Seismic data reconstruction based on compressed sensing and Contourlet transform

Training a dictionary is time-consuming when using a standard algorithm for the reconstruction of dictionary learning based on compressed sensing.The algorithm for the reconstruction of sparse transforms based on compressed sensing is also problematic, as it has high requirements for sparse basis.Therefore, weighing the signal-to-noise ratio (SNR) and time consumption, introducing the Contourlet sparse basis which could be used in seismic data reconstruction, the paper proposes seismic data reconstruction using Contourlet transform based on compressed sensing.The method uses the fast iterative shrinkage-thresholding algorithm (FISTA) to reconstruct the missing sparse coefficients in the Contourlet domain according to the designed measurement matrix, and then performs a Contourlet inverse transform to reconstruct the missing seismic data.Testing on both synthetic data and field data indicates that the proposed method is effective.In comparison with the short-time Fourier transform and the wavelet transform, the proposed Contourlet transform based on compressed sensing has a higher SNR, and improved time efficiency.