Using the Gelfand-Graev formula, the interior problem of tomography reduces to invertion of the finite Hilbert transform (FHT) from incomplete data. In this talk we study several aspects of inverting the FHT when the data are incompelte. Using the Cauchy transform and an approach based on the Riemann-Hilbert problem we derive a differential operator that commutes with the FHT. Our second result is the characterization of the null-space of the FHT in the case of incomplete data. Also we derive the asymptotics of the singular values of the FHT in three different cases of incomplete data.