Methods of solving certain two-dimensional problems of Doppler tomography

In the development of methods of recovering a vector field using radiolocation systems by continuous unmodulated radiation the problem arises of recovering a vector-valued function from information determined by a family of oriented lines. In the two-dimensional case this problem has a nonunique solution in the class of continuous functions of compact support. In the present paper the problem is studied on the set of solenoidal functions and the set of piecewise-constant functions. We give a method of solving the problem and study its stability. © 1998 Plenum Publishing Corporation.