Methods of processing seismic data to remove unwanted noise from meaningful reflection signals are provided for. The seismic data is transformed from the offset-time domain to the time-slowness domain using a high resolution Radon transformation. That is, the Radon transformation is performed according to an index j of the slowness set and a sampling variable p; wherein ##EQU1##

p is from about 0.5 to about 4.0 sec/m, p_max is a predetermined maximum slowness, and p_min is a predetermined minimum slowness. A corrective filter is then applied to 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. Suitable forward and reverse Radon transformations incorporating an offset weighting factor xⁿ and its inverse pⁿ, where 0n1, include the following continuous transform equations, and discrete versions thereof that approximate the continuous transform equations: ##EQU2## ##EQU3##