A technique includes decomposing a signal that is derived from a seismic acquisition into a plurality of signals such that each signal is associated with a different frequency band. For each signal of the plurality of signals, the technique includes performing the following: decomposing the signal into subbands in successive stages, where the subbands are associated with at least different frequency ranges of the signal; selectively applying adaptive noise attenuation in between the successive stages such that the stages decompose noise-attenuated subbands; and reconstructing the signal from the subbands resulting from the decomposition. The technique includes combining the reconstructed signals.