• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권2호
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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.

• 한국의학물리학회지:의학물리
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• 제23권4호
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• pp.252-260
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• 2012

최근 Computed tomography (CT) 조사선량의 인체에 대한 부정적 영향이 부각됨에 따라 선량을 줄이는 연구가 활발히 진행되고 있고, 이로 인하여 소 동물에 관한 연구는 점점 임상전의 연구로서 필수적으로 여겨지고 있다. 최근에는 피폭 선량을 줄일 수 있는 방법으로서 이론적으로 투영 데이터가 충분하지 않을 때 정확하게 영상을 재구성 하는 것이 가능한 Total Variation (TV) minimization 알고리즘이 각광받고 있다. 이에 본 연구에서는 micro-CT (DRGem, Harmony80H series, Korea) 시스템에서 획득한 적은 수의 투영 데이터를 가지고 TV minimization에 기초한 반복적 영상 재구성 알고리즘과 기존의 Feldkamp-Davis-Kress (FDK) 알고리즘을 사용하여 영상을 재구성하고 두 알고리즘의 영상 화질을 비교 및 평가하였다. TV minimization 알고리즘의 효과를 평가하기 위해서, 먼저 서로 다른 농도의 조영제, 물, 공기가 들어있는 원통형 팬톰을 제작하였고, micro-CT를 사용하여 영상을 획득하였다. Tube와 검출기 일회전 당 최대 400개의 투영 데이터를 획득할 수 있으며, TV minimization 알고리즘의 영상 복원의 정도를 평가하기 위해서 20, 50, 90, 180장의 적은 투영 데이터를 추출하였다. 영상 비교평가를 위한 참고 영상(FDK-reference 영상)은 마찬가지로 400개의 투영데이터를 이용하여 FDK 알고리즘으로 재구성하였고, 20, 50, 90, 180장의 투영데이터를 가지고 TV minimization 알고리즘, FDK 알고리즘을 이용하여 재구성한 영상과 FDK-reference 영상의 프로파일, Contrast-to-noise ratio (CNR), Universal quality index(UQI)를 각각 비교평가 하였다. 또한, 소 동물에 관한 연구를 위하여 mouse 영상에 관하여 프로파일과 UQI를 분석하여 비교평가 하였다. 결과적으로 90개의 투영데이터를 사용하여 재구성한 원통형 팬톰 영상을 분석하였을 때, TV minimization 영상(TV-90) 및 FDK 영상(FDK-90)의 CNR과 UQI를 비교하였을 때 FDK-90보다 TV-90에서 CNR이 0.21, UQI가 0.18 증가하였다. 원통형 팬톰 영상과 같은 조건에서 mouse 영상을 사용하였을 때, UQI는 FDK-90보다 TV-90에서 0.08 증가하였다. 결론적으로 본 연구결과는 기존의 micro-CT의 투영 데이터의 사분의 일이 되는 투영데이터를 사용하여 영상을 재구성하여 비교평가 한 결과 투영영상 데이터의 수가 제한되는 경우에 FDK 알고리즘보다 TV minimization 알고리즘이 X-ray 조사시간을 줄임으로서 피폭선량을 줄이는데 효과적으로 기여할 것으로 기대된다. 특히, 조사시간의 단축은 물체의 움직임으로 인한 영상 화질의 저하를 감소시키는데 기여할 것으로 사려된다.

• 한국의학물리학회지:의학물리
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• 제29권4호
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• pp.150-156
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• 2018

This study aims to develop an improved Feldkamp-Davis-Kress (FDK) reconstruction algorithm using anisotropic total variation (ATV) minimization to enhance the image quality of low-dose cone-beam computed tomography (CBCT). The algorithm first applies a filter that integrates the Shepp-Logan filter into a cosine window function on all projections for impulse noise removal. A total variation objective function with anisotropic penalty is then minimized to enhance the difference between the real structure and noise using the steepest gradient descent optimization with adaptive step sizes. The preserving parameter to adjust the separation between the noise-free and noisy areas is determined by calculating the cumulative distribution function of the gradient magnitude of the filtered image obtained by the application of the filtering operation on each projection. With these minimized ATV projections, voxel-driven backprojection is finally performed to generate the reconstructed images. The performance of the proposed algorithm was evaluated with the catphan503 phantom dataset acquired with the use of a low-dose protocol. Qualitative and quantitative analyses showed that the proposed ATV minimization provides enhanced CBCT reconstruction images compared with those generated by the conventional FDK algorithm, with a higher contrast-to-noise ratio (CNR), lower root-mean-square-error, and higher correlation. The proposed algorithm not only leads to a potential imaging dose reduction in repeated CBCT scans via lower mA levels, but also elicits high CNR values by removing noisy corrupted areas and by avoiding the heavy penalization of striking features.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권3호
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• pp.156-184
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• 2022

In this article, we propose a novel variational model for restoring color images corrupted by mixed multiplicative Gamma noise and additive Gaussian noise. The model involves a data-fidelity term that characterizes the mixed noise as an infimal convolution of two noise distributions and the saturation-value total variation (SVTV) regularization. The data-fidelity term facilitates suitable separation of the multiplicative Gamma and Gaussian noise components, promoting simultaneous elimination of the mixed noise. Furthermore, the SVTV regularization enables adequate denoising of homogeneous regions, while maintaining edges and details and diminishing the color artifacts induced by noise. To solve the proposed nonconvex model, we exploit an alternating minimization approach, and then the alternating direction method of multipliers is adopted for solving subproblems. This contributes to an efficient iterative algorithm. The experimental results demonstrate the superior performance of the proposed model compared to other existing or related models, with regard to visual inspection and image quality measurements.

• 한국정보통신학회논문지
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• 제10권12호
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• pp.2271-2282
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• 2006

본 논문은 총 변화량 최소화와 같은 편 미분방정식을 기본으로 한 영상 복원에 제기된 이슈에 관련된다. 총 변화량 최소화방법과 같은 평활화 연산자의 과도한 분산과 계단화와 같은 문제점들에 대하여 특별히 연구한다. 계단화와 과도한 분산을 방지하기 위하여 대수시스템에서의 축척과 비 오목형 최소화 기법이 각각 고려된다. 더군다나 에지를 좀더 잘 보존하기 위한 다양한 제약 매개변수가 소개된다. 제안된 알고리즘이 소음제거에 있어서 효율적이고 합리적임이 수학적으로 증명되며 다양한 실험 결과가 보여진다.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2000년도 춘계공동학술대회 논문집
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• pp.469-472
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• 2000

Replacement policy of a degradation of system is investigated by incorporating the loss function defined by the deviation of the value of quality characteristic from its target value, which determines the loss cost . Two cost minimization problems are formulated : 1)determination of an optimal inspection period given the state for the replacement and 2)determination of an optimal state for replacement under fixed inspect ion period. Simulation analysis is performed to observe the variation of total cost with respect to the variation of the parameters of loss function, inspection cost, respectively. As a result, parameters of loss function are seen to be the most sensitive to the total cost. On the contrary, inspect ion cost is observed to be insensitive.

• 한국신뢰성학회지:신뢰성응용연구
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• 제1권1호
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• pp.35-46
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• 2001

Replacement policy of a degradation system is investigated by incorporating the loss function. Loss function is defined by the deviation of the value of quality characteristic from its target value, which determines the loss cost. Cost function is comprised of the inspection cost, replacement cost and loss cost. Two cost minimization problems are formulated : 1)determination of an optimal inspection period given the state for the replacement and 2)determination of an optimal state for replacement under fixed inspection period. Simulation analysis is performed to observe the variation of total cost with respect to the variation of the parameters of loss function and inspection cost, respectively As a result, parameters of loss function are seen to be the most sensitive to the total cost. On the contrary, inspection cost is observed to be insensitive. This study can be applied to the replacement policy of a degradation system which has to produce the quality critical product.

• 한국지하수토양환경학회:학술대회논문집
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• 한국지하수토양환경학회 2003년도 추계학술발표회
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• pp.217-221
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• 2003

Variation of decision variables for optimal remediation using the pump-and-treat method is examined to estimate the effect of the degree of concentration constraint. Simulation-optimization method using genetic algorithm is applied to minimize the total pumping volume. In total volume minimization strategy, the remediation time increases rapidly prior to significant increase in pumping rates. When the concentration constraint is set severer, the more wells are required and the well on the down-gradient direction from the plume hot-spot gives more efficient remediation performance than that on the hot-spot position. These results show that the more profitable strategy for remediation can be achieved by increasing the required remediation time than raising the pumping rate until the time reaches a certain limitation level. So, the remediation time has to be considered as one of the essential decision variables fer optimal remediation design.

• IEIE Transactions on Smart Processing and Computing
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• 제4권6호
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• pp.413-421
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• 2015

Regularized Blind Deconvolution is a problem applicable in degraded images in order to bring the original image out of blur. Multichannel blind Deconvolution considered as an optimization problem. Each step in the optimization is considered as variable splitting problem using an algorithm called Alternating Minimization Algorithm. Each Step in the Variable splitting undergoes Augmented Lagrangian method (ALM) / Bregman Iterative method. Regularization is used where an ill posed problem converted into a well posed problem. Two well known regularizers are Tikhonov class and Total Variation (TV) / L2 model. TV can be isotropic and anisotropic, where isotropic for L2 norm and anisotropic for L1 norm. Based on many probabilistic model and Fourier Transforms Image deblurring can be solved. Here in this paper to improve the performance, we have used an adaptive regularization filtering and isotropic TV model Lp norm. Image deblurring is applicable in the areas such as medical image sensing, astrophotography, traffic signal monitoring, remote sensors, case investigation and even images that are taken using a digital camera / mobile cameras.

• Journal of the Optical Society of Korea
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• 제20권6호
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• pp.752-761
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• 2016

Hyperspectral images are often contaminated with stripe noise, which severely degrades the imaging quality and the precision of the subsequent processing. In this paper, a variational model is proposed by employing spectral-spatial adaptive unidirectional variation and a sparse representation. Unlike traditional methods, we exploit the spectral correction and remove stripes in different bands and different regions adaptively, instead of selecting parameters band by band. The regularization strength adapts to the spectrally varying stripe intensities and the spatially varying texture information. Spectral correlation is exploited via dictionary learning in the sparse representation framework to prevent spectral distortion. Moreover, the minimization problem, which contains two unsmooth and inseparable $l_1$-norm terms, is optimized by the split Bregman approach. Experimental results, on datasets from several imaging systems, demonstrate that the proposed method can remove stripe noise effectively and adaptively, as well as preserve original detail information.