Abstract The equivalent source method (ESM)-based sound field separation technique has been successfully introduced into near-field acoustic holography as a preprocessing tool to eliminate the influence of disturbing sources or reflections from the opposite side of the array. In this paper, that technique is further extended in a sparsity framework, which makes it possible to take the advantage of the theory of compressive sensing to achieve reasonable separation accuracy with a limited number of spatial sampling points. In this study, three sparse bases are considered, including two existing bases that are suitable for spatially sparse and spatially extended sources, respectively, and a more flexible, redundant sparse basis that is constructed by combining the two sparse bases above, and the l 1 - norm minimization is used to promote sparse solutions. Numerical simulation and experimental results demonstrate the validity of the proposed technique and show the superiority of the use of the redundant sparse basis. Besides, the effects of the relative strength of the target source to the disturbing source, the number of spatial sampling points and the signal-to-noise ratio on the separation accuracy are analyzed numerically.