• 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.

• Fire Science and Engineering
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• v.24 no.2
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• pp.114-119
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• 2010

The fire at a Busan indoor shooting range on November 14, 2009 was reconstructed by using a computational fluid dynamics model for fire simulations, in order to investigate the cause of the heavy death toll in a short period of time. Spread of the flame and smoke, and temperature distribution obtained by fire simulation were compared with the results of fire investigation based on the CCTV recordings. The flame and smoke flew out violently through the door into the cafeteria from the shooting range, and the cafeteria was filled with smoke just within 3 seconds followed by the onset of fire. This is consistent with the CCTV recordings. It was confirmed, as a result, that people in the cafeteria did not have enough evacuation time. The computed temperature at the door knob reached about $1400^{\circ}C$, near its melting point.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.10B
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• pp.1111-1116
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• 2009

In this paper, we discuss distortion-tolerant pattern recognition using computational integral imaging reconstruction. Three-dimensional object information is captured by the integral imaging pick-up process. The captured information is numerically reconstructed at arbitrary depth-levels by averaging the corresponding pixels. We apply Fisher linear discriminant analysis combined with principal component analysis to computationally reconstructed images for the distortion-tolerant recognition. Fisher linear discriminant analysis maximizes the discrimination capability between classes and principal component analysis reduces the dimensionality with the minimum mean squared errors between the original and the restored images. The presented methods provide the promising results for the classification of out-of-plane rotated objects.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.9
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• pp.1207-1214
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• 1995

We present an optimized integer cosine transform(OICT) as an alternative approach to the conventional discrete cosine transform(DCT), and its fast computational algorithm. In the actual implementation of the OICT, we have used the techniques similar to those of the orthogonal integer transform(OIT). The normalization factors are approximated to single one while keeping the reconstruction error at the best tolerable level. By obtaining a single normalization factor, both forward and inverse transform are performed using only the integers. However, there are so many sets of integers that are selected in the above manner, the best OICT matrix obtained through value minimizing the Hibert-Schmidt norm and achieving fast computational algorithm. Using matrix decomposing, a fast algorithm for efficient computation of the order-8 OICT is developed, which is minimized to 20 integer multiplications. This enables us to implement a high performance 2-D DCT processor by replacing the floating point operations by the integer number operations. We have also run the simulation to test the performance of the order-8 OICT with the transform efficiency, maximum reducible bits, and mean square error for the Wiener filter. When the results are compared to those of the DCT and OIT, the OICT has out-performed them all. Furthermore, when the conventional DCT coefficients are reduced to 7-bit as those of the OICT, the resulting reconstructed images were critically impaired losing the orthogonal property of the original DCT. However, the 7-bit OICT maintains a zero mean square reconstruction error.

• The KIPS Transactions:PartB
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• v.11B no.3
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• pp.303-308
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• 2004

The Gabor cosine and sine transform can be applied to image and video compression algorithm by representing image frequency components locally The computational complexity of forward and inverse matrix transforms used in the compression and decompression requires O($N^3$)operations. In this paper, the length of basis functions is truncated to produce a sparse basis matrix, and the computational burden of transforms reduces to deal with image compression and reconstruction in a real-time processing. As the length of basis functions is decreased, the truncation effects to the energy of basis functions are examined and the change in various Qualify measures is evaluated. Experiment results show that 11 times fewer multiplication/addition operations are achieved with less than 1% performance change.

• Journal of the Optical Society of Korea
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• v.19 no.3
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• pp.248-254
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• 2015

In this paper we propose an improved version of the computational integral imaging reconstruction (CIIR) for visualizing a partially occluded object by utilizing an image inpainting technique. In the proposed method the elemental images for a partially occluded three-dimensional (3D) object are recorded through the integral imaging pickup process. Next, the depth of occlusion within the elemental images is estimated using two different CIIR methods, and the weight mask pattern for occlusion is generated. After that, we apply our image inpainting technique to the recorded elemental images to fill in the occluding area with reliable data, using information from neighboring pixels. Finally, the inpainted elemental images for the occluded region are reconstructed using the CIIR process. To verify the validity of the proposed system, we carry out preliminary experiments in which faces are the objects. The experimental results reveal that the proposed system can dramatically improve the quality of a reconstructed CIIR image.

• Journal of the Optical Society of Korea
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• v.17 no.6
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• pp.494-499
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• 2013

In this paper, we present an optical encryption and information authentication of 3D objects considering wireless channel characteristics. Using the optical encryption such as double random phase encryption (DRPE) and 3D integral imaging, a 3D scene with encryption can be transmitted. However, the wireless channel causes the noise and fading effects of the 3D transmitted encryption data. When the 3D encrypted data is transmitted via wireless channel, the information may be lost or distorted because there are a lot of factors such as channel noise, propagation fading, and so on. Thus, using digital modulation and maximum likelihood (ML) detection, the noise and fading effects are mitigated, and the encrypted data is estimated well at the receiver. In addition, using computational volumetric reconstruction of integral imaging and advanced correlation filters, the noise effects may be remedied and 3D information may be authenticated. To prove our method, we carry out an optical experiment for sensing 3D information and simulation for optical encryption with DRPE and authentication with a nonlinear correlation filter. To the best of our knowledge, this is the first report on optical encryption and information authentication of 3D objects considering the wireless channel characteristics.

• Current Optics and Photonics
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• v.2 no.2
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• pp.165-171
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• 2018

Fourier ptychographic microscopy (FPM) is a recently proposed computational imaging method that achieves both high resolution (HR) and wide field of view. In the FPM framework, a series of low-resolution (LR) images at different illumination angles is used for high-resolution image reconstruction. On the basis of previous research, image noise can significantly degrade the FPM reconstruction result. Since the captured LR images contain a lot of dark-field images with low signal-to-noise ratio, it is very important to apply a noise-reduction process to the FPM raw dataset. However, the thresholding method commonly used for the FPM data preprocessing cannot separate signals from background noise effectively. In this work, we propose an improved thresholding method that provides a reliable background-noise threshold for noise reduction. Experimental results show that the proposed method is more efficient and robust than the conventional thresholding method.

• 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.

• Korean Journal of Computational Design and Engineering
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• v.15 no.4
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• pp.297-305
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• 2010

Medical image acquisition techniques such as CT and MRI have disadvantages in that the numerous time and efforts are needed. Furthermore, a great amount of radiation exposure is an inherent proberty of the CT imaging technique, a number of side-effects are expected from such method. To improve such conventional methods, a number of novel methods that can obtain 3D medical images from a few X-ray images, such as algebraic reconstruction technique (ART), have been developed. Such methods deform a generic model of the internal body part and fit them into the X-ray images to obtain the 3D model; the initial shape, therefore, affects the entire fitting process in a great deal. From this fact, we propose a novel method that can generate a 3D vertebraic generic model based on the statistical database of CT scans in this study. Moreover, we also discuss a method to generate patient-tailored generic model using the facts obtained from the statistical analysis. To do so, the mesh topologies of CT-scanned 3D vertebra models are modified to be identical to each other, and the database is constructed based on them. Furthermore, from the results of a statistical analysis on the database, the tendency of shape distribution is characterized, and the modeling parameters are extracted. By using these modeling parameters for generating the patient-tailored generic model, the computational speed and accuracy of ART can greatly be improved. Furthermore, although this study only includes an application to the C1 (Atlas) vertebra, the entire framework of our method can be applied to other body parts generally. Therefore, it is expected that the proposed method can benefit the various medical imaging applications.