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We propose a fast and efficient method for interpolation of nonstationary seismic data. The proposed method utilizes a fast and nonredundant S transform to identify the space-wavenumber evolution of nonstationary spatial signals at each temporal frequency. The nonredundant nature of used transform renders a big computational advantage to the proposed interpolation method. Next, a least-squares fitting scheme is used to retrieve the optimal set of coefficients representative of the ideal interpolated data. For randomly sampled data on a regular grid we seek a sparse representation of the coefficients in order to retrieve the missing samples. Also, to interpolate the regularly sampled seismic data at a given frequency, we use a mask function derived from the coefficients of the low frequencies. Synthetic and real data examples are provided to examine the performance of the proposed method.