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This article is the second work in our series of papers dedicated to imageprocessing models based on the fractional order total variation $TV^r$. In ourfirst work of this series, we studied key analytic properties of thesesemi-norms.  Here we focus on the more applied aspects of such models: first, in order toobtain a better reconstructed image, we propose several extensions of thefractional order total variation. Such generalizations, collectively denoted byRVL, will be modular, i.e. the parameters therein are mutually independent, andcan be fine tuned to the particular task. Then, we will study the bileveltraining schemes based on RVL, and show that such schemes are well defined,i.e. they admit minimizers. Finally, we will provide some numerical examples,showing that training schemes based on RVL are effectively better than thosebased on classical regularizer $TV$ and $TGV^2$.

Real order (an)-isotropic total variation in image processing - Part II: Learning of optimal structures