  This paper is concerned with the inverse problem of determining an obstacle
and the corresponding incident point sources in the Helmholtz equation from
near-field scattering data. An optimization method is proposed to
simultaneously recover both the obstacle and source locations. Moreover, a
two-step sampling scheme with novel indicator functions is proposed to produce
a good initial guess for solving the optimization problem. Theoretically, we
analyze the convergence properties of the optimization method and the
indicating behaviors of the indicator functions. Several numerical examples are
presented to show the effectiveness of the proposed method.
