[hal-01002958] Mathematical analysis of a inf-convolution model for image processing

We deal with a second order image decomposition model to perform denoising and texture extraction that was previously presented in \citeBP2 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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