Interpolating solutions of the Helmholtz equation with compressed sensing

We present an algorithm which allows us to model wavefields with frequency-domain methods using a much smaller number of frequencies than that typically required by the classical sampling theory in order to obtain an alias-free result. The foundation of the algorithm is the recent results on the compressed sensing, which state that data can be successfully recovered from an incomplete measurement if the data is sufficiently sparse. Results from numerical experiment show that only 30% of the total frequency spectrum is need to capture the full wavefield information when working in the hard 2D synthetic Marmousi model.