Off-the-Grid Low-Rank Matrix Recovery and Seismic Data Reconstruction

López, Oscar; Kumar, Rajiv; Yılmaz, Özgür; Herrmann, Felix J.

doi:10.1109/jstsp.2016.2555482

Cited by 26 publications

(15 citation statements)

References 16 publications

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“…For instance, in astrophysics specific observational conditions make the sampling instants rather arbitrary [28], [29]. Seismic data processing is another example [30]. Due to different physical conditions involved in seismic surveys, sensors locations are often placed off the regular grid.…”

Section: B Contributions Relative To the Literaturementioning

confidence: 99%

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Frequency Estimation From Arbitrary Time Samples

Mahata

Hyder

2016

IEEE Trans. Signal Process.

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We consider the problem of estimating the line spectrum of a signal from finitely many time domain samples. We present a gridless algorithm for solving the total variation minimization approach associated with this problem. Unlike the related previous results, our method does not require the sampling instants to lie on an uniform grid. The resulting algorithm is a semidefinite program, structurally similar to some of the existing methods. One key observation made in our analysis also allows us to develop a gridless version of the SPICE algorithm. The simulation results demonstrate the superiority of these in performance compared to other related methods.

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Section: B Contributions Relative To the Literaturementioning

confidence: 99%

“…for some positive measure µ. Substituting θ = 2πf t M /d, and denotingμ(θ) = µ(dθ/(2πt M )) we can rewrite (30) as…”

Section: Proof Of Lemmamentioning

confidence: 99%

Frequency Estimation From Arbitrary Time Samples

Mahata

Hyder

2016

IEEE Trans. Signal Process.

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“…Besides traditional processing methods such as transform representations [4,5,6], low-rank approximation [7], multichannel singular spectrum analysis (MSSA) [8] and its interpolated version I-MSSA [9], many seismic interpolation methods based on Convolutional Neural Networks (CNNs) have been proposed [10,11,12,13] A different approach has been proposed interpreting the CNN architecture as a Deep Prior, in the framework of inverse problems, to address tasks such as interpolation, denoising or super-resolution [14]. In this paradigm, the CNN learns the inner structure of a 2D image from the corrupted data itself, without pre-training: this prevents any over-fitting issue as well as the need for training data.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Anti-Aliasing Add-On For Deep Prior Seismic Data Interpolation

Picetti

Lipari

Bestagini

et al. 2021

2021 IEEE International Conference on Image Processing (ICIP)

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Data interpolation is a fundamental step in any seismic processing workflow. Among machine learning techniques recently proposed to solve data interpolation as an inverse problem, Deep Prior paradigm aims at employing a convolutional neural network to capture priors on the data in order to regularize the inversion. However, this technique lacks of reconstruction precision when interpolating highly decimated data due to the presence of aliasing. In this work, we propose to improve Deep Prior inversion by adding a directional Laplacian as regularization term to the problem. This regularizer drives the optimization towards solutions that honor the slopes estimated from the interpolated data low frequencies. We provide some numerical examples to showcase the methodology devised in this manuscript, showing that our results are less prone to aliasing also in presence of noisy and corrupted data.

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“…In the low rank domain, matrix completion and rank reduction methods are widely used in missing traces reconstruction [49][50]. Based on a linear event assumption, Lopezet et al [51] extended matrix completion to seismic data regularization on unstructured grids with discretized Fourier transform (DFT) and NDFT, then it can project the data on the regular grid to the irregular grid. For 3D off-the-grid data regularization, Da Silva and Herrmann [52] proposed a tensor completion, and it shows a good performance in stationary field data.…”

Section: Introductionmentioning

confidence: 99%

Iterative Deblending of off-the-Grid Simultaneous Source Data

et al. 2021

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Simultaneous source acquisition can enhance the seismic data quality or improve the field acquisition efficiency. However, one of the disadvantages is that the simultaneous source data are often obtained on a non-uniform sampled grid in realistic acquisition. Except for the blending noise introduced by the temporal overlap, the non-uniform samplings usually causes serious artifacts which also greatly reduces the data quality and imaging resolution, such that data regularization must be implemented during the deblending. At present, most deblending algorithms are suitable for the uniformly sampled data. Thus, we propose the nonequispaced fast discrete curvelet transform-based deblending approach to deal with the nonuniformly sampled simultaneous source data. In order to enhance the deblending efficiency, we introduce the iterative shrinkage thresholding algorithm to solve the undetermined problem via a soft thresholding operator. Once the coefficients in the curvelet domain are acquired, uniformly sampled deblended data can be obtained via inverse curvelet transform. During the iterations, the threshold is decreased from a large value to a small value according to the new exponential function. Compared with the existing deblending methods that are applied on uniform grids, the key contribution is that the proposed method can directly work on the non-uniformly sampled simultaneous source data. The numerical examples are used to demonstrate the successful performance of the proposed method in attenuating blending noise and correcting the distorted events.

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Off-the-Grid Low-Rank Matrix Recovery and Seismic Data Reconstruction

Cited by 26 publications

References 16 publications

Frequency Estimation From Arbitrary Time Samples

Frequency Estimation From Arbitrary Time Samples

Anti-Aliasing Add-On For Deep Prior Seismic Data Interpolation

Iterative Deblending of off-the-Grid Simultaneous Source Data

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