Methods of processing seismic data to remove unwanted noise from meaningful reflection signals are provided for. The methods comprise the steps of assembling seismic data into common geometry gathers in an offset-time domain without correcting the data for normal moveout. The amplitude data are then transformed from the offset-time domain to the time-slowness domain using a limited Radon transformation. That is, the Radon transformation is applied within defined slowness limits pmin and pmax, where pmin is a predetermined minimum slowness and pmax is a predetermined maximum slowness. A corrective filter is then applied to the transformed data enhance the primary reflection signal content of the data and to eliminate unwanted noise events. After filtering, the enhanced signal content is inverse transformed from the time-slowness domain back to the offset-time domain using an inverse Radon transformation.