Random noise attenuation via the randomized canonical polyadic decomposition

ABSTRACT Tensor algebra provides a robust framework for multi‐dimensional seismic data processing. A low‐rank tensor can represent a noise‐free seismic data volume. Additive random noise will increase the rank of the tensor. Hence, tensor rank‐reduction techniques can be used to filter random noise....

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Bibliographic Details
Published in:Geophysical Prospecting Vol. 68; no. 3; pp. 872 - 891
Main Authors: Gao, Wenlei, Sacchi, Mauricio D.
Format: Journal Article
Language:English
Published: Houten Wiley Subscription Services, Inc 01.03.2020
Subjects:
Additives
Algorithms
Attenuation
Computing costs
Data processing
Decomposition
Dimensional analysis
Filtration
Least squares method
Mathematical analysis
Multi‐linear algebra
Noise
Noise reduction
Random noise
Randomization
Seismic data processing
Signal processing
Singular value decomposition
Spectrum analysis
Tensors
ISSN:0016-8025, 1365-2478
Online Access:Get full text
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Summary:ABSTRACT Tensor algebra provides a robust framework for multi‐dimensional seismic data processing. A low‐rank tensor can represent a noise‐free seismic data volume. Additive random noise will increase the rank of the tensor. Hence, tensor rank‐reduction techniques can be used to filter random noise. Our filtering method adopts the Candecomp/Parafac decomposition to approximates a N‐dimensional seismic data volume via the superposition of rank‐one tensors. Similar to the singular value decomposition for matrices, a low‐rank Candecomp/Parafac decomposition can capture the signal and exclude random noise in situations where a low‐rank tensor can represent the ideal noise‐free seismic volume. The alternating least squares method is adopted to compute the Candecomp/Parafac decomposition with a provided target rank. This method involves solving a series of highly over‐determined linear least‐squares subproblems. To improve the efficiency of the alternating least squares algorithm, we uniformly randomly sample equations of the linear least‐squares subproblems to reduce the size of the problem significantly. The computational overhead is further reduced by avoiding unfolding and folding large dense tensors. We investigate the applicability of the randomized Candecomp/Parafac decomposition for incoherent noise attenuation via experiments conducted on a synthetic dataset and field data seismic volumes. We also compare the proposed algorithm (randomized Candecomp/Parafac decomposition) against multi‐dimensional singular spectrum analysis and classical f−xy prediction filtering. We conclude the proposed approach can achieve slightly better denoising performance in terms of signal‐to‐noise ratio enhancement than traditional methods, but with a less computational cost.
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ISSN:0016-8025
1365-2478
DOI:10.1111/1365-2478.12894