• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.9
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• pp.1759-1771
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• 1994

We proposed the iterative image restoration method based on the method of steepest descent with a regularization constraint for restoring the noisy motion-blurred images. The conventional method proposed by Jan Biemond et al, had drawback to amplify the additive noise and make ringing effects in the restored images by determining the value of regularization parameter experimentally from the degraded image to be restored without considering local information of the restored one. The method we proposed had a merit to suppress the noise amplification and restoration error by using the regularization parameter which estimate the value of it adaptively from each pixels of the image being restored in order to reduce the noise amplification and ringing effects efficiently. Also we proposed the termination rule to stop the iteration automatically when restored results approach into or diverse from the original solution in satisfaction. Through the experiments, proposed method showed better result not only in a MSE of 196 and 453 but also in the suppression of the noise amplification in the flat region compared with those proposed by Jan Biemond et al. of which MSE of 216 and 467 respectively when we used 'Lean' and 'Jaguar' images as original images.

• 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.

• The KIPS Transactions:PartB
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• v.16B no.1
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• pp.1-6
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• 2009

It is very difficult to restore the images degraded by motion blur and additive noise. In conventional methods, regularization usually applies to all the images without considering local characteristics of the images. As a result, ringing artifacts appear in the edge regions and noise amplification is in the flat regions, as well. To solve these problems, we propose an adaptive iterative regularization method, using the way of regularization operator considering edge directions. In addition, we suggest an adaptive regularization parameter and an relaxation parameter. In conclusion, We have verified that the new method shows the suppression of the noise amplification in the flat regions, also does less ringing artifacts in the edge regions. Furthermore, it offers better images and improves the quality of ISNR, comparing with those of conventional methods.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.11C
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• pp.1073-1078
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• 2007

In this paper, we propose an iterative mixed norm image restoration algorithm using multi regularization parameters. A functional which combines the regularized $l_2$ norm functional and the regularized $l_4$ norm functional is proposed to efficiently remove arbitrary noise. The smoothness of each functional is determined by the regularization parameters. Also, a regularization parameter is used to determine the relative importance between the regularized $l_2$ norm functional and the regularized $l_4$ norm functional using kurtosis. An iterative algorithm is utilized for obtaining a solution and its convergence is analyzed. Experimental results demonstrate the capability of the proposed algorithm.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.59-71
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• 2016

To obtain more accurate approximation of the true images in the deblurring problems, the weighted global generalized cross validation(GCV) function to the inverse problem with multiple right-hand sides is suggested as an efficient way to determine the regularization parameter. We analyze the experimental results for many test problems and was able to obtain the globally useful range of the weight when the preconditioned global conjugate gradient linear least squares(Gl-CGLS) method with the weighted global GCV function is applied.

• Korean Journal of Remote Sensing
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• v.28 no.5
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• pp.561-571
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• 2012

The MTF(Modulation Transfer Function) is one of quality assesment factors to evaluate the performance of satellite images. Image restoration is needed for MTF compensation, but it is an ill-posed problem and doesn't have a certain solution. Lots of filters were suggested to solve this problem, such as Inverse Filter(IF), Pseudo Inverse Filter(PIF) and Wiener Filter(WF). The most commonly used filter is a WF, but it has a limitation on distinguishing signal and noise. The L-curve-based Modified Wiener Filter(MWF) is a solution technique using a Tikhonov regularization method. The L-curve is used for estimating an optimal regularization parameter. The image restoration was performed with Dubaisat-1 images for PIF, WF, and MWF. It is found that the image restored with MWF results in more improved MTF by 20.93% and 10.85% than PIF and WF, respectively.

• Journal of Korea Multimedia Society
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• v.2 no.3
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• pp.320-328
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• 1999

The Laplacian operator is usually used as a regularization operator which may be used as any differential operator in the regularization iterative restoration. In this paper, several kinds of differential operator and 1-H operator that has been used in our lab as well, as a regularization operator, were compared with each other. In the restoration of noisy motion-blurred images, 1-H operator worked better than Laplacian operator in flat region, but in the edge the Laplacian operator operated better. For noisy gaussian-blurred image, 1-H operator worked better in the edge, while in flat region the Laplacian operator resulted better. In regularization, smoothing the noise and resorting the edges should be considered at the same time, so the regions divided into the flat, the middle, and the detailed, which were processed in separate and compared their MSE. Laplacian and 1-H operator showed to be suitable as the regularization operator, while the other differential operators appeared to be diverged as iterations proceeded.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.46 no.2
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• pp.78-88
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• 2009

In many face recognition problems, the number of available images is limited compared to the dimension of the input space which is usually equal to the number of pixels. This problem is called as the 'small sample size' problem and regularization methods are typically used to solve this problem in feature extraction methods such as LDA. By using regularization methods, the modified within class matrix becomes nonsingu1ar and LDA can be performed in its original form. However, in the process of adding a scaled version of the identity matrix to the original within scatter matrix, the scale factor should be set heuristically and the performance of the recognition system depends on highly the value of the scalar factor. By using the proposed resampling method, we can generate a set of images similar to but slightly different from the original image. With the increased number of images, the small sample size problem is alleviated and the classification performance increases. Unlike regularization method, the resampling method does not suffer from the heuristic setting of the parameter producing better performance.

• Smart Structures and Systems
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• v.21 no.6
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• pp.741-749
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• 2018

Structural health monitoring (SHM) systems are necessary to achieve smart predictive maintenance and repair planning as well as they lead to a safe operation of mechanical structures. In the context of vibration-based SHM the measured structural responses are employed to draw conclusions about the structural integrity. This usually leads to a mathematically illposed inverse problem which needs regularization. The restriction of the solution set of this inverse problem by using prior information about the damage properties is advisable to obtain meaningful solutions. Compared to the undamaged state typically only a few local stiffness changes occur while the other areas remain unchanged. This change can be described by a sparse damage parameter vector. Such a sparse vector can be identified by employing $L_1$-regularization techniques. This paper presents a novel framework for damage parameter identification by combining sparse solution techniques with an Extended Kalman Filter. In order to ensure sparsity of the damage parameter vector the measurement equation is expanded by an additional nonlinear $L_1$-minimizing observation. This fictive measurement equation accomplishes stability of the Extended Kalman Filter and leads to a sparse estimation. For verification, a proof-of-concept example on a quadratic aluminum plate is presented.

• Structural Engineering and Mechanics
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• v.75 no.4
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• pp.477-485
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• 2020

Finite element (FE) model based structural damage detection (SDD) methods play vital roles in effectively locating and quantifying structural damages. Among these methods, structural model updating should be conducted before SDD to obtain benchmark models of real structures. However, the characteristics of updating parameters are not reasonably considered in existing studies. Inspired by the l_∞ norm regularization, a novel anti-sparse representation method is proposed for structural model updating in this study. Based on sensitivity analysis, both frequencies and mode shapes are used to define an objective function at first. Then, by adding l_∞ norm penalty, an optimization problem is established for structural model updating. As a result, the optimization problem can be solved by the fast iterative shrinkage thresholding algorithm (FISTA). Moreover, comparative studies with classical regularization strategy, i.e. the l₂ norm regularization method, are conducted as well. To intuitively illustrate the effectiveness of the proposed method, a 2-DOF spring-mass model is taken as an example in numerical simulations. The updating results show that the proposed method has a good robustness to measurement noises. Finally, to further verify the applicability of the proposed method, a six-storey aluminum alloy frame is designed and fabricated in laboratory. The added mass on each storey is taken as updating parameter. The updating results provide a good agreement with the true values, which indicates that the proposed method can effectively update the model parameters with a high accuracy.