• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.4
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• pp.301-327
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• 2019

The proper orthogonal decomposition (POD) method for time-dependent problems significantly reduces the computational time as it reduces the original problem to the lower dimensional space. Even a higher degree of reduction can be reached if the solution is smooth in space and time. However, if the solution is discontinuous and the discontinuity is parameterized e.g. with time, the POD approximations are not accurate in the reduced space due to the lack of ability to represent the discontinuous solution as a finite linear combination of smooth bases. In this paper, we propose to post-process the sample solutions and re-initialize the POD approximations to deal with discontinuous solutions and provide accurate approximations while the computational time is reduced. For the post-processing, we use the Gegenbauer reconstruction method. Then we regularize the Gegenbauer reconstruction for the construction of POD bases. With the constructed POD bases, we solve the given PDE in the reduced space. For the POD approximation, we re-initialize the POD solution so that the post-processed sample solution is used as the initial condition at each sampling time. As a proof-of-concept, we solve both one-dimensional linear and nonlinear hyperbolic problems. The numerical results show that the proposed method is efficient and accurate.

• Korean Journal of Digital Imaging in Medicine
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• v.9 no.1
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• pp.21-30
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• 2007

Our objective was to evaluate the CT attenuation coefficient and noise of spatial domain filtering as an alternative to additional image reconstruction using different kernels in abdominal CT. Derived from thin collimated source images was generated using abdomen B10 (very smooth), B20 (smooth), B30 (medium smooth), B40 (medium), B50 (medium sharp), B60 (sharp), B70 (very sharp) and B80 (ultra sharp) kernels. Quantitative CT coefficient and noise measurements provided comparable HU (hounsfield) units in this respect. CT attenuation coefficient (mean HU) values in the abdominal were 60.4$\sim$62.2 HU and noise (7.6$\sim$63.8 HU) in the liver parenchyma. In the stomach a mean (CT attenuation coefficient) of -2.2$\sim$0.8 HU and noise (10.1$\sim$82.4 HU) was measured. Image reconstructed with a convolution kernel led to an increase in noise, whereas the results for CT attenuation coefficient were comparable. Image medications of image sharpness and noise eliminate the need for reconstruction using different kernels in the future. CT images increase the diagnostic accuracy may be controlled by adjusting CT various kernels, which should be adjusted to take into account the kernels of the CT undergoing the examination.

• Journal of Broadcast Engineering
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• v.19 no.2
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• pp.240-249
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• 2014

According to the compressive sensing theory, it is possible to perfectly reconstruct a signal only with a fewer number of measurements than the Nyquist sampling rate if the signal is a sparse signal which satisfies a few related conditions. From practical viewpoint for image applications, it is important to reduce its computational complexity and memory burden required in reconstruction. In this regard, a Block-based Compressive Sensing (BCS) scheme with Smooth Projected Landweber (BCS-SPL) has been already introduced. However, it still has the computational complexity problem in reconstruction. In this paper, we propose a method which modifies its stopping criterion, tolerance, and convergence control to make it converge faster. Experimental results show that the proposed method requires less iterations but achieves better quality of reconstructed image than the conventional BCS-SPL.

• Journal of Biomedical Engineering Research
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• v.36 no.5
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• pp.211-220
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• 2015

Recently, model-based iterative reconstruction (MBIR) has played an important role in transmission tomography by significantly improving the quality of reconstructed images for low-dose scans. MBIR is based on the penalized-likelihood (PL) approach, where the penalty term (also known as the regularizer) stabilizes the unstable likelihood term, thereby suppressing the noise. In this work we further improve MBIR by using a more expressive regularizer which can restore the underlying image more accurately. Here we used a spline regularizer derived from a linear combination of the two-dimensional splines with first- and second-order spatial derivatives and applied it to a non-quadratic convex penalty function. To derive a PL algorithm with the spline regularizer, we used a separable paraboloidal surrogates algorithm for convex optimization. The experimental results demonstrate that our regularization method improves reconstruction accuracy in terms of both regional percentage error and contrast recovery coefficient by restoring smooth edges as well as sharp edges more accurately.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1994.10a
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• pp.719-724
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• 1994

This paper describes a hybrid surface-based method for smooth 3D surface approximation to a sequence of 2D cross sections. The resulting surface is a hybrid G $^{1}$ surface represented by a mesh of triangular and rectangular Bezier patches defined on skinning, branching, or capping regions. Each skinning region is approximated with a closed B_spline surface, which is transformed into a mesh of Bezier patches. Triangular G $^{1}$ surfaces are constructed over brabching and capping regions such that the transitions between each capping regions such that the transitions between each triangular surface and its neighboring skinning surfaces are G $^{1}$ continuous. Since each skinning region is represented by an approximated rectangular C $^{2}$ suface instead of an interpolated trctangular G $^{[-1000]}$ surface, the proposed method can provide more smooth surfaces and realize more efficient data reduction than triangular surfacebased method.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.7
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• pp.138-146
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• 2003

A critical issue in area-based stereo matching lies in selecting a fixed rectangular window size. Previous stereo methods doesn't deal effectively with occluding boundary due to inevitable window-based problems, and so give inaccurate and noisy matching results in areas with steep disparity variations. In this paper, a variable window approach is presented to estimate accurate, detailed and smooth disparities for three-dimensional structure reconstruction. It makes the smoothing of depth discontinuity reduced by evaluating corresponding correlation values and intensity gradient-based similarity in the three-dimensional disparity space. In addition, it investigates maximum connected match candidate points and then devise the novel arbitrarily shaped variable window representative of a same disparity to treat with disparity variations of various structure shapes. We demonstrate the performance of the proposed variable window method with synthetic images, and show how our results improve on those of closely related techniques for accuracy, robustness, matching density and computing speed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.47-56
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• 2015

In this paper, we present an implicit method for reconstructing a 3D solid model from two 2D cross section images. The proposed method is based on the Cahn-Hilliard model for the image inpainting. Image inpainting is the process of reconstructing lost parts of images based on information from neighboring areas. We treat the empty region between the two cross sections as inpainting region and use two cross sections as neighboring information. We initialize the empty region by the linear interpolation. We perform numerical experiments demonstrating that our proposed method can generate a smooth 3D solid model from two cross section data.

• Proceedings of the KOSOMBE Conference
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• v.1994 no.12
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• pp.134-137
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• 1994

In this paper, we describe an approach to ECG data coding based on a fractal theory of iterated contractive transformations defined piecewise. The main characteristic of this approach is that it relies on the assumption that signal redundancy can be efficiently captured and exploited through piecewise self-transformability on a block-wise basis. The variable range size technique is employed to reduce the reconstruction error. Large ranges are used for encoding the smooth waveform to yield high compression efficiency, and the smaller ranges are used for encoding rapidly varying parts of the signal to preserve the signal quality. The suggested algorithm was evaluated using MIT/BIH arrhythmia database. A high compression ratio is achieved with a relatively low reconstruction error.

• Proceedings of the Acoustical Society of Korea Conference
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• spring
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• pp.403-408
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• 1999

In this paper, ultrasonic tomography by the Mode-Converted Rayleigh wave (MCRW) in the back-scattered direction is presented. When a beam with a short pulse and narrow beam width enters a reflector with smooth surface, in general, two major arrivals can be observed in the output waveform: the specular reflection and the radiation of the MCRW from the reflector surface. The time-delay between the two waves is relatively large and thus can be measured easily. This large time-delay is due to the fact that the MCRW is slower than incident wave. In our method, this large time- delay is used for ultrasonic image reconstruction. To effectively detect the MCRW, the arrayed-receiving transducers are circularly arranged around the transmitter. In addition, a deconvolution method is employed to remove specular echo signals for reconstructing the MCRW image.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1998.06a
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• pp.13-16
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• 1998

본 논문에서는 입체 영상 시스템 중 전송단에서의 영상의 입체감 분석을 위한 변이추정 방식에 대해 중점적으로 연구하였다. 변이추정은 기본적으로 MAE(mean absolute error)를 최소가 되도록 하는 동시에 변이를 각 방향에서의 경계값의 크기에 반비례한 정도로 평활화하는 반복적 블록 매칭 방식을 적용하였다. 수신단에서는 복원된 영상과 변이 정보를 이용하여 IVR(Intermediate View Reconstruction)을 수행하였으며, 보간법(interpolation)을 사용하는 동시에 occlusion 영역에서의 좌우 영상중 한 영상에서 외삽법(extrapolation)을 택하였다. 이 알고리즘으로 영상의 smooth 영역에서 일정하게 평활화된 변이를 추정하였고, 경계부분에서는 평활화방식에서 흔히 발생하는 oversmoothing 문제를 해결하였다. 또한 IVR에서는 다른 알고리즘에 비해 영상의 경계 부분을 살리며, occlusion 영역을 잘 보존하는 특성을 보였다.