• Journal of the Korean Mathematical Society
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• v.61 no.3
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• pp.427-444
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• 2024

The matrix completion problem is to predict missing entries of a data matrix using the low-rank approximation of the observed entries. Typical approaches to matrix completion problem often rely on thresholding the singular values of the data matrix. However, these approaches have some limitations. In particular, a discontinuity is present near the thresholding value, and the thresholding value must be manually selected. To overcome these difficulties, we propose a shrinkage and thresholding function that smoothly thresholds the singular values to obtain more accurate and robust estimation of the data matrix. Furthermore, the proposed function is differentiable so that the thresholding values can be adaptively calculated during the iterations using Stein unbiased risk estimate. The experimental results demonstrate that the proposed algorithm yields a more accurate estimation with a faster execution than other matrix completion algorithms in image inpainting problems.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.6
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• pp.276-286
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• 2013

SVD-based deconvolution algorithm has been known as the most effective technique for CT perfusion image analysis. In this algorithm, in order to reduce noise effects, SVD coefficients smaller than a certain threshold are removed. As the truncation threshold, either a fixed value or a variable threshold yielding a predetermined OI (oscillation index) is frequently employed. Each of these two thresholding methods has an advantage to the other either in accuracy or efficiency. In this paper, we propose a Monte Carlo simulation method to evaluate the accuracy of the two methods. An extension of the proposed method is presented as well to measure the effects of image smoothing on the accuracy of the thresholding methods. In this paper, after the simulation method is described, experimental results are presented using both simulated data and real CT images.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.42 no.3
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• pp.604-611
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• 2017

In wireless sensor networks, an energy efficient operation is important since the energy of the sensors is limited. This paper proposes an energy efficient method that reduces a packet generation with Matrix Completion method where sensor value matrix has low-rank and decreases a collision rate and an overhead by transmitting only sensor ID to a time slot corresponding to the sensor value. Computer simulations demonstrates that the proposed method shows 17% of transmission failure and 73% of the packet generation compared to a conventional CSMA/CS. Delay time of transmitting information of the proposed method exhibits 22% of the CSMA/CA and the MSE error after reconstructing sensor values by Singular Value Thresholding(SVT) in Fusion Center is 87% of the CSMA/CA.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2018.06a
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• pp.20-21
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• 2018

행렬의 rank 최소화 기법은 영상 잡음 제거, 행렬 완성(completion), low rank 행렬 복원 등 다양한 영상처리 분야에서 효과적으로 이용되어 왔다. 특히 nuclear norm 을 이용한 low rank 최소화 기법은 convex optimization 을 통하여 대상 행렬의 특이값(singular value)을 thresholding 함으로써 간단하게 low rank 행렬을 얻을 수 있다. 하지만, nuclear norm 을 이용한 low rank 최소화 방법은 행렬의 rank 값을 정확하게 근사하지 못하기 때문에 잡음 제거가 효과적으로 이루어지지 못한다. 본 논문에서는 영상의 잡음을 제거 하기 위해 다중 잡음 제거 영상을 이용하여 유사도가 높은 유사 패치 행렬을 구성하고, 유사 패치 행렬의 rank 를 non-convex function 을 이용하여 최소화시키는 방법을 통해 잡음을 제거하는 방법을 제안한다.

• Proceedings of the Korea Society of Information Technology Applications Conference
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• 2002.11a
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• pp.407-411
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• 2002

Ternary sequences are digital codes consisting of discrete values -1, 0, and 1 only. They are advantageous in that the correlation can be carried out using additions only. Also, they feature an ideal circular autocorrelation function, but in channel characterization tasks, the usual requirement is that the linear autocorrelation function be ideal, i.e., a Kronecker delta function. In this article, we consider two approaches to improving their linear autocorrelation or crosscorrelation properties: one is an inverse filtering method with thresholding, and the other is a singular value decomposition (SVD) method. Both methods are simulated under noisy circumstances. The inverse filtering method resulted in an improvement in peak sidelobe level of about 11 dB at an SNR of 30 dB, and the SVD method showed similar performances, albeit more sensitive to noise depending on the singular value selection strategy.