Simultaneous Inpainting and Denoising by Directional Global Three-part Decomposition: Connecting Variational and Fourier Domain Based Image Processing
This addresses image restoration for applications like medical imaging or photography where combined inpainting and denoising is needed, but it appears incremental as it builds on prior DG3PD work.
The paper tackles the challenging problem of restoring images with large missing pixels, noise corruption, and both cartoon and texture elements, proposing a method based on directional global three-part decomposition (DG3PD) that decouples inpainting and denoising, showing advantages over existing approaches.
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.