singular values
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Geophysics ◽  
2022 ◽  
pp. 1-85
Author(s):  
Peng Lin ◽  
Suping Peng ◽  
Xiaoqin Cui ◽  
Wenfeng Du ◽  
Chuangjian Li

Seismic diffractions encoding subsurface small-scale geologic structures have great potential for high-resolution imaging of subwavelength information. Diffraction separation from the dominant reflected wavefields still plays a vital role because of the weak energy characteristics of the diffractions. Traditional rank-reduction methods based on the low-rank assumption of reflection events have been commonly used for diffraction separation. However, these methods using truncated singular-value decomposition (TSVD) suffer from the problem of reflection-rank selection by singular-value spectrum analysis, especially for complicated seismic data. In addition, the separation problem for the tangent wavefields of reflections and diffractions is challenging. To alleviate these limitations, we propose an effective diffraction separation strategy using an improved optimal rank-reduction method to remove the dependence on the reflection rank and improve the quality of separation results. The improved rank-reduction method adaptively determines the optimal singular values from the input signals by directly solving an optimization problem that minimizes the Frobenius-norm difference between the estimated and exact reflections instead of the TSVD operation. This improved method can effectively overcome the problem of reflection-rank estimation in the global and local rank-reduction methods and adjusts to the diversity and complexity of seismic data. The adaptive data-driven algorithms show good performance in terms of the trade-off between high-quality diffraction separation and reflection suppression for the optimal rank-reduction operation. Applications of the proposed strategy to synthetic and field examples demonstrate the superiority of diffraction separation in detecting and revealing subsurface small-scale geologic discontinuities and inhomogeneities.


Sensors ◽  
2021 ◽  
Vol 22 (1) ◽  
pp. 195
Author(s):  
Qinghua Wang ◽  
Lijuan Wang ◽  
Hongtao Yu ◽  
Dong Wang ◽  
Asoke K. Nandi

In view of the fact that vibration signals of rolling bearings are much contaminated by noise in the early failure period, this paper presents a new denoising SVD-VMD method by combining singular value decomposition (SVD) and variational mode decomposition (VMD). SVD is used to determine the structure of the underlying model, which is referred to as signal and noise subspaces, and VMD is used to decompose the original signal into several band-limited modes. Then the effective components are selected from these modes to reconstruct the denoised signal according to the difference spectrum (DS) of singular values and kurtosis values. Simulated signals and experimental signals of roller bearing faults have been analyzed using this proposed method and compared with SVD-DS. The results demonstrate that the proposed method can effectively retain the useful signals and denoise the bearing signals in extremely noisy backgrounds.


2021 ◽  
pp. 1-14
Author(s):  
Qingjiang Xiao ◽  
Shiqiang Du ◽  
Yao Yu ◽  
Yixuan Huang ◽  
Jinmei Song

In recent years, tensor-Singular Value Decomposition (t-SVD) based tensor nuclear norm has achieved remarkable progress in multi-view subspace clustering. However, most existing clustering methods still have the following shortcomings: (a) It has no meaning in practical applications for singular values to be treated equally. (b) They often ignore that data samples in the real world usually exist in multiple nonlinear subspaces. In order to solve the above shortcomings, we propose a hyper-Laplacian regularized multi-view subspace clustering model that joints representation learning and weighted tensor nuclear norm constraint, namely JWHMSC. Specifically, in the JWHMSC model, firstly, in order to capture the global structure between different views, the subspace representation matrices of all views are stacked into a low-rank constrained tensor. Secondly, hyper-Laplace graph regularization is adopted to preserve the local geometric structure embedded in the high-dimensional ambient space. Thirdly, considering the prior information of singular values, the weighted tensor nuclear norm (WTNN) based on t-SVD is introduced to treat singular values differently, which makes the JWHMSC more accurately obtain the sample distribution of classification information. Finally, representation learning, WTNN constraint and hyper-Laplacian graph regularization constraint are integrated into a framework to obtain the overall optimal solution of the algorithm. Compared with the state-of-the-art method, the experimental results on eight benchmark datasets show the good performance of the proposed method JWHMSC in multi-view clustering.


2021 ◽  
Vol 13 (2) ◽  
pp. 56-61
Author(s):  
Iwan Setiawan ◽  
Akbari Indra Basuki ◽  
Didi Rosiyadi

High performance computing (HPC) is required for image processing especially for picture element (pixel) with huge size. To avoid dependence to HPC equipment which is very expensive to be provided, the soft approach has been performed in this work. Actually, both hard and soft methods offer similar goal which are to reach time computation as short as possible. The discrete cosine transformation (DCT) and singular values decomposition (SVD) are conventionally performed to original image by consider it as a single matrix. This will result in computational burden for images with huge pixel. To overcome this problem, the second order matrix has been performed as block matrix to be applied on the original image which delivers the DCT-SVD hybrid formula. Hybrid here means the only required parameter shown in formula is intensity of the original pixel as the DCT and SVD formula has been merged in derivation. Result shows that when using Lena as original image, time computation of the singular values using the hybrid formula is almost two seconds faster than the conventional. Instead of pushing hard to provide the equipment, it is possible to overcome computational problem due to the size simply by using the proposed formula.


2021 ◽  
Author(s):  
Yangyang Ge ◽  
Zhimin Wang ◽  
Wen Zheng ◽  
Yu Zhang ◽  
Xiangmin Yu ◽  
...  

Abstract Quantum singular value thresholding (QSVT) algorithm, as a core module of many mathematical models, seeks the singular values of a sparse and low rank matrix exceeding a threshold and their associated singular vectors. The existing all-qubit QSVT algorithm demands lots of ancillary qubits, remaining a huge challenge for realization on near-term intermediate-scale quantum computers. In this paper, we propose a hybrid QSVT (HQSVT) algorithm utilizing both discrete variables (DVs) and continuous variables (CVs). In our algorithm, raw data vectors are encoded into a qubit system and the following data processing is fulfilled by hybrid quantum operations. Our algorithm requires O[log(MN)] qubits with O(1) qumodes and totally performs O(1) operations, which significantly reduces the space and runtime consumption.


Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3123
Author(s):  
Andrei Tănăsescu ◽  
Mihai Carabaş ◽  
Florin Pop ◽  
Pantelimon George Popescu

Singular value decomposition has recently seen a great theoretical improvement for k-tridiagonal matrices, obtaining a considerable speed up over all previous implementations, but at the cost of not ordering the singular values. We provide here a refinement of this method, proving that reordering singular values does not affect performance. We complement our refinement with a scalability study on a real physical cluster setup, offering surprising results. Thus, this method provides a major step up over standard industry implementations.


Author(s):  
Modjtaba Ghorbani ◽  
Mardjan Hakimi-Nezhaad ◽  
Lihua Feng

Following Estrada's method, as given in [1], Ghorbani et al. communicated in [2], and later also in [3], the following result on A-energy.


2021 ◽  
Vol 20 ◽  
pp. 625-629
Author(s):  
Ahmad Abu Rahma ◽  
Aliaa Burqan ◽  
Özen Özer

Matrix theory is very popular in different kind of sciences such as engineering, architecture, physics, chemistry, computer science, IT, so on as well as mathematics many theoretical results dealing with the structure of the matrices even this topic seems easy to work. That is why many scientists still consider some open problem in matrix theory. In this paper, generalizations of the arithmetic-geometric mean inequality is presented for singular values related to block matrices. Singular values are also given for sums, products and direct sums of the matrices.


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