Seismic data recorded in a marine streamer are obtained, sorted as a common receiver gather. A complex Laplace frequency parameter is used to transform the seismic data from a space-time domain to a spectral domain. An iterative conjugate gradient scheme, using a physically-based preconditioner, is applied to the transformed seismic data, to provide a least squares solution to a normal set of equations for a source deghosting system of equations. The solution is inverse-transformed back to a space-time domain to provide source deghosted seismic data, which is useful for imaging the earth's subsurface.