We propose a three-step solution methodology to increase the discrete set of acoustic far-field pattern (FFP) measurements, available in a small range of observation angles (small aperture). The first two steps of the proposed procedure allow the extension of the data to an aperture larger than !=2. They use a regularized Newton algorithm where the total variation of the FFP is incorporated as a regularization term. The third step consists in applying the standard Tikhonov regularization technique to recover the full aperture of the FFP from the previously extended field. Numerical results obtained using synthetic data illustrate the potential of the proposed procedure for reconstructing the full aperture of the FFP from data given in an aperture as small as backscattering measurements.