Mud-roll comprises of dispersive seismic waves that propagate along the unconsolidated sediment layers at the sea floor in shallow water marine environments, where the water depth is normally less than 30 m. Mud-roll's characteristics are spatially variable, i.e. the dispersion properties change from one shot to another across a seismic survey area. These complex kinematic properties make noise elimination very challenging using conventional seismic processing workflows. Our proposed method is a hybrid, Curvelet transform-based workflow that takes advantage of conventional seismic processing filtering to estimate the noise components, followed by the Curvelet transform that attenuates the residual noise energy that is difficult to remove with a conventional subtraction algorithm. In this paper, we illustrate the proposed Curvelet transform-based workflow using both synthetic and field data and demonstrate its effectiveness.