Multi-dimensional Seismic Data Reconstruction via De-Aliased and De-Noise Cadzow Filtering

The Cadzow filtering is currently considered as one of the most effective approaches for seismic data reconstruction. The basic version of Cadzow filtering technique first realigns each frequency slice of the seismic data (to be reconstructed) to a block Hankel/Toeplitz matrix, and then implements a rank-reduction operator to the Hankel/Toeplitz matrix. However, the basic Cadzow filtering cannot deal with the problem of recovering regularly missed data (up-sampling) because of the strong aliasing energy, since the regularly missed data will mix with signals in the singular spectrum. This problem can be solved by following the idea of Spitz's method. Therefore, We propose a new Cadzow filtering for reconstructing regularly missed seismic data, in which the high-frequency components are projected onto the sub-space spanned by several singular vectors of the low-frequency components. The reconstruction of each frequency component is involved in an iteration pattern where the filtered data at each stage of the iteration are weighted to the original data as a feedback. The weighting factor is related to the background noise level and changes with iteration. The feasibility of the proposed technique is validated via a 3D pre-stack field data example in this abstract.