Simultaneous Inpainting and Denoising by Directional Global Three-part Decomposition: Connecting Variational and Fourier Domain Based Image Processing

TL;DR

This paper introduces a novel image restoration method that simultaneously performs inpainting and denoising of images with complex textures and noise, leveraging directional decomposition and Bayesian insights.

Contribution

The work proposes a new approach combining directional global three-part decomposition with advanced norms for improved image inpainting and denoising, connecting variational and Fourier methods.

Findings

Outperforms existing inpainting and denoising methods

Effectively separates cartoon and texture components

Provides a Bayesian perspective on image restoration

Abstract

We consider the very challenging task of restoring images (i) which have a large number of missing pixels, (ii) whose existing pixels are corrupted by noise and (iii) the ideal image to be restored contains both cartoon and texture elements. The combination of these three properties makes this inverse problem a very difficult one. The solution proposed in this manuscript is based on directional global three-part decomposition (DG3PD) [ThaiGottschlich2016] with directional total variation norm, directional G-norm and $\ell_\infty$-norm in curvelet domain as key ingredients of the model. Image decomposition by DG3PD enables a decoupled inpainting and denoising of the cartoon and texture components. A comparison to existing approaches for inpainting and denoising shows the advantages of the proposed method. Moreover, we regard the image restoration problem from the viewpoint of a Bayesian framework and we discuss the connections between the proposed solution by function space and related image representation by harmonic analysis and pyramid decomposition.