• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.11
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• pp.1129-1134
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• 2016

This paper suggests a new method of finding regularization parameter for image restoration problems. If the prior information is not available, separate optimization functions for Tikhonov regularization parameter are suggested in the literature such as generalized cross validation and L-curve criterion. In this paper, unified Bayesian interpretation of Tikhonov regularization is introduced and applied to the image restoration problems. The relationship between Tikhonov regularization parameter and Bayesian hyper-parameters is established. Update formular for the regularization parameter using both maximum a posteriori(: MAP) and evidence frameworks is suggested. Experimental results show the effectiveness of the proposed method.

• The Journal of the Korea institute of electronic communication sciences
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• v.17 no.1
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• pp.41-48
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• 2022

This paper presents the unified Bayesian Tikhonov regularization method as a solution to total variation regularization. The integrated method presents a formula for obtaining the regularization parameter by transforming the total variation term into a weighted Tikhonov regularization term. It repeats until the reconstructed image converges to obtain a regularization parameter and a new weighting factor based on it. The experimental results show the effectiveness of the proposed method for the image restoration problem.

• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.1
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• pp.45-52
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• 2016

This paper suggests a new method of finding regularization parameter for image restoration problems. Wiener filter requires priori information such that power spectrums of original image and noise. Constrained least squares restoration also requires knowledge of the noise level. If the prior information is not available, separate optimization functions for Tikhonov regularization parameter are suggested in the literature such as generalized cross validation and L-curve criterion. In this paper, self-regularization method that connects bias term of augmented linear system and smoothing term of Tikhonov regularization is introduced in the frequency domain and applied to the image restoration problems. Experimental results show the effectiveness of the proposed method.

• The Journal of the Korea institute of electronic communication sciences
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• v.15 no.1
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• pp.161-166
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• 2020

This paper suggests an extension of the unified Bayesian Tikhonov regularization method. The unified method establishes the relationship between Tikhonov regularization parameter and Bayesian hyper-parameters, and presents a formula for obtaining the regularization parameter using the maximum posterior probability and the evidence framework. When the dimension of the data matrix is m by n (m >= n), we derive that the total misfit has the range of m ± n instead of m. Thus the search range is extended from one to 2n + 1 integer points. Golden section search rather than linear one is applied to reduce the time. A new benchmark for optimizing relative error and new model selection criteria to target it are suggested. The experimental results show the effectiveness of the proposed method in the image restoration problem.

• Journal of the Korea Computer Graphics Society
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• v.22 no.5
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• pp.1-16
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• 2016

In this paper, we propose and efficient curve reconstruction method based on the classical least-square fitting scheme. Specifically, given planar sample points equipped with normals, we reconstruct the objective curve as the zero set of a hierarchical implicit ZP(Zwart-Powell)-spline that can recover large holes of dataset without loosing the fine details. As regularizers, we adopted two: a Tikhonov regularizer to reduce the singularity of the linear system and a discrete Laplacian operator to smooth out the isocurves. Benchmark tests with quantitative measurements are done and our method shows much better quality than polynomial methods. Compared with the hierarchical bi-quadratic spline for datasets with holes, our method results in compatible quality but with less than 90% computational overhead.