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The inverse scattering problem for an acoustic medium is considered within the homogeneous background Born approximation. A constant-density acoustic medium is probed by a wide-band plane-wave source. The scattered field is observed along a receiver array located outside the medium. Two methods for partial reconstruction of the medium velocities are presented. In the first method (the slant-stack method), the projections of the velocity potential at a range of angles are obtained from the plane-wave components of the scattered field. The range of available projection angles is determined by the receiver array aperture and the incidence direction of the probing plane wave. The medium velocities are, then, partially reconstructed from available projections via well-known methods of straight-line tomography. In the second method (the imaging-filtering method), the observed traces are filtered, back-propagated into the medium, and imaged at the source traveltimes, in the same way as in migration. The resulting image is, then, filtered by a linear space-invariant filter to obtain a partial reconstruction of the medium velocities. Both reconstruction methods are illustrated by some synthetic examples for several receiver geometries.