A low rank based seismic data interpolation via frequency-patches transform and low rank space projection

We propose a new algorithm to improve computational efficiency for low rank based interpolation. The interpolation is carried out in the frequency spatial domain where each frequency slice is first transferred to the frequency-patches domain. A nice feature of this domain is that the number of non-zero singular values can be better related to seismic events, which favors low rank reduction. During the interpolation iteration, instead of applying singular value decomposition to limit low rank, the low rank reduction is carried out with a predetermined low rank space projection matrix. Moreover, the technique of matrix completion is employed to avoid repeated transforms during the interpolation iteration. Compared with conventional low rank Interpolation methods, our method has the advantage of increased computational efficiency. Data examples also show that this method can be applied to complicated seismic data sets with highly satisfactory results.