  We present an extension of the linear sampling method for solving the
sound-soft inverse acoustic scattering problem with randomly distributed point
sources. The theoretical justification of our sampling method is based on the
Helmholtz--Kirchhoff identity, the cross-correlation between measurements, and
the volume and imaginary near-field operators, which we introduce and analyze.
Implementations in MATLAB using boundary elements, the SVD, Tikhonov
regularization, and Morozov's discrepancy principle are also discussed. We
demonstrate the robustness and accuracy of our algorithms with several
numerical experiments in two dimensions.
