• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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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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• v.28 no.5_6
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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.

• Progress in Medical Physics
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• v.32 no.4
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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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.10
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• pp.1961-1966
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• 2016

Compressive sensing has proved that a signal can be restored from less samples than the Nyquist rate. Reducing the required data rate is essential for a variety of fields including compression, transmission, and storage. It has been made lots of attempt to apply the compressive sensing theory into data intensive fields, such as image processing which needs to cover 4K and 8K pictures. In this paper, an image acquisition algorithm based on compressive sensing is proposed. It combines DCT, which can compact the energy of a image into a few coefficients, and the Noiselet transform, which is incoherent with DCT. The DCT coefficients represent the coarse structure of the images while the Noiselet information holds the fine details. Performance experiments with several images show that the proposed image acquisition algorithm not only outperforms the previous results, but also improves the reconstruction quality faster as the number of measurements increases.