demonstrates stability near discontinuities

Outperforms linear Lagrange reconstruction in experiments

Abstract

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, achieving high-order accuracy in smooth regions and 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.