In common-reflection-surface imaging the reflection arrival time field is parameterized by operators that are of higher dimension or order than in conventional methods. Using the common-reflection-surface approach locally in the unmigrated prestack data domain opens a potential for trace regularization and interpolation. In most data interpolation methods based on local coherency estimation, a single operator is designed for a target sample and the output amplitude is defined as a weighted average along the operator. This approach may fail in presence of interfering events or strong amplitude and phase variations. In this paper we introduce an alternative scheme in which there is no need for an operator to be defined at the target sample itself. Instead, the amplitude at a target sample is constructed from multiple operators estimated at different positions. In this case one operator may contribute to the construction of several target samples. Vice versa, a target sample might receive contributions from different operators. Operators are determined on a grid which can be sparser than the output grid. This allows to dramatically decrease the computational costs. In addition, the use of multiple operators for a single target sample stabilizes the interpolation results and implicitly allows several contributions in case of interfering events. Due to the considerable computational expense, common-reflection-surface interpolation is limited to work in subsets of the prestack data. We present the general workflow of a common-reflection-surface-based regularization/interpolation for 3D data volumes. This workflow has been applied to an OBC common-receiver volume and binned common-offset subsets of a 3D marine data set. The impact of a common-reflection-surface regularization is demonstrated by means of a subsequent time migration. In comparison to the time migrations of the original and DMO-interpolated data, the results show particular improvements in view of the continuity of reflections events. This gain is confirmed by an automatic picking of a horizon in the stacked time migrations.