A computer-implemented method for deghosting marine seismic streamer data, comprising: receiving marine seismic data recorded from a single streamer; defining a representation of an upgoing wavefield in the marine seismic data, wherein the representation comprises a first wave component in a plane and a second wave component that is perpendicular to the plane; wherein defining the representation of the upgoing wavefield comprises determining a wavenumber sampling for inline propagation based on receiver sampling along the streamer cable and determining a crossline sampling such that a ghost delay is adequately sampled by the Nyquist criteria, wherein determining the crossline sampling comprises: receiving a user-defined maximum crossline angle of propagation that together with a maximum inline angle of propagation, defines an ellipse in k ( x) - k ( y) space, where k ( x) represents the inline wavenumber and k ( y) represents the crossline wavenumber; calculating the maximum phase difference between primary and ghost events for each k ( x); calculating a minimum number of plane-waves required to avoid cycle-skipping; and selecting k ( y) values to regularly sample the maximum phase difference; building a linear system that models a wavefield using the representation, wherein the wavefield comprises the upgoing wavefield and a downgoing ghost wavefield; estimating the upgoing wavefield, within the representation, by inverting the linear system; and outputting the estimated upgoing wavefield for use in a drilling operation. receiving marine seismic data recorded from a single streamer; defining a representation of an upgoing wavefield in the marine seismic data, wherein the representation comprises a first wave component in a plane and a second wave component that is perpendicular to the plane; wherein defining the representation of the upgoing wavefield comprises determining a wavenumber sampling for inline propagation based on receiver sampling along the streamer cable and determining a crossline sampling such that a ghost delay is adequately sampled by the Nyquist criteria, wherein determining the crossline sampling comprises: receiving a user-defined maximum crossline angle of propagation that together with a maximum inline angle of propagation, defines an ellipse in k ( x) - k ( y) space, where k ( x) represents the inline wavenumber and k ( y) represents the crossline wavenumber; calculating the maximum phase difference between primary and ghost events for each k ( x); calculating a minimum number of plane-waves required to avoid cycle-skipping; and selecting k ( y) values to regularly sample the maximum phase difference; building a linear system that models a wavefield using the representation, wherein the wavefield comprises the upgoing wavefield and a downgoing ghost wavefield; estimating the upgoing wavefield, within the representation, by inverting the linear system; and outputting the estimated upgoing wavefield for use in a drilling operation. receiving a user-defined maximum crossline angle of propagation that together with a maximum inline angle of propagation, defines an ellipse in k ( x) - k ( y) space, where k ( x) represents the inline wavenumber and k ( y) represents the crossline wavenumber; calculating the maximum phase difference between primary and ghost events for each k ( x); calculating a minimum number of plane-waves required to avoid cycle-skipping; and selecting k ( y) values to regularly sample the maximum phase difference; building a linear system that models a wavefield using the representation, wherein the wavefield comprises the upgoing wavefield and a downgoing ghost wavefield; estimating the upgoing wavefield, within the representation, by inverting the linear system; and outputting the estimated upgoing wavefield for use in a drilling operation.