Statistical Interpolation of Spatially Varying but Sparsely Measured 3D Geo-Data Using Compressive Sensing and Variational Bayesian Inference

Zhao, Tengyuan; Wang, Yu

doi:10.1007/s11004-020-09913-x

Cited by 19 publications

(2 citation statements)

References 57 publications

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“…Compressibility or sparsity means that the signal has few dominating elements under some proper basis. CS has been used in a variety of applications such as the single-pixel camera, missing pixels and inpainting removal of images, biomedical such as heart rate estimation, internet of things (IoT), geostatistical data analysis, seismic tomography, communications such as blind multi-narrowband signals sampling and recovery, the direction of arrival (DoA) estimation, spectrum sharing of radar and communication signals, wireless networks and many more [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ]. In the linear CS framework, the problem is posed as

where

contains the measurements,

is the sparse signal of interest,

is the noise representing either the measurement noise or the insignificant coefficients of

and, generally,

[ 1 , 2 ].…”

Section: Introductionmentioning

confidence: 99%

Compressive Sensing via Variational Bayesian Inference under Two Widely Used Priors: Modeling, Comparison and Discussion

Shekaramiz

Moon

2023

Entropy

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Compressive sensing is a sub-Nyquist sampling technique for efficient signal acquisition and reconstruction of sparse or compressible signals. In order to account for the sparsity of the underlying signal of interest, it is common to use sparsifying priors such as Bernoulli–Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) priors on the components of the signal. With the introduction of variational Bayesian inference, the sparse Bayesian learning (SBL) methods for solving the inverse problem of compressive sensing have received significant interest as the SBL methods become more efficient in terms of execution time. In this paper, we consider the sparse signal recovery problem using compressive sensing and the variational Bayesian (VB) inference framework. More specifically, we consider two widely used Bayesian models of BGiG and GiG for modeling the underlying sparse signal for this problem. Although these two models have been widely used for sparse recovery problems under various signal structures, the question of which model can outperform the other for sparse signal recovery under no specific structure has yet to be fully addressed under the VB inference setting. Here, we study these two models specifically under VB inference in detail, provide some motivating examples regarding the issues in signal reconstruction that may occur under each model, perform comparisons and provide suggestions on how to improve the performance of each model.

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where

contains the measurements,

is the sparse signal of interest,

is the noise representing either the measurement noise or the insignificant coefficients of

and, generally,

[ 1 , 2 ].…”

Section: Introductionmentioning

confidence: 99%

Compressive Sensing via Variational Bayesian Inference under Two Widely Used Priors: Modeling, Comparison and Discussion

Shekaramiz

Moon

2023

Entropy

View full text Add to dashboard Cite

show abstract

“…Mikhailiuk A et al [19] first achieved the restoration of the full picture of seismic data from 20% of actual data through a deep autoencoder. Wang G [20], Liu Z [21], Zhao T [22], Fisher P F [23], and others have also used three-dimensional interpolation methods to carry out related work in the field of geoscience. Araya Polo [24] and others used deep neural network (DNN) and feature extraction steps to interpolate and establish velocity models from seismic trace sets, reducing computational costs.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Velocity Field Interpolation Based on Attention Mechanism

Yao,

Cui,

Wang

et al. 2023

Applied Sciences

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The establishment of a three-dimensional velocity field is an essential step in seismic exploration, playing a crucial role in understanding complex underground geological structures. Accurate 3D velocity fields are significant for seismic imaging, observation system design, precise positioning of underground geological targets, structural interpretation, and reservoir prediction. Therefore, obtaining an accurate 3D velocity field is a focus and challenge in this field of study. To achieve intelligent interpolation of the 3D velocity field more accurately, we have built a network model based on the attention mechanism, JointA 3DUnet. Based on the traditional U-Net, we have added triple attention blocks and channel attention blocks to enhance dimension information interaction, while adapting to the different changes of geoscience data in horizontal and vertical directions. Moreover, the network also incorporates dilated convolution to enlarge the receptive field. During the training process, we introduced transfer learning to further enhance the network’s performance for interpolation tasks. At the same time, our method is a deep learning interpolation algorithm based on an unsupervised model. It does not require a training set and learns information solely from the input data, automatically interpolating the missing velocity data at the missing positions. We tested our method on both synthetic and real data. The results show that, compared with traditional intelligent interpolation methods, our approach can effectively interpolate the three-dimensional velocity field. The SNR increased to 36.22 dB, and the pointwise relative error decreased to 0.89%.

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Prediction of Uniaxial Compressive Strength Using Fully Bayesian Gaussian Process Regression (fB-GPR) with Model Class Selection

Zhao

Chen

et al. 2022

Rock Mech Rock Eng

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Statistical Interpolation of Spatially Varying but Sparsely Measured 3D Geo-Data Using Compressive Sensing and Variational Bayesian Inference

Cited by 19 publications

References 57 publications

Compressive Sensing via Variational Bayesian Inference under Two Widely Used Priors: Modeling, Comparison and Discussion

Compressive Sensing via Variational Bayesian Inference under Two Widely Used Priors: Modeling, Comparison and Discussion

Three-Dimensional Velocity Field Interpolation Based on Attention Mechanism

Prediction of Uniaxial Compressive Strength Using Fully Bayesian Gaussian Process Regression (fB-GPR) with Model Class Selection

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