Seismic data reconstruction via weighted nuclear-norm minimization

Wang, Jing; Ma, Jianwei; Han, Bo; Cheng, Yuanfeng

doi:10.1080/17415977.2014.890616

Cited by 15 publications

(2 citation statements)

References 25 publications

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“…Based on the rank-reduction Cadzow method such as truncated singular value decomposition (SVD)-based matrix rank reduction of constant frequency slices for trace interpolation [13], multichannel singular spectrum analysis [3], adaptive rank-reduction based on the energy entropy [14] in solving rank reduction were proposed. Low-rank matrix completion [15,16], tensor higher order SVD [17], and nuclearnorm minimization-based matrix completion [18] have been proposed in seismic data restoration as an extension of Cadzow method.…”

Section: Introductionmentioning

confidence: 99%

Sparse Regularization Based on Orthogonal Tensor Dictionary Learning for Inverse Problems

Gemechu

2024

Mathematical Problems in Engineering

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In seismic data processing, data recovery including reconstruction of the missing trace and removal of noise from the recorded data are the key steps in improving the signal-to-noise ratio (SNR). The reconstruction of seismic data and removal of noise becomes a sparse optimization problem that can be solved by using sparse regularization. Sparse regularization is a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed inverses feasible. It deals with ill-posedness by replacing an ill-posed inverse problem with a well-posed problem that has a solution close to the true solution. In the last 2 decades, interest has shifted from linear toward nonlinear regularization methods even for linear inverse problems. In inverse problems, regularizations serve as stabilizing the solution of ill-posed inverse problems and give a solution that adequately fits measurements without producing unjustifiably complex artifacts. In this paper, we present a novel sparse regularization based on a tensor-based dictionary method for inverse problems (seismic data interpolation and denoising). This regularization avoids the vectorization step for sparse representation of seismic data during the reconstruction process. The key step in sparsifying signals is the choice of sparsity-promoting dictionary learning. The learning-based approach can adaptively sparsify datasets but has high computational complexity and involves no prior-constraint pattern information for the dataset. Many existing dictionary learning methods would be computationally infeasible for the high dimensional seismic data processing. These methods also destroy the essential information as well as it reduces the discriminability and expressibility of the signal, since they deal with vectorization. In this paper, the orthogonal tensor dictionary learning that learns a dictionary from the input data by employing orthogonality and separability is proposed as sparse regularization for the inverse problems. The performance of the proposed method was validated in seismic data interpolation and denoising individually as well as simultaneously. Numerical examples of synthetic and real seismic datasets demonstrate the validity of the proposed method. The SNR of the recovered data confirms that the proposed method is the most effective method than K-singular value decomposition and orthogonal dictionary learning methods.

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Section: Introductionmentioning

confidence: 99%

Sparse Regularization Based on Orthogonal Tensor Dictionary Learning for Inverse Problems

Gemechu

2024

Mathematical Problems in Engineering

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“…Then, two matrix completion algorithms, the accelerated proximal gradient method (APG) [21] and a low-rank matrix fitting algorithm (LMaFit) [28], are used in the seismic data reconstruction. Wang et al [27] proposed a weighted nuclear-norm model based on texture-patch pre-transformation to reconstruct seismic data with missing traces. Ma [13] extended the texture-patch pre-transformation method to the reconstruction of three-dimensional (3D) seismic data.…”

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confidence: 99%

Two-dimensional seismic data reconstruction using patch tensor completion

Li¹,

Fu²,

Zhang³

et al. 2020

Inverse Problems &Amp; Imaging

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Seismic data are often undersampled owing to physical or financial limitations. However, complete and regularly sampled data are becoming increasingly critical in seismic processing. In this paper, we present an efficient two-dimensional (2D) seismic data reconstruction method that works on texture-based patches. It performs completion on a patch tensor, which folds texture-based patches into a tensor. Reconstruction is performed by reducing the rank using tensor completion algorithms. This approach differs from past methods, which proceed by unfolding matrices into columns and then applying common matrix completion approaches to deal with 2D seismic data reconstruction. Here, we first re-arrange the seismic data matrix into a third-order patch tensor, by stacking texture-based patches that are divided from seismic data. Then, the seismic data reconstruction problem is formulated into a low-rank tensor completion problem. This formulation avoids destroying the spatial structure, and better extracts the underlying useful information. The proposed method is efficient and gives an improved performance compared with traditional approaches. The effectiveness of our patch tensor-based framework is validated using two classical tensor completion algorithms, low-rank tensor completion (LRTC), and the parallel matrix factorization algorithm (TMac), on both synthetic and field data experiments.

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