This paper addresses the problem of joint wideband localization and acquisition of acoustic sources. The source locations as well as acquisition of the original source signals are obtained in a joint fashion by solving a sparse recovery problem. Spatial sparsity is enforced by discretizing the acoustic scene into a grid of predefined dimensions. In practice, energy leakage from the source location to the neighboring grid points is expected to produce spurious location estimates, since the source location will not coincide with one of the grid points. To alleviate this problem we introduce the concept of grid-shift. A particular source is then near a point on the grid in at least one of a set of shifted grids. For the selected grid, other sources will generally not be on a grid point, but their energy is distributed over many points. A large number of experiments on real speech signals show the localization and acquisition effectiveness of the proposed approach under clean, noisy and reverberant conditions.