For passive seismic data, surface multiples are used to obtain an estimate of the subsurface responses, usually by a crosscorrelation process. This crosscorrelation process relies on the assumption that the surface has been uniformly illuminated by subsurface sources in terms of incident angles and strengths. If this is not the case, the crosscorrelation process cannot give a true amplitude estimation of the subsurface response. Furthermore, cross terms in the crosscorrelation result are not related to actual subsurface inhomogeneities. We have developed a method that can obtain true amplitude subsurface responses without a uniform surface-illumination assumption. Our methodology goes beyond the crosscorrelation process and estimates primaries only from the surface-related multiples in the available signal. We use the recently introduced estimation of primaries by sparse inversion (EPSI) methodology, in which the primary impulse responses are considered to be the unknowns in a large-scale inversion process. With some modifications, the EPSI method can be used for passive seismic data. The output of this process is primary impulse responses with point sources and receivers at the surface, which can be used directly in traditional imaging schemes. The methodology was tested on 2D synthetic data.