# American Institute of Mathematical Sciences

August  2010, 4(3): 379-395. doi: 10.3934/ipi.2010.4.379

## Simultaneous cartoon and texture inpainting

 1 Temasek Laboratories and Department Mathematics, National University of Singapore, 2 Science Drive 2, 117543 2 Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong, China 3 Department of Mathematics, National University of Singapore, 2 Science Drive 2, 117543, Singapore

Received  May 2009 Revised  January 2010 Published  July 2010

Real images usually have two layers, namely, cartoons (the piecewise 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.
Citation: Jian-Feng Cai, Raymond H. Chan, Zuowei Shen. Simultaneous cartoon and texture inpainting. Inverse Problems & Imaging, 2010, 4 (3) : 379-395. doi: 10.3934/ipi.2010.4.379
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