  We introduce two data completion algorithms for the limited-aperture problems
in inverse acoustic scattering. Both completion algorithms are independent of
the topological and physical properties of the unknown scatterers. The main
idea is to relate the limited-aperture data to the full-aperture data via the
prolate matrix. The data completion algorithms are simple and fast since only
the approximate inversion of the prolate matrix is involved. We then combine
the data completion algorithms with imaging methods such as factorization
method and direct sampling method for the object reconstructions. A variety of
numerical examples are presented to illustrate the effectiveness and robustness
of the proposed algorithms.
