On a nonlinear laplacian based filter for noise removal

TL;DR

This paper introduces a nonlinear Laplacian-based filter utilizing a fourth-order PDE for noise removal, effectively preserving discontinuities and avoiding staircase artifacts in 1D and 2D data.

Contribution

It presents a novel nonlinear filtering method based on a fourth-order PDE that improves noise removal while maintaining data discontinuities.

Findings

Preserves discontinuities effectively.

Avoids staircase effect common in total variation methods.

Demonstrates superior noise filtering in numerical experiments.

Abstract

We propose a nonlinear filter for noise removal based on the Laplacian for 1D and 2D data. The method utilizes the solution to a fourth-order nonlinear PDE involving the Laplacian for data reconstruction. Evolution equations are introduced to solve this fourth-order nonlinear equation. Numerical experiments show that the new filter preserves discontinuities while filtering out noise. The restored data are piecewise linear and avoid the staircase effect commonly observed with total variation denoising methods.