• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.1
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• pp.1-22
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• 2020

An accurate and efficient gradient estimation method on unstructured grid is presented by proposing a switching process between two Least-Square methods. Diverse test cases show that the gradient estimation by Least-Square methods exhibit better characteristics compared to Green-Gauss approach. Based on the investigation, switching between the two Least-Square methods, whose merit complements each other, is pursued. The condition number of the Least-Square matrix is adopted as the switching criterion, because it shows clear correlation with the gradient error, and it can be easily calculated from the geometric information of the grid. To illustrate switching process on general grid, condition number is analyzed using stencil vectors and trigonometric relations. Then, the threshold of switching criterion is established. Finally, the capability of Switching Weighted Least-Square method is demonstrated through various two- and three-dimensional applications.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.29A no.11
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• pp.14-18
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• 1992

A gradient matrix method in conjunction with the transmission-reflection method to determine the complex permittivity and permeability of a microwave material is presented. This method does not incur the phase ambiguity due to an improper sample length, and is applicable to the measurement of low-loss materials of a half wavelength. A gradient matrix for a coaxial cable sample is derived, and the results are illustrated.

• Proceedings of the IEEK Conference
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• 2007.07a
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• pp.389-390
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• 2007

In this paper, we propose a modified watershed algorithm to obtain exact edge of region. The proposed method adjusts priority at zero-crossing point of gradient in order to make the point of region decision time postponed. We compare the proposed method with a previous method and prove that this method can extract more correct edge of region.

• Journal of Biomedical Engineering Research
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• v.17 no.1
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• pp.93-98
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• 1996

The purpose of this paper is to propose a new localized imaging method of reduced imaging time luting a locally-linear gradient. Since most fast MR(Magnetic Resonance) imaging methods need the whole $\kappa$-space(Spatial frequency space) data corresponding to the whole imaging area, there are limitstions in reducing the minimum imaging time. The imaging method proposed in this paper uses a specially-made gradient coil generating a local ramp-shape field and uniform field outside of the imaging areal Conventional imaging sequences can be used without any RF/gradient pulse sequence modifiestions except the change in the number of encoding steps and the field of view.

• Proceedings of the KOSOMBE Conference
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• v.1990 no.11
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• pp.48-51
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• 1990

A new in vivo high resolution imaging method which is performed with a newly developed three channel surface gradient coil (SGC) is described. The surface gradient coil can produce more than an order of magnitude stronger gradient fields with good linearity within a limited imaging region. To increase the signal to noise ratio (SNR), we have developed an RF coil integrated surface gradient coil set. In this paper, the geometrical structures and characteristics of the proposed surface gradient coil are discussed and experimentally obtained high resolution images ($50\;{\mu}m$ to $100\;{\mu}m$) of a water filled phantom and a human volunteer's knee using the new surface RF coil integrated SGC set are presented for the demonstration of the in vivo high resolution imaging capability of the new imaging method.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.9
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• pp.875-881
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• 2011

This paper describes a new method of estimating the gradient of a function with perturbation and correlation. We impose a known periodic perturbation to the input variable and observe the output of the function in order to obtain much richer and more reliable information. By taking the correlation between the input perturbation and the resultant function outputs, we can determine the gradient of the function. The computation of the correlation does not require derivatives; therefore the gradient can be estimated reliably. Robust estimation of the gradient using perturbation/correlation, which is very effective when an analytical solution is not available, is described. To verify the effectiveness of perturbation/correlation based estimation, the results of gradient estimation are compared with the analytical solutions of an example function. The effects of amplitude of the perturbation and number of samplings in a period are investigated. A minimization of a function with the gradient estimation method is performed.

• 전기의세계
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• v.21 no.3
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• pp.48-52
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• 1972

The application of pontryagin's Maximum Principle to the optimal control eventually leads to the problem of solving the two point boundary value problem. Most of problems have been related to their own special factors, therfore it is very hard to recommend the best method of deriving their optimal solution among various methods, such as iterative Runge Kutta, analog computer, gradient method, finite difference and successive approximation by piece-wise linearization. The gradient method has been applied to the optimal control of two point boundary value problem in the power systems. The most important thing is to set up some objective function of which the initial value is the function of terminal point. The next procedure is to find out any global minimum value from the objective function which is approaching the zero by means of gradient projection. The algorithm required for this approach in the relevant differential equations by use of the Runge Kutta Method for the computation has been established. The usefulness of this approach is also verified by solving some examples in the paper.

• Journal of Korea Society of Digital Industry and Information Management
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• v.9 no.1
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• pp.95-102
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• 2013

This paper covers nulling algorithm. In this algorithm, we assume that nulling points are already known. In general, nulling algorithm using matrix equation was utilized. But, this algorithm is pointed out that computational complexity is disadvantage. So, we choose gradient method to reduce the computational complexity. In order to further reduce the computational complexity, we propose approximate gradient method using characteristic of trigonometric functions. The proposed method has same performance compared with conventional method while having half the amount of computation when the number of antenna and nulling point are 20 and 1, respectively. In addition, we could virtually eliminate the trigonometric functions arithmetic. Trigonometric functions arithmetic cause a big problem in actual implementation like FPGA processor(Field Programmable gate array). By utilizing the above algorithm in a multi-cell environment, beamforming gain can be obtained and interference can be reduced at same time. By the above results, the algorithm can show excellent performance in the cell boundary.

• Journal of Biomedical Engineering Research
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• v.28 no.6
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• pp.817-824
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• 2007

Tractography using Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) is a method to determine the architecture of axonal fibers in the central nervous system by computing the direction of the principal eigenvector in the white matter of the brain. However, the fiber tracking methods suffer from the noise included in the diffusion tensor images that affects the determination of the principal eigenvector. As the fiber tracking progresses, the accumulated error creates a large deviation between the calculated fiber and the real fiber. This problem of the DT-MRI tractography is known mathematically as the ill-posed problem which means that tractography is very sensitive to perturbations by noise. To reduce the noise in DT-MRI measurements, a tensor-valued median filter which is reported to be denoising and structure-preserving in fiber tracking, is applied in the tractography. In this paper, we proposed the modified gradient descent method which converges fast and accurately to the optimal tensor-valued median filter by changing the step size. In addition, the performance of the modified gradient descent method is compared with others. We used the synthetic image which consists of 45 degree principal eigenvectors and the corticospinal tract. For the synthetic image, the proposed method achieved 4.66%, 16.66% and 15.08% less error than the conventional gradient descent method for error measures AE, AAE, AFA respectively. For the corticospinal tract, at iteration number ten the proposed method achieved 3.78%, 25.71 % and 11.54% less error than the conventional gradient descent method for error measures AE, AAE, AFA respectively.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2021.05a
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• pp.2-4
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• 2021

In a distributed machine learning system, sharing gradients was considered safe because it did not share original training data. However, recent studies found that malicious attacker could completely restore the original training data from shared gradients. Gradient Leakage Attack is a technique that restoring original training data by exploiting theses vulnerability. In this study, we present the image transformation method based on Discrete Cosine Transform to defend against the Gradient Leakage Attack on the federated learning setting, which training in local devices and sharing gradients to the server. Experiment shows that our image transformation method cannot be completely restored the original data from Gradient Leakage Attack.