Abstract
Real images usually have two layers, namely, cartoons (the piece-wise smooth part of the image) and textures (the oscillating pattern part of the image). Both these two layers have sparse approximations under some tight frame systems such as framelet, translation invariant wavelet, curvelet, and local DCTs. In this paper, we solve image inpainting problems by using two separate tight frame systems which can sparsely represent cartoons and textures respectively. Different from existing schemes in the literature which are either analysis-based or synthesis-based sparsity priors, our minimization formulation balances these two priors. We also derive iterative algorithms to find their solutions and prove their convergence. Numerical simulation examples are given to demonstrate the applicability and usefulness of our proposed algorithms in image inpainting.
Original language | English |
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Pages (from-to) | 379-395 |
Number of pages | 17 |
Journal | Inverse Problems and Imaging |
Volume | 4 |
Issue number | 3 |
DOIs | |
Publication status | Published - Aug 2010 |
Externally published | Yes |
Funding
The first author is supported by the Wavelets and Information Processing Programme under a grant from DSTA, Singapore, and the second author is supported in part by HKRGC Grant CUHK 400508.
Keywords
- Cartoon and texture
- Image inpainting
- Tight frame