Generalized Matching Pursuit has been proven capable of achieving joint crossline interpolation and 3D receiver deghosting on severely aliased marine seismic measurements in real scenarios. In fact, theoretically GMP is capable of reconstructing the upgoing wave under aliasing of any order, as long as there is no spectral overlap between replicas of different events in the crossline wavenumber spectrum of the measured data. Therefore, severely undersampled shallow seismic reflections, with their highfrequency content and broad crossline spectrum, represent the greatest challenge for GMP. We propose an algorithm using moveout correction to reduce spatial aliasing and to improve the GMP performance in shallow seismic reflections. In addition, we propose a simple yet effective criterion to automatically activate the correction. We also show how 3D deghosting can still be performed. These concepts are illustrated using real data examples.