Nuclear norm minimization and tensor completion in exploration seismology

Kreimer, Nadia; Sacchi, Mauricio D.

doi:10.1109/icassp.2013.6638466

Cited by 11 publications

(8 citation statements)

References 21 publications

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“…in which R(f ) is a penalty that promotes low multilinear rank solutions. Interestingly, whenever R is chosen to be a MSP, (37) can be shown to be equivalent to an instance of the general problem formulation in (29). This is an immediate consequence of the following proposition.…”

Section: Multilinear Multitask Learningmentioning

confidence: 82%

“…In a distinct (but not unrelated) second line of research, parametric models consisting of higher order tensors made their way in inductive as well as transductive learning methods [44,39,51]. Within transductive techniques, in particular, tensor completion and tensor recovery emerged as a useful higher order generalization of their matrix counterpart [30,19,45,44,49,33,29,10,31]. By dealing with the estimation of tensors in the unifying framework of reproducing kernel Hilbert spaces (RKHSs), this paper positions itself within this second line of research.…”

Section: Introductionmentioning

confidence: 99%

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Learning Tensors in Reproducing Kernel Hilbert Spaces with Multilinear Spectral Penalties

Signoretto¹,

Lathauwer²,

Suykens³

2013

Preprint

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We present a general framework to learn functions in tensor product reproducing kernel Hilbert spaces (TP-RKHSs). The methodology is based on a novel representer theorem suitable for existing as well as new spectral penalties for tensors. When the functions in the TP-RKHS are defined on the Cartesian product of finite discrete sets, in particular, our main problem formulation admits as a special case existing tensor completion problems. Other special cases include transfer learning with multimodal side information and multilinear multitask learning. For the latter case, our kernel-based view is instrumental to derive nonlinear extensions of existing model classes. We give a novel algorithm and show in experiments the usefulness of the proposed extensions.

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Section: Multilinear Multitask Learningmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Learning Tensors in Reproducing Kernel Hilbert Spaces with Multilinear Spectral Penalties

Signoretto¹,

Lathauwer²,

Suykens³

2013

Preprint

View full text Add to dashboard Cite

show abstract

“…In other seismic processing fields, [35] has investigated mixed ℓ p -ℓ 1 loss functions for deconvolution. Recently, in [36,37] the use of the nuclear norm is promoted for interpolation, combined with a standard ℓ 2 -norm penalty. Yet, to the authors' knowledge, no work in multiple removal has endeavored a more systematic study of variational and sparsity constraints on the adaptive filters, in the line of [38].…”

Section: Related and Proposed Workmentioning

confidence: 99%

A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Pham

Duval

Chaux

et al. 2014

IEEE Trans. Signal Process.

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Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data.

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“…The sumof-nuclear-norms (SNN) is served as a simple convex surrogate for tensor Tucker rank. This idea, after first being proposed in [12], has been studied in [13], [14], and successfully applied to various problems [15], [16]. Unlike the matrix cases, the recovery theory for low Tucker rank tensor estimation problems is far from being well established.…”

Section: Introductionmentioning

confidence: 99%

Exact Recovery of Tensor Robust Principal Component Analysis under Linear Transforms

Lu,

Zhou

2019

Preprint

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This work studies the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is motivated by the recently proposed linear transforms based tensor-tensor product and tensor SVD. We define a new transforms depended tensor rank and the corresponding tensor nuclear norm. Then we solve the TRPCA problem by convex optimization whose objective is a weighted combination of the new tensor nuclear norm and the 1-norm. In theory, we show that under certain incoherence conditions, the convex program exactly recovers the underlying low-rank and sparse components. It is of great interest that our new TRPCA model generalizes existing works. In particular, if the studied tensor reduces to a matrix, our TRPCA model reduces to the known matrix RPCA [1]. Our new TRPCA which is allowed to use general linear transforms can be regarded as an extension of our former TRPCA work [2] which uses the discrete Fourier transform. But their proof of the recovery guarantee is different. Numerical experiments verify our results and the application on image recovery demonstrates the superiority of our method.

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Nuclear norm minimization and tensor completion in exploration seismology

Cited by 11 publications

References 21 publications

Learning Tensors in Reproducing Kernel Hilbert Spaces with Multilinear Spectral Penalties

Learning Tensors in Reproducing Kernel Hilbert Spaces with Multilinear Spectral Penalties

A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Exact Recovery of Tensor Robust Principal Component Analysis under Linear Transforms

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