We introduce a technique that uses multicomponent seismic measurements to reconstruct the seismic wavefield at any desired crossline position between towed streamers. This method, called multichannel interpolation by matching pursuit (MIMAP), operates on pressure and crossline particle-motion measurements. It is based on the matching-pursuit technique and iteratively reconstructs the signal as a combination of optimal basis functions. Being a data-dependent technique, MIMAP can interpolate severely aliased data without assumptions about seismic events such as linearity or the model related to the seismic wavefield. MIMAP has the capability to perform well in the presence of irregular sampling and is robust when only a small number of samples are available. Using synthetic data examples, we show that the new method has the potential to interpolate signals that are sampled at realistic crossline streamer spacing and in the presence of noise.