• Title, Summary, Keyword: Gauss-Newton method

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Performance Evaluation of a Time-domain Gauss-Newton Full-waveform Inversion Method (시간영역 Gauss-Newton 전체파형 역해석 기법의 성능평가)

  • Kang, Jun Won;Pakravan, Alireza
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.26 no.4
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    • pp.223-231
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    • 2013
  • This paper presents a time-domain Gauss-Newton full-waveform inversion method for the material profile reconstruction in heterogeneous semi-infinite solid media. To implement the inverse problem in a finite computational domain, perfectly-matchedlayers( PMLs) are introduced as wave-absorbing boundaries within which the domain's wave velocity profile is to be reconstructed. The inverse problem is formulated in a partial-differential-equations(PDE)-constrained optimization framework, where a least-squares misfit between measured and calculated surface responses is minimized under the constraint of PML-endowed wave equations. A Gauss-Newton-Krylov optimization algorithm is utilized to iteratively update the unknown wave velocity profile with the aid of a specialized regularization scheme. Through a series of one-dimensional examples, the solution of the Gauss-Newton inversion was close enough to the target profile, and showed superior convergence behavior with reduced wall-clock time of implementation compared to a conventional inversion using Fletcher-Reeves optimization algorithm.

EXTENDING THE APPLICABILITY OF INEXACT GAUSS-NEWTON METHOD FOR SOLVING UNDERDETERMINED NONLINEAR LEAST SQUARES PROBLEMS

  • Argyros, Ioannis Konstantinos;Silva, Gilson do Nascimento
    • Journal of the Korean Mathematical Society
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    • v.56 no.2
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    • pp.311-327
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    • 2019
  • The aim of this paper is to extend the applicability of Gauss-Newton method for solving underdetermined nonlinear least squares problems in cases not covered before. The novelty of the paper is the introduction of a restricted convergence domain. We find a more precise location where the Gauss-Newton iterates lie than in earlier studies. Consequently the Lipschitz constants are at least as small as the ones used before. This way and under the same computational cost, we extend the local as well the semilocal convergence of Gauss-Newton method. The new developmentes are obtained under the same computational cost as in earlier studies, since the new Lipschitz constants are special cases of the constants used before. Numerical examples further justify the theoretical results.

Construction the pseudo-Hessian matrix in Gauss-Newton Method and Seismic Waveform Inversion (Gauss-Newton 방법에서의 유사 Hessian 행렬의 구축과 이를 이용한 파형역산)

  • Ha, Tae-Young
    • Geophysics and Geophysical Exploration
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    • v.7 no.3
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    • pp.191-196
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    • 2004
  • Seismic waveform inversion can be solved by using the classical Gauss-Newton method, which needs to construct the huge Hessian by the directly computed Jacobian. The property of Hessian mainly depends upon a source and receiver aperture, a velocity model, an illumination Bone and a frequency content of source wavelet. In this paper, we try to invert the Marmousi seismic data by controlling the huge Hessian appearing in the Gauss-Newton method. Wemake the two kinds of he approximate Hessian. One is the banded Hessian and the other is the approximate Hessian with automatic gain function. One is that the 1st updated velocity model from the banded Hessian is nearly the same of the result from the full approximate Hessian. The other is that the stability using the automatic gain function is more improved than that without automatic gain control.

Study on Levenberg-Marquardt for Target Motion Analysis (표적기동분석을 위한 Levenberg-Marquardt 적용에 관한 연구)

  • Cho, Sunil
    • Journal of the Institute of Electronics and Information Engineers
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    • v.52 no.8
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    • pp.148-155
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    • 2015
  • The Levenberg-Marquardt method is a well known solution about the least square problem. However, in a Target Motion Analysis(TMA) application most of researches have used the Gauss-Newton method as a batch estimator, which of inverse matrix calculation may causes instability problem. In this paper, Levenberg-Marquardt method is applied to TMA problem to prevent its divergence. In experiment, its performance is compared with Gauss-Newton in domain of range, course and speed. Monte Carlo simulation reveals the convergence time and reliability of the TMA based on Levenberg-Marquardt.

Time Domain Seismic Waveform Inversion based on Gauss Newton method (시간영역에서 가우스뉴튼법을 이용한 탄성파 파형역산)

  • Sheen, Dong-Hoon;Baag, Chang-Eob
    • 한국지구물리탐사학회:학술대회논문집
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    • pp.131-135
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    • 2006
  • A seismic waveform inversion for prestack seismic data based on the Gauss-Newton method is presented. The Gauss-Newton method for seismic waveform inversion was proposed in the 80s but has rarely been studied. Extensive computational and memory requirements have been principal difficulties. To overcome this, we used different sizes of grids in the inversion stage from those of grids in the wave propagation simulation, temporal windowing of the simulation and approximation of virtual sources for calculating partial derivatives, and implemented this algorithm on parallel supercomputers. We show that the Gauss-Newton method has high resolving power and convergence rate, and demonstrate potential applications to real seismic data.

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LOCAL CONVERGENCE OF THE GAUSS-NEWTON METHOD FOR INJECTIVE-OVERDETERMINED SYSTEMS

  • Amat, Sergio;Argyros, Ioannis Konstantinos;Magrenan, Angel Alberto
    • Journal of the Korean Mathematical Society
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    • v.51 no.5
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    • pp.955-970
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    • 2014
  • We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than in earlier studies such us [10, 11, 13, 14, 18]. Special cases and numerical examples are also included in this study.

ON THE SEMILOCAL CONVERGENCE OF THE GAUSS-NEWTON METHOD USING RECURRENT FUNCTIONS

  • Argyros, Ioannis K.;Hilout, Said
    • The Pure and Applied Mathematics
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    • v.17 no.4
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    • pp.307-319
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    • 2010
  • We provide a new semilocal convergence analysis of the Gauss-Newton method (GNM) for solving nonlinear equation in the Euclidean space. Using our new idea of recurrent functions, and a combination of center-Lipschitz, Lipschitz conditions, we provide under the same or weaker hypotheses than before [7]-[13], a tighter convergence analysis. The results can be extented in case outer or generalized inverses are used. Numerical examples are also provided to show that our results apply, where others fail [7]-[13].

A Comparison of Image Reconstruction Techniques for Electrical Resistance Tomography (Electrical Resistance Tomography의 영상복원 기법의 비교)

  • Kim, Ho-Chan;Boo, Chang-Jin;Lee, Yoon-Joon
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.19 no.3
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    • pp.119-126
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    • 2005
  • Electrical resistance tomography(ERT) maps resistivity values of the soil subsurface and characterizes buried objects. The characterization includes location, size and resistivity of buried objects. In this paper, Gauss-Newton, truncated least squares(TLS) and simultaneous iterative reconstruction technique(SIRT) methods are presented for the solution of the ERT image reconstruction. Computer simulations show that the spatial resolution of the reconstructed images by the TLS approach is improved as compared to those obtained by the Gauss-Newton and SIRT method.

Conductivity Image Reconstruction Using Modified Gauss-Newton Method in Electrical Impedance Tomography (전기 임피던스 단층촬영 기법에서 수정된 가우스-뉴턴 방법을 이용한 도전율 영상 복원)

  • Kim, Bong Seok;Park, Hyung Jun;Kim, Kyung Youn
    • Journal of IKEEE
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    • v.19 no.2
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    • pp.219-224
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    • 2015
  • Electrical impedance tomography is an imaging technique to reconstruct the internal conductivity distribution based on applied currents and measured voltages in a domain of interest. In this paper, a modified Gauss-Newton method is proposed for conductivity image reconstruction. In the proposed method, the dimension of the inverse term is reduced by replacing the number of elements with the number of measurement data in the conductivity updating equation of the conventional Gauss-Newton method. Therefore, the computation time is greatly reduced as compared to the conventional Gauss-Newton method. Moreover, the regularization parameter is selected by computing the minimum-maximum from the diagonal components of the Jacobian matrix at every iteration. The numerical experiments with several scenarios were carried out to evaluate the reconstruction performance of the proposed method.

2D Image Reconstruction of Earth Model by Electrical Resistance Tomography (ERT를 이용한 2차원 대지모델 영상복원)

  • Boo, Chang-Jin;Kim, Ho-Chan;Kang, Min-Jae
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.14 no.7
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    • pp.3460-3467
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    • 2013
  • The In this paper, we have made numerical experiments to compare 2D image reconstruction algorithm of earth model by electrical resistance tomograpy (ERT). Gauss-Newton, simultaneous iterative reconstruction technieque (SIRT) and truncated least squares (TLS) approaches for Wenner and Schlumberger electrode arrays are presented for the solution of the ERT image reconstruction. Computer simulations show that the Gauss-Newton and TLS approach in ERT are proper for 2D image reconstruction of an earth model.