Seismic interferometry is widely used for passive subsurface investigation using seismic noise. The technique requires much storage for long noise records to suppress interferometric noise, which consists of spurious arrivals that do not correspond to the inter‐receiver surface waves. Such long recordings may not be available in practice. Compressive sensing (CS), which is a wavefield reconstruction technique operating on incomplete data, may increase the availability, and reduce storage limitations of long noise time series. Using a numerical example of a linear array surrounded by sources and the Fourier basis for a sparse transform, we show that inter‐receiver wavefields can be recovered at the locations where seismometers are unavailable, reducing the storage required for interferometry. We propose and develop a weighted CS algorithm that helps suppress the spurious arrivals by incorporating a priori information about the arrivals of surface waves that can be expected.

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