Fast dictionary learning for noise attenuation of multidimensional seismic data

2020 ◽  
Vol 222 (3) ◽  
pp. 1717-1727 ◽  
Author(s):  
Yangkang Chen
Keyword(s):  
Dictionary Learning ◽  
Computational Efficiency ◽  
Seismic Data ◽  
Learning Algorithm ◽  
Computational Cost ◽  
Noise Attenuation ◽  
Arithmetic Average ◽  
Sparse Dictionary Learning ◽  
Singular Value Decompositions ◽  
High Computational Cost

SUMMARY The K-SVD algorithm has been successfully utilized for adaptively learning the sparse dictionary in 2-D seismic denoising. Because of the high computational cost of many singular value decompositions (SVDs) in the K-SVD algorithm, it is not applicable in practical situations, especially in 3-D or 5-D problems. In this paper, I extend the dictionary learning based denoising approach from 2-D to 3-D. To address the computational efficiency problem in K-SVD, I propose a fast dictionary learning approach based on the sequential generalized K-means (SGK) algorithm for denoising multidimensional seismic data. The SGK algorithm updates each dictionary atom by taking an arithmetic average of several training signals instead of calculating an SVD as used in K-SVD algorithm. I summarize the sparse dictionary learning algorithm using K-SVD, and introduce SGK algorithm together with its detailed mathematical implications. 3-D synthetic, 2-D and 3-D field data examples are used to demonstrate the performance of both K-SVD and SGK algorithms. It has been shown that SGK algorithm can significantly increase the computational efficiency while only slightly degrading the denoising performance.

scholarly journals Non-parallel dictionary learning for voice conversion using non-negative Tucker decomposition

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yuki Takashima ◽  
Toru Nakashika ◽  
Tetsuya Takiguchi ◽  
Yasuo Ariki
Keyword(s):  
Dictionary Learning ◽  
Computational Cost ◽  
Tensor Decomposition ◽  
Gaussian Mixture ◽  
Voice Conversion ◽  
Specific Information ◽  
Learning Method ◽  
Tucker Decomposition ◽  
Parallel Data ◽  
High Computational Cost

Abstract Voice conversion (VC) is a technique of exclusively converting speaker-specific information in the source speech while preserving the associated phonemic information. Non-negative matrix factorization (NMF)-based VC has been widely researched because of the natural-sounding voice it achieves when compared with conventional Gaussian mixture model-based VC. In conventional NMF-VC, models are trained using parallel data which results in the speech data requiring elaborate pre-processing to generate parallel data. NMF-VC also tends to be an extensive model as this method has several parallel exemplars for the dictionary matrix, leading to a high computational cost. In this study, an innovative parallel dictionary-learning method using non-negative Tucker decomposition (NTD) is proposed. The proposed method uses tensor decomposition and decomposes an input observation into a set of mode matrices and one core tensor. The proposed NTD-based dictionary-learning method estimates the dictionary matrix for NMF-VC without using parallel data. The experimental results show that the proposed method outperforms other methods in both parallel and non-parallel settings.

Retrieving the leaked signals from noise using a fast dictionary learning method

Geophysics ◽  
2021 ◽  
pp. 1-86
Author(s):  
Wei Chen ◽  
Omar M. Saad ◽  
Yapo Abolé Serge Innocent Oboué ◽  
Liuqing Yang ◽  
Yangkang Chen
Keyword(s):  
Dictionary Learning ◽  
Seismic Data ◽  
State Of The Art ◽  
Computational Cost ◽  
Learning Method ◽  
Global Parameter ◽  
Radius Parameter ◽  
Orthogonalization Method ◽  
Value Decomposition ◽  
Learned Features

Most traditional seismic denoising algorithms will cause damages to useful signals, which are visible from the removed noise profiles and are known as signal leakage. The local signal-and-noise orthogonalization method is an effective method for retrieving the leaked signals from the removed noise. Retrieving leaked signals while rejecting the noise is compromised by the smoothing radius parameter in the local orthogonalization method. It is not convenient to adjust the smoothing radius because it is a global parameter while the seismic data is highly variable locally. To retrieve the leaked signals adaptively, we propose a new dictionary learning method. Because of the patch-based nature of the dictionary learning method, it can adapt to the local feature of seismic data. We train a dictionary of atoms that represent the features of the useful signals from the initially denoised data. Based on the learned features, we retrieve the weak leaked signals from the noise via a sparse co ding step. Considering the large computational cost when training a dictionary from high-dimensional seismic data, we leverage a fast dictionary up dating algorithm, where the singular value decomposition (SVD) is replaced via the algebraic mean to update the dictionary atom. We test the performance of the proposed method on several synthetic and field data examples, and compare it with that from the state-of-the-art local orthogonalization method.

Data-driven multitask sparse dictionary learning for noise attenuation of 3D seismic data

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. V385-V396 ◽  
Author(s):  
Mohammad Amir Nazari Siahsar ◽  
Saman Gholtashi ◽  
Amin Roshandel Kahoo ◽  
Wei Chen ◽  
Yangkang Chen
Keyword(s):  
Dictionary Learning ◽  
Seismic Data ◽  
Random Noise ◽  
Data Driven ◽  
Superior Performance ◽  
Noise Attenuation ◽  
3D Seismic ◽  
Random Noise Attenuation ◽  
3D Data ◽  
3D Seismic Data

Representation of a signal in a sparse way is a useful and popular methodology in signal-processing applications. Among several widely used sparse transforms, dictionary learning (DL) algorithms achieve most attention due to their ability in making data-driven nonanalytical (nonfixed) atoms. Various DL methods are well-established in seismic data processing due to the inherent low-rank property of this kind of data. We have introduced a novel data-driven 3D DL algorithm that is extended from the 2D nonnegative DL scheme via the multitasking strategy for random noise attenuation of seismic data. In addition to providing parts-based learning, we exploit nonnegativity constraint to induce sparsity on the data transformation and reduce the space of the solution and, consequently, the computational cost. In 3D data, we consider each slice as a task. Whereas 3D seismic data exhibit high correlation between slices, a multitask learning approach is used to enhance the performance of the method by sharing a common sparse coefficient matrix for the whole related tasks of the data. Basically, in the learning process, each task can help other tasks to learn better and thus a sparser representation is obtained. Furthermore, different from other DL methods that use a limited random number of patches to learn a dictionary, the proposed algorithm can take the whole data information into account with a reasonable time cost and thus can obtain an efficient and effective denoising performance. We have applied the method on synthetic and real 3D data, which demonstrated superior performance in random noise attenuation when compared with state-of-the-art denoising methods such as MSSA, BM4D, and FXY predictive filtering, especially in amplitude and continuity preservation in low signal-to-noise ratio cases and fault zones.

scholarly journals Recursive Dictionary Learning Approach Exploiting Between-Channel Correlations for EEG Signal Reconstruction

2020 ◽  
Author(s):  
Masoud Vazifehkhahi ◽  
Tohid Yousefi Rezaii
Keyword(s):  
Dictionary Learning ◽  
Learning Algorithm ◽  
Signal To Noise Ratio ◽  
Signal Reconstruction ◽  
Computational Cost ◽  
Recursive Least Squares ◽  
Low Rank ◽  
Eeg Signal ◽  
Eeg Signals ◽  
Recording Time

In tele-monitoring, wireless body area networks (WBANs), sleep analysis and other applications involving electroencephalogram (EEG) signal, due to the high number of EEG recording channels, long recording time and several repetition of recordings to reach the highest signal-to-noise ratio, the amount of acquired data by the sensors is too large, demanding use of some compression procedure. Compressed sensing can be considered as one of the most effective compression methods in terms of compression ratio, which needs the underlying signal be sparse or have sparse representation in an appropriate domain. EEG signal is not sparse in time domain, therefore, in this paper correlation based weighted recursive least squares dictionary learning algorithm (CBW-RLS) is proposed that uses between-channel correlations to sparsify EEG signals. Due to the low-rank structure of EEG signals, exploiting between-channel correlations increase the sparsity level of the model while reducing the computational cost of dictionary learning procedure. This is done by merely updating the dictionary atoms which are involved in the sparse model of the previous data, reducing the total number of data used at each iteration and speeding up the dictionary learning algorithm. The simulation results show that the proposed method has better performance in terms of both quality of the EEG reconstruction and the computational cost compared to the other methods.

Robust high-dimensional seismic data interpolation based on elastic half norm regularization and tensor dictionary learning

Geophysics ◽  
2021 ◽  
pp. 1-52
Author(s):  
Nanying Lan ◽  
Zhang Fanchang ◽  
Chuanhui Li
Keyword(s):  
Compressed Sensing ◽  
Dictionary Learning ◽  
Seismic Data ◽  
Learning Algorithm ◽  
Interpolation Method ◽  
Superior Performance ◽  
Dimensional Structure ◽  
High Dimensional ◽  
Data Interpolation ◽  
Interpolation Model

Due to the limitations imposed by acquisition cost, obstacles, and inaccessible regions, the originally acquired seismic data are often sparsely or irregularly sampled in space, which seriously affects the ability of seismic data to image under-ground structures. Fortunately, compressed sensing provides theoretical support for interpolating and recovering irregularly or under-sampled data. Under the framework of compressed sensing, we propose a robust interpolation method for high-dimensional seismic data, based on elastic half norm regularization and tensor dictionary learning. Inspired by the Elastic-Net, we first develop the elastic half norm regularization as a sparsity constraint, and establish a robust high-dimensional interpolation model with this technique. Then, considering the multi-dimensional structure and spatial correlation of seismic data, we introduce a tensor dictionary learning algorithm to train a high-dimensional adaptive tensor dictionary from the original data. This tensor dictionary is used as the sparse transform for seismic data interpolation because it can capture more detailed seismic features to achieve the optimal and fast sparse representation of high-dimensional seismic data. Finally, we solve the robust interpolation model by an efficient iterative thresholding algorithm in the transform space and perform the space conversion by a modified imputation algorithm to recover the wavefields at the unobserved spatial positions. We conduct high-dimensional interpolation experiments on model and field seismic data on a regular data grid. Experimental results demonstrate that, this method has superior performance and higher computational efficiency in both noise-free and noisy seismic data interpolation, compared to extensively utilized dictionary learning-based interpolation methods.

scholarly journals Attenuating seismic noise via incoherent dictionary learning

2018 ◽  
Vol 15 (4) ◽  
pp. 1327-1338
Author(s):  
Juan Wu ◽  
Min Bai
Keyword(s):  
Sparse Representation ◽  
Image Denoising ◽  
Dictionary Learning ◽  
Seismic Data ◽  
Learning Algorithm ◽  
Random Noise ◽  
Learning Technology ◽  
Image Patches ◽  
Seismic Images ◽  
Traditional Image

Abstract We propose to apply an incoherent dictionary learning algorithm for reducing random noise in seismic data. The image denoising algorithm based on incoherent dictionary learning is proposed for solving the problem of losing partial texture information using traditional image denoising methods. The noisy image is firstly divided into different image patches, and those patches are extracted for dictionary learning. Then, we introduce the incoherent dictionary learning technology to update the dictionary. Finally, sparse representation problem is solved to obtain sparse representation coefficients by sparse coding algorithm. The denoised data can be obtained by reconstructing the image using the sparse coefficients. Application of the incoherent dictionary learning method to seismic images presents successful performance and demonstrates its superiority to the state-of-the-art denoising methods.

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