State of the art methods to image the Earth's subsurface using active-source seismic reflection data involve reverse-time migration (RTM). This, and other standard seismic processing methods such as velocity analysis, provide best results only when all waves in the data set are primaries (waves reflected only once). A variety of methods are therefore deployed as pre-processing to predict multiples (waves reflected several times); however, accurate removal of those predicted multiples from recorded data using adaptive subtraction techniques proves challenging, even in cases where they can be predicted with reasonable accuracy. We describe a new, alternative strategy: we construct a parallel data set consisting of only primaries, which is calculated directly from recorded data. This obviates the need for both multiple prediction and removal methods. Primaries are constructed using convolutional interferometry to combine first arriving events of up-going and direct-wave down-going Green's functions to virtual receivers in the subsurface. The required up-going wavefields to virtual receivers are constructed by Marchenko redatuming. Crucially, this is possible without detailed models of the Earth's subsurface velocity structure. The method is shown both to be particularly robust against errors in the reference velocity model used, and to improve migrated images substantially. @en