For marine towed-streamer seismic data, the sparse crossline sampling imposes a Nyquist limitation for many processing steps that require either f -k (frequency-wavenumber) or f -p (frequency-slowness) transforms in the crossline direction. For this reason, 3D deghosting and crossline interpolation have been considered extremely difficult to perform using only single-component towed-streamer seismic data. We present a progressive sparse -p x -p y inversion scheme to perform 3D deghosting and crossline interpolation using single-component seismic data. Using field data examples, we demonstrate that our 3D deghosting algorithm effectively attenuates the ghost and works better than the GWE (Ghost Wavefield Elimination) method for full-azimuth data with strong 3D effects. We also demonstrate that by using our algorithm, it is possible to perform single-component joint 3D deghosting and crossline interpolation in the presence of strong spatial aliasing in the crossline direction. We show that the interpolation of the high-frequency events may be sub-optimal in deep time windows when the signal-to-noise ratio of high-frequency events is low.