Image Denoising by Fourth-Order PDEs

Seongjai Kim (USA)

Keywords

Variational approach, PDEbased restoration model, fourthorder PDEs, piecewise planarity condition (PPC).

Abstract

It has been known that fourth-order PDE-based denois ing models may restore images better than second-order ones. This article introduces and analyzes piecewise pla narity conditions (PPCs) with which unconstrained fourth order variational models in continuum converge to piece wise planar images. Although the PPCs may not be sat isfied by discrete data (images) in the same way, they can provide a mathematical background for the advancement of PDE-based denoising methods. It has been observed that fourth-order variational models can restore better images than second-order ones, in particular when they satisfy the PPCs. Fourth-order models have proved to restore texture components favorably, while second-order models tend to produce clearer edges. Numerical examples are provided to verify the claims.

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