• Geophysics and Geophysical Exploration
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• v.17 no.2
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• pp.95-103
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• 2014

This paper presents a practical inversion method for recovering a three-dimensional (3D) resistivity model and static shifts simultaneously. Although this method is based on a Gauss-Newton approach that requires a sensitivity matrix, the computer time can be greatly reduced by implementing a simple and effective procedure for updating the sensitivity matrix using the Broyden's algorithm. In this research, we examine the approximate inversion procedure and the weighting factor ${\beta}$ for static shifts through inversion experiments using synthetic MT data. In methods using the full sensitivity matrix constructed only once in the iteration process, a procedure using the full sensitivity in the earlier stage is useful to produce the smallest rms data misfit. The choice of ${\beta}$ is not critical below some threshold value. Synthetic examples demonstrate that the method proposed in this paper is effective in reconstructing a 3D resistivity structure from static-shifted MT data.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.271-282
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• 1993

Unit root test for temporally aggregated first order autoregressive process is considered. The temporal aggregate of fist order autoregression is an autoregressive moving average of order (1,1) with moving average parameter being function of the autoregressive parameter. One-step Gauss-Newton estimators are proposed and are shown to have the same limiting distribution as the ordinary least squares estimator for unit root when complete observations are available. A Monte-Carlo simulation shows that the temporal aggregation have no effect on the size. The power of the suggested test are nearly the same as the powers of the test based on complete observations.

• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.133-140
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• 1995

The D-optimal design criterion for precise parameter estimation in nonlinear regression analysis is called the determinant criterion because the determinant of a matrix is to be maximized. In this thesis, we derive the gradient and the Hessian of the determinant criterion, and apply a QR decomposition for their efficient computations. We also propose an approximate form of the Hessian matrix which can be calculated from the first derivative of a model function with respect to the design variables. These equations can be used in a Gauss-Newton type iteration procedure.

• Geophysics and Geophysical Exploration
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• v.10 no.2
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• pp.147-153
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• 2007

The conjugate gradient (CG) method is one of the most efficient algorithms for solving a linear system of equations. In addition to being used as a linear equation solver, it can be applied to a least-squares problem. When the CG method is applied to large-scale three-dimensional inversion of magnetotelluric data, two approaches have been pursued; one is the linear CG inversion in which each step of the Gauss-Newton iteration is incompletely solved using a truncated CG technique, and the other is referred to as the nonlinear CG inversion in which CG is directly applied to the minimization of objective functional for a nonlinear inverse problem. In each procedure we only need to compute the effect of the sensitivity matrix or its transpose multiplying an arbitrary vector, significantly reducing the computational requirements needed to do large-scale inversion.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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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.

• Radiation Oncology Journal
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• v.24 no.4
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• pp.300-308
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• 2006

$\underline{Purpose}$: To develop a wireless CCTV system in semi-beam's eye view (BEV) to monitor daily patient setup in radiation therapy. $\underline{Materials\;and\;Methods}$: In order to get patient images in semi-BEV, CCTV cameras are installed in a custom-made acrylic applicator below the treatment head of a linear accelerator. The images from the cameras are transmitted via radio frequency signal (${\sim}2.4\;GHz$ and 10 mW RF output). An expected problem with this system is radio frequency interference, which is solved utilizing RF shielding with Cu foils and median filtering software. The images are analyzed by our custom-made software. In the software, three anatomical landmarks in the patient surface are indicated by a user, then automatically the 3 dimensional structures are obtained and registered by utilizing a localization procedure consisting mainly of stereo matching algorithm and Gauss-Newton optimization. This algorithm is applied to phantom images to investigate the setup accuracy. Respiratory gating system is also researched with real-time image processing. A line-laser marker projected on a patient's surface is extracted by binary image processing and the breath pattern is calculated and displayed in real-time. $\underline{Results}$: More than 80% of the camera noises from the linear accelerator are eliminated by wrapping the camera with copper foils. The accuracy of the localization procedure is found to be on the order of $1.5{\pm}0.7\;mm$ with a point phantom and sub-millimeters and degrees with a custom-made head/neck phantom. With line-laser marker, real-time respiratory monitoring is possible in the delay time of ${\sim}0.17\;sec$. $\underline{Conclusion}$: The wireless CCTV camera system is the novel tool which can monitor daily patient setups. The feasibility of respiratory gating system with the wireless CCTV is hopeful.