• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.137-147
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• 2001

Nonconvex Quadratic Optimization Problems (QOP) are solved approximately by SDP (semidefinite programming) relaxation and SOCP (second order cone programmming) relaxation. Nonconvex QOPs with special structures can be solved exactly by SDP and SOCP. We propose a method to formulate general nonconvex QOPs into the special form of the QOP, which can provide a way to find more accurate solutions. Numerical results are shown to illustrate advantages of the proposed method.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1395-1408
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• 2010

In this paper, a pair of Wolfe type second-order nondifferentiable multiobjective symmetric dual program over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order (F, $\alpha$, $\rho$, d)-convexity assumptions. An illustration is given to show that second-order (F, $\alpha$, $\rho$, d)-convex functions are generalization of second-order F-convex functions. Several known results including many recent works are obtained as special cases.

• 한국의학물리학회지:의학물리
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• 제32권4호
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• pp.165-171
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• 2021

Purpose: This study aimed to evaluate the effect of collimator width on effective atomic number (EAN), relative electron density (RED), and stopping power ratio (SPR) measured by dual-layer dual-energy computed tomography (DL-DECT). Methods: CIRS electron density calibration phantoms with two different arrangements of material plugs were scanned by DL-DECT with two different collimator widths. The first phantom included two dense bone plugs, while the second excluded dense bone plugs. The collimator widths selected were 64 mm×0.625 mm for wider collimators and 16 mm×0.625 mm for narrow collimators. The scanning parameters were 120 kVp, 0.33 second gantry rotation, 3 mm slice thickness, B reconstruction filter, and spectral level 4. An image analysis portal system provided by a computed tomography (CT) manufacturer was used to derive the EAN and RED of the phantoms from the combination of low energy and high energy CT images. The EAN and RED were compared between the images scanned using the two different collimation widths. Results: The CT images with the wider collimation width generated more severe artifacts, particularly with high-density material (i.e., dense bone). RED and EAN for tissues (excluding lung and bones) with the wider collimation width showed significant relative differences compared to the theoretical value (4.5% for RED and 20.6% for EAN), while those with the narrow collimation width were closer to the theoretical value of each material (2.2% for EAN and 2.3% for RED). Scanning with narrow collimation width increased the accuracy of SPR estimation even with high-density bone plugs in the phantom. Conclusions: The effect of CT collimation width on EAN, RED, and SPR measured by DL-DECT was evaluated. In order to improve the accuracy of the measured EAN, RED, and SPR by DL-DECT, CT scanning should be performed using narrow collimation widths.

• 한국정보통신학회논문지
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• 제20권10호
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• pp.1961-1966
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• 2016

최근 활발히 연구되고 있는 압축센싱 (compressive sensing) 이론에 따르면 나이퀴스트 주파수보다 적은 샘플율으로도 원 신호를 충실히 복원할 수 있음이 알려져 있다. 압축, 전송, 저장 등의 여러 분야에서 압축센싱 방법을 적용하려는 시도가 꾸준히 이어지고 있다. 특히 4K, 8K 등으로 요구되는 화소수가 제곱의 형태로 증가되는 영상처리 분야에서는 압축센싱에 기대하는 바가 크다. 본 논문에서는 압축센싱 기법을 적용한 영상의 획득 알고리듬을 제안한다. 영상의 일반적인 특성을 활용하여 높은 에너지 압축 성능을 가지는 DCT와 저상관도의 특성을 갖는 Noiselet 변환을 결합하여 영상 획득 과정을 구성한다. 원 영상은 2차 콘 프로그램 (SOCP)을 풀어 복원할 수 있다. 여러 영상에 대해 획득 및 복원 성능을 측정 및 비교하였으며 제안된 알고리듬이 우수한 복원 성능을 보임을 알 수 있다.