• Title, Summary, Keyword: Gauss-Newton방법

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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.

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.

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.

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.

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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Block-Coordinate Gauss-Newton Optimization for Image Registration (영상 정합을 위한 Block-Coordinate Gauss-Newton 최적화)

  • Kim, Dong-Sik
    • Journal of the Institute of Electronics Engineers of Korea SP
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    • v.44 no.6
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    • pp.1-8
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    • 2007
  • In this paper, research on joint optimization of the image spatial registration and the exposure compensation is conducted. The exposure compensation is performed in a frame work of the intensity compensation based on the polynomial approximation of the relationship between images. This compensation is jointly combined with the registration problem employing the Gauss-Newton nonlinear optimization method. In this paper, to perform for a simple and stable optimization, the block-coordinate method is combined with the Gauss-Newton optimization and extensively compared with the traditional approaches. Furthermore, regression analysis is considered in the compensation part for a better stable performance. By combining the block-coordinate method with the Gauss-Newton optimization, we can obtain a compatible performance reducing the computational complexity and stabilizing the performance. In the numerical result for a particular image, we obtain a satisfactory result for 10 repeats of the iteration, which implies a 50% reduction of the computational complexity. The error is also further reduced by 1.5dB compared to the ordinary method.

Gauss Newton Variable forgetting factor RLS algorithm for Time Varying Parameter Estimation. (Gauss Newton Variable Forgetting Factor Recursive Least Squares 알고리듬을 이용한 시변 신호 추정)

  • Song Seongwook;Lim Jun-Seok;Sung Koeng-Mo
    • Proceedings of the Acoustical Society of Korea Conference
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    • pp.173-176
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    • 2000
  • 시변 신호 추적 특성을 향상시키기 위하여, Gauss-Newton Variable Forgetting Factor RLS (GN-VFF-RLS) Algorithm을 제안한다. 최적화된 망각인자를 가정한 기존의 RLS 알고리듬과 비교하여, 제안된 방법은 특히 신호의 변화가 급격히 일어날 경우 주목할만한 추정 성능의 향상을 보여준다. 제안된 알고리듬의 시변 추정 특성을 신호 대 잡음비와 시변 정도에 대하여 모의 실험하고 기존의 추정 알고리듬들과 비교한다.

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Low Complexity Gauss Newton Variable Forgetting Factor RLS for Time Varying System Estimation (시변 시스템 추정을 위한 연산량이 적은 가우스 뉴턴 가변 망각인자를 사용하는 RLS 알고리즘)

  • Lim, Jun-Seok;Pyeon, Yong-Guk
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.41 no.9
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    • pp.1141-1145
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    • 2016
  • In general, a variable forgetting factor is applied to the RLS algorithm for the time-varying parameter estimation in the non-stationary environments. The introduction of a variable forgetting factor to RLS needs heavy additional calculation complexity. We propose a new Gauss Newton variable forgetting factor RLS algorithm which needs small amount of calculation as well as estimates the better parameters in time-varying nonstationary environment. The algorithm performs as good as the conventional Gauss Newton variable forgetting factor RLS and the required additional calculation complexity reduces from $O(N^2)$ to O(N).

Gauss-Newton Based Estimation for Moving Emitter Location Using TDOA/FDOA Measurements and Its Analysis (TDOA/FDOA 정보를 이용한 Gauss-Newton 기법 기반의 이동 신호원 위치 및 속도 추정 방법과 성능 분석)

  • Kim, Yong-Hee;Kim, Dong-Gyu;Han, Jin-Woo;Song, Kyu-Ha;Kim, Hyoung-Nam
    • Journal of the Institute of Electronics and Information Engineers
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    • v.50 no.6
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    • pp.62-71
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    • 2013
  • The passive emitter location method using TDOA and FDOA measurements has higher accuracy comparing to the single TDOA or FDOA based method. Moreover, it is able to estimate the velocity vector of a moving platform. Recently, several non-iterative methods were suggested using the nuisance parameter but the common reference sensor is needed for each pair of sensors. They show also relatively low performance in the case of a long range between the sensor groups and the emitter. To solve this, we derive the estimation method of the position and velocity of a moving platform based on the Gauss-Newton method. In addition, to analyze the estimation performance of the position and velocity, respectively, we decompose the CRLB matrix into each subspace. Simulation results show the estimation performance of the derived method and the CEP planes according to the given geometry of the sensors.