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

摘要

We consider the very challenging task of restoring images (i) which have alarge number of missing pixels, (ii) whose existing pixels are corrupted bynoise and (iii) the ideal image to be restored contains both cartoon andtexture elements. The combination of these three properties makes this inverseproblem a very difficult one. The solution proposed in this manuscript is basedon 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. Imagedecomposition by DG3PD enables a decoupled inpainting and denoising of thecartoon and texture components. A comparison to existing approaches forinpainting and denoising shows the advantages of the proposed method. Moreover,we regard the image restoration problem from the viewpoint of a Bayesianframework and we discuss the connections between the proposed solution byfunction space and related image representation by harmonic analysis andpyramid decomposition.