Full Waveform Inversion (FWI) has been one of the hottest topics of earth model building. However, the lack of sufficient low frequency components restricts FWI for the real data, especially in the case that the initial model is not good. Based on inversion technique with a sparse constrain, we propose a low frequency recovery method in this paper. A L1 norm constrained inversion problem is established and solved by the Fast Iterative Thresholding Algorithm (FISTA). The low frequency components of the recovered data and high frequency components of the original data are combined to reconstruct the time domain data. A real example is used to demonstrate the performance of the proposed method.


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