Tensor completion via nuclear norm minimization for 5D seismic data reconstruction

Kreimer, Nadia; Sacchi, Mauricio D.

doi:10.1190/segam2012-0529.1

Cited by 5 publications

(4 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Given tensor T, we must find a low-rank approximation R. There are many strategies for this, including Tucker decomposition or HOSVD (Kreimer and Sacchi, 2011) and nuclear norm minimization (Kreimer and Sacchi, 2012).…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Interpolation using Hankel tensor completion

Trickett

Burroughs

Milton

2013

SEG Technical Program Expanded Abstracts 2013

View full text Add to dashboard Cite

We present a novel multidimensional seismic trace interpolator that works on constant-frequency slices. It performs completion on Hankel tensors whose order is twice the number of spatial dimensions. Completion is done by fitting a PARAFAC model using an Alternating Least Squares algorithm. The new interpolator runs quickly and can better handle large gaps and high sparsity than existing completion methods.

show abstract

Section: Methodsmentioning

confidence: 99%

“…We will call this Hankel matrix completion. The second method takes the grid of complex values as a tensor without rearranging the values (Kreimer and Sacchi, 2012), so that the number of spatial dimensions equals the tensor order. We will call this direct tensor completion.…”

Section: Introductionmentioning

confidence: 99%

Interpolation using Hankel tensor completion

Trickett

Burroughs

Milton

2013

SEG Technical Program Expanded Abstracts 2013

View full text Add to dashboard Cite

show abstract

“…Tensor plays an important role in various fields, such as image processing [17,26,35], remote sensing [3,8,48,50], and machine learning [2,40], due to its ability of expressing the complex interactions within high-dimensional data. Tensor completion aims to estimate the missing entries or damaged parts from the observed data, which is a fundamental problem in multidimensional image processing, e.g., color image inpainting [19,25,46], video inpainting [4,44], hyperspectral images recovery [21,39], and seismic data reconstruction [20].…”

Section: Introductionmentioning

confidence: 99%

Tensor completion via nonconvex tensor ring rank minimization with guaranteed convergence

Ding¹,

Huang²,

Zhao³

et al. 2020

Preprint

View full text Add to dashboard Cite

In recent studies, the tensor ring (TR) rank has shown high effectiveness in tensor completion due to its ability of capturing the intrinsic structure within high-order tensors. A recently proposed TR rank minimization method is based on the convex relaxation by penalizing the weighted sum of nuclear norm of TR unfolding matrices. However, this method treats each singular value equally and neglects their physical meanings, which usually leads to suboptimal solutions in practice. In this paper, we propose to use the logdet-based function as a nonconvex smooth relaxation of the TR rank for tensor completion, which can more accurately approximate the TR rank and better promote the low-rankness of the solution. To solve the proposed nonconvex model efficiently, we develop an alternating direction method of multipliers algorithm and theoretically prove that, under some mild assumptions, our algorithm converges to a stationary point. Extensive experiments on color images, multispectral images, and color videos demonstrate that the proposed method outperforms several state-of-the-art competitors in both visual and quantitative comparison.

show abstract

“…For the tensor completion problem, the authors in [17] consider the problem of recovering a Tucker tensor with missing entries using the Douglas-Rachford splitting technique, which decouples interpolation and regularization by nuclear norm penalization of different matricizations of the tensor into subproblems that are then solved via a particular proximal mapping. An application of this approach to seismic data is detailed in [29] for the interpolation problem and [30] for denoising. Depending on the size and ranks of the tensor to be recovered, there are theoretical and numerical indications that this approach is no better than penalizing the nuclear norm in a single matricization (see [36] for a theoretical justification in the Gaussian measurement case, as well as [39] for an experimental demonstration of this effect).…”

Section: Introductionmentioning

confidence: 99%

Optimization on the Hierarchical Tucker manifold - applications to tensor completion

Silva¹,

Herrmann²

2014

Preprint

View full text Add to dashboard Cite

In this work, we develop an optimization framework for problems whose solutions are wellapproximated by Hierarchical Tucker (HT) tensors, an efficient structured tensor format based on recursive subspace factorizations. By exploiting the smooth manifold structure of these tensors, we construct standard optimization algorithms such as Steepest Descent and Conjugate Gradient for completing tensors from missing entries. Our algorithmic framework is fast and scalable to large problem sizes as we do not require SVDs on the ambient tensor space, as required by other methods. Moreover, we exploit the structure of the Gramian matrices associated with the HT format to regularize our problem, reducing overfitting for high subsampling ratios. We also find that the organization of the tensor can have a major impact on completion from realistic seismic acquisition geometries. These samplings are far from idealized randomized samplings that are usually considered in the literature but are realizable in practical scenarios. Using these algorithms, we successfully interpolate large-scale seismic data sets and demonstrate the competitive computational scaling of our algorithms as the problem sizes grow.

show abstract

Tensor completion via nuclear norm minimization for 5D seismic data reconstruction

Cited by 5 publications

References 12 publications

Interpolation using Hankel tensor completion

Interpolation using Hankel tensor completion

Tensor completion via nonconvex tensor ring rank minimization with guaranteed convergence

Optimization on the Hierarchical Tucker manifold - applications to tensor completion

Contact Info

Product

Resources

About