A multi-stage inversion method for deblending seismic data includes: a) acquiring blended seismic data from a plurality of seismic sources; b) constructing an optimization model that includes the acquired blended seismic data and unblended seismic data; c) performing sparse inversion, via a computer processor, on the optimization model; d) estimating high-amplitude coherent energy from result of the performing sparse inversion in c); e) re-blending the estimated high-amplitude coherent energy; and f) computing blended data with an attenuated direct arrival energy.