IMAGE RECOVERY USING FUNCTIONS OF BOUNDED VARIATION AND SOBOLEV SPACES OF NEGATIVE DIFFERENTIABILITY
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- IMAGE RECOVERY USING FUNCTIONS OF BOUNDED VARIATION AND SOBOLEV SPACES OF NEGATIVE DIFFERENTIABILITY
- Kim, Yunho; Vese, Luminita A.
- Issue Date
- AMER INST MATHEMATICAL SCIENCES
- INVERSE PROBLEMS AND IMAGING, v.3, no.1, pp.43 - 68
- 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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