An important problem in image analysis is the separation of larger scales (cartoon-like objects) from smaller oscillatory scales (noise, texture). Many energy minimization methods can be seen as image decomposition models into cartoon and texture, as it was suggested by Yves Meyer. The cartoon part can be modeled by a piecewise-smooth function of bounded variation, but appropriate spaces of (possibly generalized) functions have to be considered to better model the oscillatory component. One of the difficulties is how to solve such models in practice, in a simple and efficient way.
In this talk, I will discuss energy minimization models that allow to decompose a given image into cartoon and texture. In particular, I will present a hierarchical multiscale image decomposition model (joint work with Eitan Tadmor and Suzanne Nezzar), as well as a new practical method that allows to represent the oscillatory part in a space suggested by Yves Meyer, div(BMO) (joint work with Triet Le). Theoretical and experimental results will be presented.
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