3-D Resistivity Inversion by the Least-Square QR Factorization Method Under Improved Smoothness Constraint

2005 ◽  
Vol 48 (2) ◽  
pp. 486-492 ◽  
Author(s):  
Xin-Lin WAN ◽  
Dao-Ying XI ◽  
Er-Gen GAO ◽  
Zhao-Wu SHEN
Keyword(s):  
Factorization Method ◽  
Least Square ◽  
Qr Factorization ◽  
Smoothness Constraint ◽  
Resistivity Inversion

A Fast Image Reconstruction Algorithm for EIT Based on Wavelet Analysis and LSQR

2014 ◽  
Vol 654 ◽  
pp. 341-345
Author(s):  
Ying Zhi Sun ◽  
Jian Ming Wang ◽  
Qi Wang
Keyword(s):  
Image Reconstruction ◽  
Electrical Impedance ◽  
Reconstruction Algorithm ◽  
Scale Space ◽  
Least Square ◽  
Qr Factorization ◽  
Impedance Tomography ◽  
Image Reconstruction Algorithm ◽  
Low Dimension ◽  
2D And 3D

The LSQR algorithm is always used to solve the inverse problem of electrical impedance tomography (EIT). However, it always has relatively low reconstruction speed. In this paper, WALSQR (wavelet multi-resolution based Least Square QR-factorization) algorithm is proposed for EIT imaging. With the aid of wavelet transformation, the LSQR solution is obtained in the low-dimension scale space, where important information on the reconstructed image is contained. Hence the computational complexity of reconstruction is reduced without affecting the image quality. In order to verify the effectiveness of the new method, experiments of 2D and 3D EIT imaging are conducted. It lays the foundation for the study of 3D dynamic EIT image reconstruction algorithm.

scholarly journals Sparse Optimistic Based on Lasso-LSQR and Minimum Entropy De-Convolution with FARIMA for the Remaining Useful Life Prediction of Machinery

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 747 ◽  
Author(s):  
Bo Wu ◽  
Yangde Gao ◽  
Songlin Feng ◽  
Theerasak Chanwimalueang
Keyword(s):  
Health Monitoring ◽  
Hybrid Method ◽  
Health Indicators ◽  
Remaining Useful Life ◽  
Least Square ◽  
Qr Factorization ◽  
Maintenance Cost ◽  
Minimum Entropy ◽  
Useful Life

To reduce the maintenance cost and safeguard machinery operation, remaining useful life (RUL) prediction is very important for long term health monitoring. In this paper, we introduce a novel hybrid method to deal with the RUL prediction for health management. Firstly, the sparse reconstruction algorithm of the optimized Lasso and the Least Square QR-factorization (Lasso-LSQR) is applied to compressed sensing (CS), which can realize the sparse optimization for long term health monitoring data. After the sparse signal is reconstructed, the minimum entropy de-convolution (MED) is used to identify the fault characteristics and to obtain significant fault information from the machinery operation. Health indicators with Skip-over, sample entropy and approximate entropy are then performed to track the degradation of the machinery process. The performance analysis of the Skip-over is superior to other indicators. Finally, Fractal Autoregressive Integrated Moving Average model (FARIMA) is employed to predict the Skip-over using the R/S method. The analysis results evidence that the novel hybrid method yields a good performance, and such method can achieve highly accurate RUL prediction and safeguard machinery operation for long term monitoring.

scholarly journals Robust Semisupervised Nonnegative Local Coordinate Factorization for Data Representation

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Wei Jiang ◽  
Qian Lv ◽  
Chenggang Yan ◽  
Kewei Tang ◽  
Jie Zhang
Keyword(s):  
Loss Function ◽  
Matrix Factorization ◽  
Nonnegative Matrix ◽  
Approximation Problem ◽  
Factorization Method ◽  
Data Representation ◽  
Least Square ◽  
Gene Clustering ◽  
Unified Framework ◽  
Label Information

Obtaining an optimum data representation is a challenging issue that arises in many intellectual data processing techniques such as data mining, pattern recognition, and gene clustering. Many existing methods formulate this problem as a nonnegative matrix factorization (NMF) approximation problem. The standard NMF uses the least square loss function, which is not robust to outlier points and noises and fails to utilize prior label information to enhance the discriminability of representations. In this study, we develop a novel matrix factorization method called robust semisupervised nonnegative local coordinate factorization by integrating robust NMF, a robust local coordinate constraint, and local spline regression into a unified framework. We use the l2,1 norm for the loss function of the NMF and a local coordinate constraint term to make our method insensitive to outlier points and noises. In addition, we exploit the local and global consistencies of sample labels to guarantee that data representation is compact and discriminative. An efficient multiplicative updating algorithm is deduced to solve the novel loss function, followed by a strict proof of the convergence. Several experiments conducted in this study on face and gene datasets clearly indicate that the proposed method is more effective and robust compared to the state-of-the-art methods.

scholarly journals The Eigenspace Spectral Regularization Method for Solving Discrete Ill-Posed Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Fredrick Asenso Wireko ◽  
Benedict Barnes ◽  
Charles Sebil ◽  
Joseph Ackora-Prah
Keyword(s):  
Regularization Method ◽  
Sparse Matrix ◽  
Circulant Matrix ◽  
Least Square ◽  
Matrix Operator ◽  
Qr Factorization ◽  
Spectral Matrix ◽  
Spectral Regularization ◽  
Ill Posed ◽  
Hilbert Matrix

This paper shows that discrete linear equations with Hilbert matrix operator, circulant matrix operator, conference matrix operator, banded matrix operator, TST matrix operator, and sparse matrix operator are ill-posed in the sense of Hadamard. Gauss least square method (GLSM), QR factorization method (QRFM), Cholesky decomposition method (CDM), and singular value decomposition (SVDM) failed to regularize these ill-posed problems. This paper introduces the eigenspace spectral regularization method (ESRM), which solves ill-posed discrete equations with Hilbert matrix operator, circulant matrix operator, conference matrix operator, and banded and sparse matrix operator. Unlike GLSM, QRFM, CDM, and SVDM, the ESRM regularizes such a system. In addition, the ESRM has a unique property, the norm of the eigenspace spectral matrix operator κ K = K − 1 K = 1 . Thus, the condition number of ESRM is bounded by unity, unlike the other regularization methods such as SVDM, GLSM, CDM, and QRFM.

scholarly journals Nonlinear Electromagnetic Inverse Scattering Imaging Based on IN-LSQR

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Huilin Zhou ◽  
Youwen Liu ◽  
Yuhao Wang ◽  
Liangbing Chen ◽  
Rongxing Duan
Keyword(s):  
Inverse Scattering ◽  
Large Scale ◽  
Linear Equations ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Least Square ◽  
Qr Factorization ◽  
Inexact Newton Method ◽  
Nonlinear Inversion ◽  
Electromagnetic Inverse Scattering

A nonlinear inversion scheme is proposed for electromagnetic inverse scattering imaging. It exploits inexact Newton (IN) and least square QR factorization (LSQR) methods to tackle the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem. A nonlinear model of the inverse scattering in functional form is developed. At every IN iteration, the sparse storage method is adopted to solve the storage and computational bottleneck of Fréchet derivative matrix, a large-scale sparse Jacobian matrix. Moreover, to address the slow convergence problem encountered in the inexact Newton solution via Landweber iterations, an LSQR algorithm is proposed for obtaining a better solution of the internal large-scale sparse linear equations in the IN step. Numerical results demonstrate the applicability of the proposed IN-LSQR method to quantitative inversion of scatterer electric performance parameters. Moreover, compared with the inexact Newton method based on Landweber iterations, the proposed method significantly improves the convergence rate with less computational and storage cost.

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