Low‐rank seismic data reconstruction and denoising by CUR matrix decompositions

Cavalcante, Quézia; Porsani, Milton J.

doi:10.1111/1365-2478.13163

Cited by 7 publications

(5 citation statements)

References 70 publications

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“…The often-neglected role of the rank, for instance, should be further investigated towards flexibility. Additionally, it is worth exploring less-costly alternatives to SVD, paying special attention to those not demanding the exact value of the rank (Carozzi and Sacchi, 2019;Cavalcante and Porsani, 2022).…”

Section: Discussionmentioning

confidence: 99%

“…It seems that SVD-based approaches lack flexibility regarding the choice of the appropriate rank: it should be the least possible value. This fact and the computational cost have motivated the search for alternatives to the SVD, such as randomized-SVD (Oropeza and Sacchi, 2011), Lanczos bidiagonalization (Gao et al, 2013), and CUR decompositions (Cavalcante and Porsani, 2022).…”

Section: More Numerical Experimentsmentioning

confidence: 99%

“…Low-rank methods constitute another important category, which has been largely investigated in recent years (Trickett et al, 2010;Oropeza and Sacchi, 2011;Kreimer and Sacchi, 2012;Ely et al, 2015;Carozzi and Sacchi, 2021;Oboué et al, 2021;Cavalcante and Porsani, 2022). They assume that regular seismic data can be represented as low-rank matrices or tensors.…”

Section: Introductionmentioning

confidence: 99%

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Rank-constrained seismic data interpolation and denoising

Cavalcante

Porsani

2022

Braz J Geophys

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Rank-constrained seismic data interpolation methods have been used to cope with spatial sampling deficiencies, but some fundamental aspects are often neglected. Understanding their underlying features is the first step for developing new solutions to overcome existing limitations. We intend to provide an intuitive description regarding low-rank strategies using the similarities between irregular samplings and noise in terms of their eigenimage representation. The interpretation of data recovery as iterative denoising helps to clarify how the traces are retrieved and the role of the rank. To emphasize either signal recovery or denoising along with the iterations, we explore non-linear versions of the decreasing weighting factor that drives the reinsertion of original samples. This type of weighting factor shows superior denoising results when raised to an integer power. Simple synthetic numerical examples illustrate the mechanics of low-rank procedures and their responses to different parameters. We also show 3D field data examples from a land survey to demonstrate the robustness of reduced-rank approaches.

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Section: Discussionmentioning

confidence: 99%

Section: More Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Rank-constrained seismic data interpolation and denoising

Cavalcante

Porsani

2022

Braz J Geophys

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“…Both methods have greatly enhanced the reconstruction performance and quality. Cavalcante and Porsani (2022) proposed the CUR matrix decomposition method to replace SVD for higher order tensors. The selection of the rank parameter of each tensor dimension has a significant impact on the reconstruction performance and time needed for this method.…”

Section: Introductionmentioning

confidence: 99%

Seismic noise attenuation method based on low‐rank adaptive symplectic geometry decomposition

Yang,

Luo,

Liu

et al. 2024

Geophysical Prospecting

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The basic assumption of low‐rank methods is that noise‐free seismic data can be represented as a low‐rank matrix. Effective noise reduction can be achieved through the low‐rank approximation of Hankel matrices composed of the data. However, selecting the appropriate rank parameter and avoiding expensive singular value decomposition are two challenges that have limited the practical application of this method. In this paper, we first propose symplectic geometric decomposition that avoids singular value decomposition. The symplectic similarity transformation preserves the essence of the original time sequence as well as the signal's basic characteristics and maintains the approximation of the Hankel matrix. To select an appropriate rank, we construct the symplectic geometric entropy according to the distribution of eigenvalues and search for high‐contributing eigenvalues to determine the needed rank parameter. Therefore, we provide an adaptive approach to selecting the rank parameter by the symplectic geometric entropy method. The synthetic examples and field data results show that our method significantly improves the computational efficiency while adaptively retaining more effective signals in complex structures. Therefore, this method has practical application value.

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“…The most traditional is the singular value decomposition (SVD). However, rank‐reduction can be more effective using Lanczos bidiagonalization, QR decomposition, randomized SVD (Liberty et al., 2007; Oropeza & Sacchi, 2010; Rokhlin et al., 2010), randomized QR decomposition (Chiron et al., 2014; Carozzi & Sacchi, 2017) and CUR decomposition (Cavalcante & Porsani, 2022; Manenti & Sacchi, 2022) as other engines for rank reduction.…”

Section: Introductionmentioning

confidence: 99%

Tensor tree decomposition as a rank‐reduction method for pre‐stack interpolation

Manenti

Sacchi

2023

Geophysical Prospecting

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Tensors have been proposed to represent pre‐stack seismic data, particularly for seismic data denoising and reconstruction. They naturally permit describing multi‐dimensional seismic signals that depend on time (or frequency) and source and receiver coordinates. A tensor representation aims to preserve the information embedded in the multi‐linear array in a reduced space. Such a representation is part of many algorithms for seismic data reconstruction via tensor completion methodologies. We investigate and apply one particular tensor tree representation to seismic data reconstruction. The Tensor Tree decomposition methodology permits decomposing a high‐order tensor into third‐order tensors. The technique relies on the truncated singular value decomposition, which branches the tensors into low‐dimensional tensors. As a benefit, the tensor tree allows us to reorganize the tensor into a matrix that demands the least singular values to have an optimal low‐rank approximation. We have developed an algorithm that uses the tensor tree for data reconstruction in an iterative optimization scheme and directly compared it to the parallel matrix factorization. At first, we demonstrated the proposed methodology results with five‐dimensional synthetic shot data and then moved forward with five‐dimensional field data, where we analysed it both pre and post‐stack. The tensor tree performs well in reconstructing both synthetic and field data with high fidelity, at the same level as the well‐established parallel matrix factorization.

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Low‐rank seismic data reconstruction and denoising by CUR matrix decompositions

Cited by 7 publications

References 70 publications

Rank-constrained seismic data interpolation and denoising

Rank-constrained seismic data interpolation and denoising

Seismic noise attenuation method based on low‐rank adaptive symplectic geometry decomposition

Tensor tree decomposition as a rank‐reduction method for pre‐stack interpolation

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