Mathematical analysis of a inf-convolution model for image processing
Résumé
We deal with a second order image decomposition model to perform denoising and texture extraction that was previously presented in \cite{BP2}. We look for the decomposition f= u+v + w where u is a first order term, v a second order term and w the remainder term (0 order). For highly textured images the model gives a two-scale texture decomposition: u can be viewed as a ''macro-texture'' (larger scale) which oscillations are not too large and w is the ''micro-texture'' (very oscillating) that contains the noise. Here, we perform mathematical analysis of the model and give qualitative properties of solutions using the dual problem and inf-convolution formulation.
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