Image Recovery Using Functions of Bounded Variation and Sobolev Spaces of Negative Differentiability

نویسندگان

  • Yunho Kim
  • Luminita A. Vese
  • Jean-Michel Morel
چکیده

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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تاریخ انتشار 2010