Abstract. In this paper we derive scale space methods for inverse problems which satisfy the fundamental axioms of fidelity and causality and we provide numerical illustrations of the use of such methods in deblurring. These scale space methods are asymptotic formulations of the Tikhonov-Morozov regularization method. The analysis and illustrations relate diffusion filtering methods in image pr...

Modern explanatory ILP methods like Progol, Residue procedure, CF-induction, HAIL and Imparo use the principle of Inverse Entailment (IE). It is based on the fact that the negation of a hypothesis is derived from a prior background theory and the negation of examples. IE-based methods commonly compute a hypothesis in two steps: by first constructing an intermediate theory and next by generalizi...