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AbstractReal 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.
All Author(s) ListCai JF, Chan RH, Shen ZW
Journal nameInverse Problems and Imaging
Volume Number4
Issue Number3
PublisherAmerican Institute of Mathematical Sciences (AIMS)
Pages379 - 395
LanguagesEnglish-United Kingdom
KeywordsCartoon and texture; Image inpainting; Tight frame
Web of Science Subject CategoriesMathematics; Mathematics, Applied; MATHEMATICS, APPLIED; Physics; Physics, Mathematical; PHYSICS, MATHEMATICAL

Last updated on 2020-27-10 at 00:26