Regularization of Mellin-type inverse problems with an application to oil engineering Original Research Article

In this paper we present a novel method for the stable inversion of Mellin convolution operators. Although the inverse operator is explicitly known for this class of operators, regularization techniques have to be used due to the ill-posedness of the problem. Considering operators which are continuously invertible between the space L2[0,∞] and a Mellin–Sobolev space H*s[0,∞], we propose a combination of a data smoothing algorithm and an exact inversion for the order optimal regularization of the equation. As application, we derive the Mellin transform of the capillary pressure operator and analyze its mapping properties. Finally, we present some numerical results.