• Journal of Information Processing Systems
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• 제19권3호
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• pp.275-288
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• 2023

Many image edge details are easily lost in the image denoising process, and the smooth image regions are prone to produce jagged. In this paper, we propose a wavelet-based image global k- singular value decomposition variational method to remove image noise. A layer of wavelet decomposition is applied to the noisy image first. Then, the image global k-singular value decomposition (IGK-SVD) method is used to remove the random noise of low-frequency components. Furthermore, a constructed variational denoising method (VDM) removes the random noise in the high-frequency component. Finally, the denoised image is obtained by wavelet reconstruction. The experimental results show that the proposed method's peak signal-to-noise ratio (PSNR) value is higher than other methods, and its structural similarity (SSIM) value is closer to one, indicating that the proposed method can effectively suppress image noise while retaining more image edge details. The denoised image has better denoising effects.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.131-164
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• 2024

In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite family of τ-demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertial extrapolation steps and adaptive non-monotonic step sizes. Under some appropriate conditions that are imposed on the parameters, the weak and linear convergence results of the proposed iterative scheme are established. Furthermore, we present some numerical examples and application of our proposed methods in comparison with other existing iterative methods. In order to show the practical applicability of our method to real word problems, we show that our algorithm has better restoration efficiency than many well known methods in image restoration problem. Our proposed iterative method generalizes and extends many existing methods in the literature.

• Communications for Statistical Applications and Methods
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• 제30권6호
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• pp.589-603
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• 2023

Deep generative models target to infer the underlying true data distribution, and it leads to a huge success in generating fake-but-realistic data. Regarding such a perspective, the data attributes can be a crucial factor in the data generation process since non-existent counterfactual samples can be generated by altering certain factors. For example, we can generate new portrait images by flipping the gender attribute or altering the hair color attributes. This paper proposes counterfactual disentangled variational autoencoder generative adversarial networks (CDVAE-GAN), specialized for data attribute level counterfactual data generation. The structure of the proposed CDVAE-GAN consists of variational autoencoders and generative adversarial networks. Specifically, we adopt a Gaussian variational autoencoder to extract low-dimensional disentangled data features and auxiliary Bernoulli latent variables to model the data attributes separately. Also, we utilize a generative adversarial network to generate data with high fidelity. By enjoying the benefits of the variational autoencoder with the additional Bernoulli latent variables and the generative adversarial network, the proposed CDVAE-GAN can control the data attributes, and it enables producing counterfactual data. Our experimental result on the CelebA dataset qualitatively shows that the generated samples from CDVAE-GAN are realistic. Also, the quantitative results support that the proposed model can produce data that can deceive other machine learning classifiers with the altered data attributes.

• Nuclear Engineering and Technology
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• 제55권6호
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• pp.2172-2194
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• 2023

A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are proposed to accelerate the within-group and power iterations. Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (k_eff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time-step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2-3.

• 한국음향학회지
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• 제41권3호
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• pp.351-358
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• 2022

심층 생성 모델의 일종인 Generative Adversarial Network(GAN)과 Variational AutoEncoder(VAE)는 비병렬 학습 데이터를 사용한 음성 변환에 새로운 방법론을 제시하고 있다. 특히, Conditional Cycle-Consistent Generative Adversarial Network(CC-GAN)과 Cycle-Consistent Variational AutoEncoder(CycleVAE)는 다수 화자 사이의 음성 변환에 우수한 성능을 보이고 있다. 그러나, CC-GAN과 CycleVAE는 비교적 적은 수의 화자를 대상으로 연구가 진행되어왔다. 본 논문에서는 100 명의 한국어 화자 데이터를 사용하여 CC-GAN과 CycleVAE의 음성 변환 성능과 확장 가능성을 실험적으로 분석하였다. 실험 결과 소규모 화자의 경우 CC-GAN이 Mel-Cepstral Distortion(MCD) 기준으로 4.5 % 우수한 성능을 보이지만 대규모 화자의 경우 CycleVAE가 제한된 학습 시간 안에 12.7 % 우수한 성능을 보였다.

• 대한수학회보
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• 제41권1호
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• pp.1-11
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• 2004

In this paper, we suggest and analyze some new classes of three step iterative algorithms for solving generalized quasivariational inclusions by using the properties of proximal maps. Our results include the Ishikawa, Mann iterations for solving variational inclusions(inequalities) as special cases. The results obtained in this paper represent an improvement and significant refinement of previously known results [3, 5-8, 10, 14-18].

• 대한수학회지
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• 제47권4호
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• pp.845-860
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• 2010

In this paper, using the Nehari manifold approach and some variational techniques, we discuss the multiplicity of positive solutions for the p(x)-Laplacian problems with non-negative weight functions and prove that an elliptic equation has at least two positive solutions.

• Structural Engineering and Mechanics
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• 제65권4호
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• pp.409-413
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• 2018

In this paper, He's Variational Approach (VA) is used to solve high nonlinear vibration equations. The proposed approach leads us to high accurate solution compared with other numerical methods. It has been established that this method works very well for whole range of initial amplitudes. The method is sufficient for both linear and nonlinear engineering problems. The accuracy of this method is shown graphically and the results tabulated and results compared with numerical solutions.

• 대한수학회지
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• 제34권1호
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• pp.1-12
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• 1997

Complementaity problem theory developed by Lemke [10], Cottle and Dantzig [8] and others in the early 1960s and thereafter, has numerous applications in diverse fields of mathematical and engineering sciences. And it is closely related to variational inquality theory and fixed point theory. Recently, fixed point methods for the solving of nonlinear complementarity problems were considered by Noor et al. [11, 12]. Also complementarity problems related to variational inequality problems were investigated by Chang [1], Cottle [7] and others.

• 대한수학회보
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• 제51권5호
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• pp.1433-1451
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• 2014

In this paper we study the existence of multiple periodic solutions of second-order ordinary differential equations. New results of multiplicity of periodic solutions are obtained when the nonlinearity may cross multiple consecutive eigenvalues. The arguments are proceeded by a combination of variational and degree theoretic methods.