Nonequispaced curvelet transform for seismic data reconstruction: A sparsity-promoting approach
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In this paper, a second generation of the fast discrete curvelet transform (NFDCT) is proposed. But the second generation is lossless unlike the first generation NFDCT.Abstract:
We extend our earlier work on the nonequispaced fast discrete curvelet transform (NFDCT) and introduce a second generation of the transform. This new generation differs from the previous one by the approach taken to compute accurate curvelet coefficients from irregularly sampled data. The first generation relies on accurate Fourier coefficients obtained by an l2 -regularized inversion of the nonequispaced fast Fourier transform (FFT) whereas the second is based on a direct l1 -regularized inversion of the operator that links curvelet coefficients to irregular data. Also, by construction the second generation NFDCT is lossless unlike the first generation NFDCT. This property is particularly attractive for processing irregularly sampled seismic data in the curvelet domain and bringing them back to their irregular record-ing locations with high fidelity. Secondly, we combine the second generation NFDCT with the standard fast discrete curvelet transform (FDCT) to form a new curvelet-based method, coined noneq...read more
Citations
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A tensor higher-order singular value decomposition for prestack seismic data noise reduction and interpolation
Nadia Kreimer,Mauricio D. Sacchi +1 more
TL;DR: In this paper, a rank-reduction process was used to reduce the rank of the prestack seismic tensor, and the higher-order singular value decompostion was used for rank reduction.
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Double Sparsity Dictionary for Seismic Noise Attenuation
TL;DR: This work has developed a double-sparsity dictionary (DSD) for seismic data to combine the benefits of both approaches and evaluated two models to learn the DSD: the synthesis model and the analysis model.
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A fast reduced-rank interpolation method for prestack seismic volumes that depend on four spatial dimensions
TL;DR: In this paper, a fast version of the Cadzow reduced-rank reconstruction method is implemented by embedding 4D spatial data into a level-four block Toeplitz matrix.
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Tensor completion based on nuclear norm minimization for 5D seismic data reconstruction
TL;DR: In this paper, a tensor completion strategy was proposed to recover unrecorded observations and to improve the signal-to-noise ratio of prestack seismic volumes by minimizing a convex objective function, which contains two terms: a data misfit and a nuclear norm.
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Simultaneous denoising and interpolation of 2D seismic data using data-driven non-negative dictionary learning
TL;DR: A parts-based 2D DDL scheme is introduced and evaluated for simultaneous denoising and interpolation of seismic data and a special case of versatile non-negative matrix factorization (VNMF) is used to learn a dictionary.
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