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Image recovery using functions of bounded variation and Sobolev spaces of negative differentiability

2009; American Institute of Mathematical Sciences; Volume: 3; Issue: 1 Linguagem: Inglês

10.3934/ipi.2009.3.43

1930-8345

Yunho Kim, Luminita A. Vese,

Medical Image Segmentation Techniques

In this work we wish to recover an unknown image from a blurry, or noisy-blurry version. We solve this inverse problem by energyminimization and regularization. We seek a solution of the form $u + v$,where $u$ is a function of bounded variation (cartoon component), while $v$ isan oscillatory component (texture), modeled by a Sobolev function withnegative degree of differentiability. We give several results of existence and characterization of minimizers of the proposed optimization problem.Experimental results show that thiscartoon + 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.