• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.3
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• pp.175-202
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• 2016

Ultrasound imaging is a widely used tool for visualizing human body's internal organs and quantifying clinical parameters. Due to its advantages such as safety, non-invasiveness, portability, low cost and real-time 2D/3D imaging, diagnostic ultrasound industry has steadily grown. Since the technology advancements such as digital beam-forming, Doppler ultrasound, real-time 3D imaging and automated diagnosis techniques, there are still a lot of demands for image quality improvement, faster and accurate imaging, 3D color Doppler imaging and advanced functional imaging modes. In order to satisfy those demands, mathematics should be used properly and effectively in ultrasound imaging. Mathematics has been used commonly as mathematical modelling, numerical solutions and visualization, combined with science and engineering. In this article, we describe a brief history of ultrasound imaging, its basic principle, its applications in obstetrics/gynecology, cardiology and radiology, domestic-industrial products, contributions of mathematics and challenging issues in ultrasound imaging.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.519-541
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• 2001

Magnetic Resonance Electrical Impedance Tomography(MREIT) is a new medical imaging technique for the cross-sectional conductivity distribution of a human body using both EIT(Electrical Impedance Tomography) and MRI(Magnetic Resonance Imaging) system. MREIT system was designed to enhance EIT imaging system which has inherent low sensitivity of boundary measurements to any changes of internal tissue conductivity values. MREIT utilizes a recent CDI (Current Density Imaging) technique of measuring the internal current density by means of MRI technique. In this paper, a mathematical modeling for MREIT and image reconstruction method called the alternating J-substitution algorithm are presented. Computer simulations show that the alternating J-substitution algorithm provides accurate high-resolution conductivity images.

• Korean Journal of Radiology
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• v.22 no.7
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• pp.1194-1202
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• 2021

Objective: To investigate the age-dependent changes in regional cerebral blood flow (CBF) in healthy adults by fitting mathematical models to imaging data. Materials and Methods: In this prospective study, 90 healthy adults underwent pseudo-continuous arterial spin labeling imaging of the brain. Regional CBF values were extracted from the arterial spin labeling images of each subject. Multivariable regression with the Akaike information criterion, link test, and F test (Ramsey's regression equation specification error test) was performed for 7 models in every brain region to determine the best mathematical model for fitting the relationship between CBF and age. Results: Of all 87 brain regions, 68 brain regions were best fitted by cubic models, 9 brain regions were best fitted by quadratic models, and 10 brain regions were best fitted by linear models. In most brain regions (global gray matter and the other 65 brain regions), CBF decreased nonlinearly with aging, and the rate of CBF reduction decreased with aging, gradually approaching 0 after approximately 60. CBF in some regions of the frontal, parietal, and occipital lobes increased nonlinearly with aging before age 30, approximately, and decreased nonlinearly with aging for the rest of life. Conclusion: In adults, the age-related perfusion patterns in most brain regions were best fitted by the cubic models, and age-dependent CBF changes were nonlinear.

• Current Optics and Photonics
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• v.7 no.5
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• pp.518-528
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• 2023

As an effective means of remotely detecting the spectral information of the object, the spectral calibration for the Savart polarization interference imaging spectrometer (SPIIS) is a basis and prerequisite of information quantification, and its experimental calibration scheme is firstly proposed in this paper. In order to evaluate the accuracy of the spectral information acquisition, the linear interpolation, cubic spline interpolation, and piecewise cubic interpolation algorithms are adopted, and the precision of the quadratic polynomial fitting is the highest, whose fitting error is better than 5.8642 nm in the wavelength range of [500 nm, 820 nm]. Besides, the inversed value of the spectral resolution for the monochromatic light is greater than the theoretical value, and the deviation between them becomes larger with the wavelength increasing, which is mainly caused by the structural design of the SPIIS, together with the rationality of the spectral restoration algorithm and the selection of the maximum optical path difference (OPD). This work demonstrates that the SPIIS has achieved high performance assuring the feasibility of its practical use in various fields.

• Current Optics and Photonics
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• v.7 no.5
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• pp.545-556
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• 2023

This paper introduces volume-sharing multi-aperture imaging (VMAI), a potential approach proposed for volume reduction in space-borne imagers, with the aim of achieving high-resolution ground spatial imagery using deep learning methods, with reduced volume compared to conventional approaches. As an intermediate step in the VMAI payload development, we present a phase-1 design targeting a 1-meter ground sampling distance (GSD) at 500 km altitude. Although its optical imaging capability does not surpass conventional approaches, it remains attractive for specific applications on small satellite platforms, particularly surveillance missions. The design integrates one wide-field and three narrow-field cameras with volume sharing and no optical interference. Capturing independent images from the four cameras, the payload emulates a large circular aperture to address diffraction and synthesizes high-resolution images using deep learning. Computational simulations validated the VMAI approach, while addressing challenges like lower signal-to-noise (SNR) values resulting from aperture segmentation. Future work will focus on further reducing the volume and refining SNR management.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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• pp.161-197
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• 2020

Total variation minimization is standard in mathematical imaging and there have been numerous researches over the last decades. In order to process large-scale images in real-time, it is essential to design parallel algorithms that utilize distributed memory computers efficiently. The aim of this paper is to illustrate recent advances of domain decomposition methods for total variation minimization as parallel algorithms. Domain decomposition methods are suitable for parallel computation since they solve a large-scale problem by dividing it into smaller problems and treating them in parallel, and they already have been widely used in structural mechanics. Differently from problems arising in structural mechanics, energy functionals of total variation minimization problems are in general nonlinear, nonsmooth, and nonseparable. Hence, designing efficient domain decomposition methods for total variation minimization is a quite challenging issue. We describe various existing approaches on domain decomposition methods for total variation minimization in a unified view. We address how the direction of research on the subject has changed over the past few years, and suggest several interesting topics for further research.

• Journal of Biosystems Engineering
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• v.43 no.4
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• pp.369-378
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• 2018

Purpose: The aim of this study was to construct a saponin content-predicting model using shortwave infrared imaging spectroscopy. Methods: The experiment used a shortwave imaging spectrometer and ENVI spectral acquisition software sampling a spectrum of 910 nm-2500 nm. The corresponding preprocessing and mathematical modeling analysis was performed by Unscrambler 9.7 software to establish a ginsenoside nondestructive spectral testing prediction model. Results: The optimal preprocessing method was determined to be a standard normal variable transformation combined with the second-order differential method. The coefficient of determination, $R^2$, of the mathematical model established by the partial least squares method was found to be 0.9999, while the root mean squared error of prediction, RMSEP, was found to be 0.0043, and root mean squared error of calibration, RMSEC, was 0.0041. The residuals of the majority of the samples used for the prediction were between ${\pm}1$. Conclusion: The experiment showed that the predicted model featured a high correlation with real values and a good prediction result, such that this technique can be appropriately applied for the nondestructive testing of ginseng quality.

• Journal of the Optical Society of Korea
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• v.5 no.3
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• pp.90-92
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• 2001

Direct and inverse mathematical operators of stereo transformation (stereo operators) are studied in this paper. The stereo operators install a one-to-one correspondence between three dimensional coordinates of any point in space and the stereo coordinates which can be displayed on the screen under the given conditions, i.e. stereo vision base and the position of viewer. The stereo operators can be applied to the analyses of stereoscopic image distortions when the stereo vision base and the position of viewer are changed.

• Journal of information and communication convergence engineering
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• v.8 no.5
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• pp.581-585
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• 2010

A grid was sandwiched between two cascaded imaging plates. Using a fan-beam X-ray tube and a single exposure scheme, the two imaging plates, respectively, recorded grid-less and grid type information of the object. Referring to the mathematical model of the Grid-less and grid technique, it was explained that the collected components whereas that of imaging plates with grid was of high together with large scattered components whereas that of imaging plate with grid was of low and suppressed scattered components. Based on this assumption and using a Gaussian convolution kernel representing the effect of scattering, the related data of the imaging plates were simulated by computer. These observed data were then employed in the developed post-processing estimation and restoration (kalman-filter) algorithms and accordingly, the quality of the resultant image was effectively improved.

• Current Optics and Photonics
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• v.8 no.2
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• pp.183-191
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• 2024

High-resolution retinal imaging based on adaptive optics (AO) is important for early diagnosis related to retinal diseases. However, in practical applications, closed-loop AO correction takes a relatively long time, and traditional open-loop correction methods have low accuracy in correction, leading to unsatisfactory imaging results. In this paper, a SH-U-net-based open-loop AO wavefront correction method is presented for a retinal AO imaging system. The SH-U-net builds a mathematical model of the entire AO system through data training, and the Root mean square (RMS) of the distorted wavefront is 0.08λ after correction in the simulation. Furthermore, it has been validated in experiments. The method improves the accuracy of wavefront correction and shortens the correction time.