Singular-spectrum analysis via optimal shrinkage of singular values

Aharchaou, Mehdi; Anderson, J.M.M.; Hughes, S. R.; Bingham, J.A.C.

doi:10.1190/segam2017-17631902.1

Cited by 12 publications

(8 citation statements)

References 8 publications

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“…When N is a Gaussian random matrix instead of a random Hankel matrix, there exist many results concerning the asymptotic and non-asymptotic expressions of its singular values (Gavish and Donoho 2014). Based on these results, Gavish and Donoho (2014) provided an optimal value for c which is approximately equal to 0.56(M/N) 3 − 0.95(M/N) 2 + 1.82 M N + 1.43 (Aharchaou et al 2017). However, when N is a random Hankel matrix (i.e.…”

Section: Optimal Rank Selectionmentioning

confidence: 97%

“…Based on these results, Gavish and Donoho () provided an optimal value for c which is approximately equal to

0.56 {(M / N)}^{3} - 0.95 {(M / N)}^{2} + 1.82 \frac{M}{N} + 1.43

(Aharchaou et al . ). However, when N is a random Hankel matrix (i.e.…”

Section: Optimal Rank Selection For Low‐rank Seismic Denoisingmentioning

confidence: 97%

“…A common strategy for addressing this issue is to implement the algorithm in local windows since the events can be approximately viewed as linear in a small window (Oropeza and Sacchi ; Aharchaou et al . ; Chen et al . , ).…”

Section: Introductionmentioning

confidence: 99%

“…Aharchaou et al . () exploit recent results from the field of LR matrix denoising to improve the performance of SSA via optimal shrinkage of singular values, while this is not suitable for Hankel matrices consisting of random Hankel matrices which corresponds to noise.…”

Section: Introductionmentioning

confidence: 99%

“…is more complicated than linear events. A common strategy for addressing this issue is to implement the algorithm in local windows since the events can be approximately viewed as linear in a small window (Oropeza and Sacchi 2011;Aharchaou et al 2017;Chen et al 2016cChen et al , 2017c. However, this poses another difficulty of choosing an appropriate rank for each local processing window.…”

mentioning

confidence: 99%

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Low‐rank seismic denoising with optimal rank selection for hankel matrices

Wang

Zhu

2019

Geophysical Prospecting

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A B S T R A C TBased on the fact that the Hankel matrix representing clean seismic data is low rank, low-rank approximation methods have been widely utilized for removing noise from seismic data. A common strategy for real seismic data is to perform the low-rank approximations for small local windows where the events can be approximately viewed as linear. This raises a fundamental question of selecting an optimal rank that best captures the number of events for each local window. Gavish and Donoho proposed a method to select the rank when the noise is independent and identically distributed. Gaussian matrix by analysing the statistical performance of the singular values of the Gaussian matrices. However, such statistical performance is not available for noisy Hankel matrices. In this paper, we adopt the same strategy and propose a rule that computes the number of singular values exceed the median singular value by a multiplicative factor. We suggest a multiplicative factor of 3 based on simulations which mimic the theories underlying Gavish and Donoho in the independent and identically distributed Gaussian setting. The proposed optimal rank selection rule can be incorporated into the classical low-rank approximation method and many other recently developed methods such as those by shrinking the singular values. The low-rank approximation methods with optimally selected rank rule can automatically suppress most of the noise while preserving the main features of the seismic data in each window. Experiments on both synthetic and field seismic data demonstrate the superior performance of the proposed rank selection rule for seismic data denoising.

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Section: Optimal Rank Selectionmentioning

confidence: 97%

“…Based on these results, Gavish and Donoho () provided an optimal value for c which is approximately equal to

0.56 {(M / N)}^{3} - 0.95 {(M / N)}^{2} + 1.82 \frac{M}{N} + 1.43

(Aharchaou et al . ). However, when N is a random Hankel matrix (i.e.…”

Section: Optimal Rank Selection For Low‐rank Seismic Denoisingmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Low‐rank seismic denoising with optimal rank selection for hankel matrices

Wang

Zhu

2019

Geophysical Prospecting

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Adaptive Damped Rank-Reduction Method for Random Noise Attenuation of Three-Dimensional Seismic Data

et al. 2023

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Seismic noise attenuation using an online subspace tracking algorithm

Zhou

Zhang

et al. 2020

Geophysical Journal International

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SUMMARY We propose a new low-rank based noise attenuation method using an efficient algorithm for tracking subspaces from highly corrupted seismic observations. The subspace tracking algorithm requires only basic linear algebraic manipulations. The algorithm is derived by analysing incremental gradient descent on the Grassmannian manifold of subspaces. When the multidimensional seismic data are mapped to a low-rank space, the subspace tracking algorithm can be directly applied to the input low-rank matrix to estimate the useful signals. Since the subspace tracking algorithm is an online algorithm, it is more robust to random noise than traditional truncated singular value decomposition (TSVD) based subspace tracking algorithm. Compared with the state-of-the-art algorithms, the proposed denoising method can obtain better performance. More specifically, the proposed method outperforms the TSVD-based singular spectrum analysis method in causing less residual noise and also in saving half of the computational cost. Several synthetic and field data examples with different levels of complexities demonstrate the effectiveness and robustness of the presented algorithm in rejecting different types of noise including random noise, spiky noise, blending noise, and coherent noise.

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Singular-spectrum analysis via optimal shrinkage of singular values

Cited by 12 publications

References 8 publications

Low‐rank seismic denoising with optimal rank selection for hankel matrices

Low‐rank seismic denoising with optimal rank selection for hankel matrices

Adaptive Damped Rank-Reduction Method for Random Noise Attenuation of Three-Dimensional Seismic Data

Seismic noise attenuation using an online subspace tracking algorithm

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