Irregularly sampled seismic data interpolation using iterative half thresholding regularization

The recent progress of compressive sensing (CS) theory shows that perfect reconstruction is possible when the data are sampled randomly and compressed greatly. This revolutionary theory strongly advocates the irregular sampling pattern in the process of seismic data acquisition, leading to a highly reduced acquisition cost. The complete seismic record can be reconstructed from the sparsely few sampled seismic data. In this paper, an analysis version of iterative half thresholding algorithm is introduced to interpolate the seismic data, using the tight frame dictionary. Inspired by the newly proposed spectral compressive sensing theory and the favorable characteristics of tight frame, we employ the redundant Fourier transform to sparsely represent the oscillating seismic data. A double zero-padding strategy in spatial direction of seismic data is suggested to further enhance the reconstruction quality, allowing for the improved interpolation performance and the increased computational cost and storage requirement. The validity of the proposed method is demonstrated by experimental result.