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Marine vibrators have been favored by seismic acquisitions in recent years because of its greater waveform control, repeatability and less environmental damage. However, it present a processing challenge not found with airgun sources: the Doppler effect. The Doppler shift correction for source movement can be performed by using 2D deconvolution prior to correlation or using an analytical correction either pre or post correlation. However, both correction methods generate spatial artifacts when the shot sampling is coarse. The passage present a method to correct moving vibrator data. To deployed the linear composite operators on the sparse inversion algorithm, including mask function, F-K domain convolution operator, sampling matrix and a dictionary mapping seismic data to a basis function, the method achieves the goals of interpolation, correction and noise attenuation simultaneously in the sparse F-K domain. The introduction of the masking function preserves the effective spectrum during interpolation or noise attenuation. Besides, the conjugate symmetry of real signal Fourier transform can halve the amount of observed data involved in the inversion.