• Title, Summary, Keyword: Hessian

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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.

Frequency domain elastic full waveform inversion using the new pseudo-Hessian matrix: elastic Marmousi-2 synthetic test (향상된 슈도-헤시안 행렬을 이용한 탄성파 완전 파형역산)

  • Choi, Yun-Seok;Shin, Chang-Soo;Min, Dong-Joo
    • 한국지구물리탐사학회:학술대회논문집
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    • pp.329-336
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    • 2007
  • For scaling of the gradient of misfit function, we develop a new pseudo-Hessian matrix constructed by combining amplitude field and pseudo-Hessian matrix. Since pseudo- Hessian matrix neglects the calculation of the zero-lag auto-correlation of impulse responses in the approximate Hessian matrix, the pseudo-Hessian matrix has a limitation to scale the gradient of misfit function compared to the approximate Hessian matrix. To validate the new pseudo- Hessian matrix, we perform frequency-domain elastic full waveform inversion using this Hessian matrix. By synthetic experiments, we show that the new pseudo-Hessian matrix can give better convergence to the true model than the old one does. Furthermore, since the amplitude fields are intrinsically obtained in forward modeling procedure, we do not have to pay any extra cost to compute the new pseudo-Hessian. We think that the new pseudo-Hessian matrix can be used as an alternative of the approximate Hessian matrix of the Gauss-Newton method.

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Laplace-domain Waveform Inversion using the Pseudo-Hessian of the Logarithmic Objective Function and the Levenberg-Marquardt Algorithm (로그 목적함수의 유사 헤시안을 이용한 라플라스 영역 파형 역산과 레벤버그-마쿼트 알고리듬)

  • Ha, Wansoo
    • Geophysics and Geophysical Exploration
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    • v.22 no.4
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    • pp.195-201
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    • 2019
  • The logarithmic objective function used in waveform inversion minimizes the logarithmic differences between the observed and modeled data. Laplace-domain waveform inversions usually adopt the logarithmic objective function and the diagonal elements of the pseudo-Hessian for optimization. In this case, we apply the Levenberg-Marquardt algorithm to prevent the diagonal elements of the pseudo-Hessian from being zero or near-zero values. In this study, we analyzed the diagonal elements of the pseudo-Hessian of the logarithmic objective function and showed that there is no zero or near-zero value in the diagonal elements of the pseudo-Hessian for acoustic waveform inversion in the Laplace domain. Accordingly, we do not need to apply the Levenberg-Marquardt algorithm when we regularize the gradient direction using the pseudo-Hessian of the logarithmic objective function. Numerical examples using synthetic and field datasets demonstrate that we can obtain inversion results without applying the Levenberg-Marquardt method.

An accelerated Levenberg-Marquardt algorithm for feedforward network

  • Kwak, Young-Tae
    • Journal of the Korean Data and Information Science Society
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    • v.23 no.5
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    • pp.1027-1035
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    • 2012
  • This paper proposes a new Levenberg-Marquardt algorithm that is accelerated by adjusting a Jacobian matrix and a quasi-Hessian matrix. The proposed method partitions the Jacobian matrix into block matrices and employs the inverse of a partitioned matrix to find the inverse of the quasi-Hessian matrix. Our method can avoid expensive operations and save memory in calculating the inverse of the quasi-Hessian matrix. It can shorten the training time for fast convergence. In our results tested in a large application, we were able to save about 20% of the training time than other algorithms.

Computer Aided Optimal Circuit Design (전자계산기에 의한 최적회로설계 방식 연구)

  • 김덕진;김선영
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.14 no.4
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    • pp.22-31
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    • 1977
  • A general equation by which the Hessian matrix of an error function can be determined directly, has been derived. It was verified to be useful in optimization processes that include the Hessian matrix. A few design examples had shown that this method had accelerated the processes of finding the minimums. The advantage of this technique is the possibility of optimizing functions that composed of both the phases and magnitudes.

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Pseudo-multiscale Waveform Inversion for Velocity Modeling

  • Yang Dongwoo;Shin Changsoo;Yoon Kwangjin;Yang Seungjin;Suh Junghee;Hong Soonduk
    • Proceedings of the KSEEG Conference
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    • pp.159-162
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    • 2002
  • We tried to obtain an initial velocity model for prestack depth migration via waveform inversion. For application of any field data we chose a smooth background layered velocity model (v=v0 + k x z) as an initial velocity model. Newton type waveform inversion needs to invert huge Hessian matrix. In order to compute full Hessian matrix arising from full aperture data and full illumination zone, we meet insurmountable difficulties of paying astronomical computing cost. For the layered media, approximate Hessian emerging from single shot aperture data can be used repeatedly for split spread source configuration. In our work of using this Hessian characteristic of layered media we attempted to obtain the approximate velocity model as close as possible to the true velocity model in first iteration.

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F-Hessian SIFT-Based Railroad Level-Crossing Vision System (F-Hessian SIFT기반의 철도건널목 영상 감시 시스템)

  • Lim, Hyung-Sup;Yoon, Hak-Sun;Kim, Chel-Huan;Ryu, Deung-Ryeol;Cho, Hwang;Lee, Key-Seo
    • The Journal of the Korea institute of electronic communication sciences
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    • v.5 no.2
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    • pp.138-144
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    • 2010
  • This paper presents the experimental analysis of a F-Hessian SIFT-Based Railroad Level-Crossing Safety Vision System. Region of surveillance, region of interests, data matching based on extracting feature points has been examined under the laboratory condition by the model rig on a small scale. Real-time system were observed by using SIFT based on F-Hessian feature tracking method and other common algorithm.

Rock Fracture Centerline Extraction based on Hessian Matrix and Steger algorithm

  • Wang, Weixing;Liang, Yanjie
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.9 no.12
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    • pp.5073-5086
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    • 2015
  • The rock fracture detection by image analysis is significant for fracture measurement and assessment engineering. The paper proposes a novel image segmentation algorithm for the centerline tracing of a rock fracture based on Hessian Matrix at Multi-scales and Steger algorithm. A traditional fracture detection method, which does edge detection first, then makes image binarization, and finally performs noise removal and fracture gap linking, is difficult for images of rough rock surfaces. To overcome the problem, the new algorithm extracts the centerlines directly from a gray level image. It includes three steps: (1) Hessian Matrix and Frangi filter are adopted to enhance the curvilinear structures, then after image binarization, the spurious-fractures and noise are removed by synthesizing the area, circularity and rectangularity; (2) On the binary image, Steger algorithm is used to detect fracture centerline points, then the centerline points or segments are linked according to the gap distance and the angle differences; and (3) Based on the above centerline detection roughly, the centerline points are searched in the original image in a local window along the direction perpendicular to the normal of the centerline, then these points are linked. A number of rock fracture images have been tested, and the testing results show that compared to other traditional algorithms, the proposed algorithm can extract rock fracture centerlines accurately.

Detection of Retinal Vessels of Fundus Photograph Using Hessian Algorithm (안저 영상에서 헤이지안 알고리즘을 이용한 혈관 검출)

  • Kang, Ho-Chul;Kim, Kwang-Gi;Oh, Whi-Vin;Hwang, Jeong-Min
    • Journal of Korea Multimedia Society
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    • v.12 no.8
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    • pp.1082-1088
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    • 2009
  • Fundus images are highly useful in evaluating patients' retinal conditions in diagnosing eye diseases. In particular, vessel regions are essential in diagnosing diabetes and hypertension. In this paper, we used top-hat filter to compensate for non-uniform background. Image contrast was enhanced by using contrast limited adaptive histogram equalization (CLAHE) method. Hessian matrix was next applied to detect vessel regions. Results indicate that our method is 1.3% more accurate than matched filter method. Our proposed method is expected to contribute to diagnosing eye diseases.

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