Total Variation Wavelet Inpainting |
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Authors: | Tony F Chan Jianhong Shen Hao-Min Zhou |
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Affiliation: | (1) Department of Mathematics, University of California, Los Angeles, CA, 90095-1555;(2) Department of Mathematics, University of Minnesota, 206 Church St. SE Minneapolis, MN, 55455;(3) School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332 |
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Abstract: | We consider the problem of filling in missing or damaged wavelet coefficients due to lossy image transmission or communication.
The task is closely related to classical inpainting problems, but also remarkably differs in that the inpainting regions are
in the wavelet domain. New challenges include that the resulting inpainting regions in the pixel domain are usually not geometrically
well defined, as well as that degradation is often spatially inhomogeneous. We propose two related variational models to meet
such challenges, which combine the total variation (TV) minimization technique with wavelet representations. The associated
Euler-Lagrange equations lead to nonlinear partial differential equations (PDE’s) in the wavelet domain, and proper numerical
algorithms and schemes are designed to handle their computation. The proposed models can have effective and automatic control
over geometric features of the inpainted images including sharp edges, even in the presence of substantial loss of wavelet
coefficients, including in the low frequencies. Existence and uniqueness of the optimal inpaintings are also carefully investigated.
Research supported in part by grants ONR-N00014-03-1-0888, NSF DMS-9973341, DMS-0202565 and DMS-0410062, and NIH contract
P 20 MH65166. |
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Keywords: | wavelet inpainting error concealment image interpolation |
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