Journal
INVERSE PROBLEMS AND IMAGING
Volume 3, Issue 1, Pages 43-68Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/ipi.2009.3.43
Keywords
Image restoration; variational models; bounded variation; Sobolev spaces; oscillatory functions
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Funding
- National Science Foundation [NSF-DMS 0714945, NSF-DMS 0312222]
- Beckenbach Dissertation Year Fellowship
- Institute for Pure and Applied Mathematics (IPAM)
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In this work we wish to recover an unknown image from a blurry, or noisy-blurry version. We solve this inverse problem by energy minimization and regularization. We seek a solution of the form u + v, where u is a function of bounded variation (cartoon component), while v is an oscillatory component (texture), modeled by a Sobolev function with negative degree of differentiability. We give several results of existence and characterization of minimizers of the proposed optimization problem. Experimental results show that this cartoon + texture model better recovers textured details in natural images, by comparison with the more standard models where the unknown is restricted only to the space of functions of bounded variation.
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