A full second order variational model for multiscale texture analysis

We present a second order image decomposition model to perform denoising and texture extraction. We look for the decomposition f=u+v+w where u is a first order term, v a second order term and w the (0 order) remainder term. For highly textured images the model gives a two‐scale texture decomposition: u can be viewed as a macro‐texture (larger scale) whose oscillations are not too large and w is the micro‐texture (very oscillating) that may contain noise. We perform mathematical analysis of the model and give numerical examples.