A criterion for the explicit reconstruction of a holomorphic function from its restrictions on lines

We deal with a problem of the explicit reconstruction of any holomorphic function f on a ball of C2 from its restrictions on a union of complex lines. The validity of such a reconstruction essentially depends on the mutual repartition of these lines. This criterion can be analytically described and it is also possible to give geometrical sufficient conditions. The motivation of this problem also comes from possible applications in mathematical economics and medical imaging.