Image recovery using functions of bounded variation and Sobolev spaces of negative differentiability
Yunho Kim, Luminita A. Vese · Inverse Problems and Imaging · 2009
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.