The retrieval of the surface profile of a reflector antenna is an important issue, especially for radioastronomical applications. Microwave holography retrieves the reflector profile starting from a set of measured far-field data. The main step of this technique is the computation of the induced currents on the reflector surface. This requires the solution of a linear inversion problem which is strongly ill-conditioned. The aim of this work is to investigate a new solution technique for this linear inversion problem based on the SVD. This new technique supplies a flexible regularization scheme, able to take into account also the noise level of the data. Some numerical results are obtained, starting from a simulated far-field.