• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.1
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• pp.91-99
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• 1994

We proposed the regularized iterative restoration method considering relaxation parameter and regularization paramenter in order to restore the noisy motion-blurred images. We used (i-H) as a regularization operator and these two kinds of constraints were applied while conventional regularization iterative restoration method proposed by Jan Biemond et al used the 2-D Laplacian filter and a predetermined regularization parameter value and relaxation parameter to 1. Through the experimental results, we showed better results compared with those by a conventional method and or regularized iterative restoration method just considering only a regularization parameter. These two kinds of constratints have good effects when applied into the regularized iterative restoration method for noisy motion-blurred images.

• Journal of IKEEE
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• v.19 no.1
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• pp.33-40
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• 2015

Inverse problem in electrical impedance tomography (EIT) is highly ill-posed therefore prior information is used to mitigate the ill-posedness. Regularization methods are often adopted in solving EIT inverse problem to have satisfactory reconstruction performance. In solving the EIT inverse problem, iterative Gauss-Newton method is generally used due to its accuracy and fast convergence. However, its performance is still suboptimal and mainly depends on the selection of regularization parameter. Although, there are few methods available to determine the regularization parameter such as L-curve method they are sometimes not applicable for all cases. Moreover, regularization parameter is a scalar and it is fixed during iteration process. Therefore, in this paper, a novel method is used to determine the regularization parameter to improve reconstruction performance. Conductivity norm is calculated at each iteration step and it used to obtain the regularization parameter which is a diagonal matrix in this case. The proposed method is applied to human thorax imaging and the reconstruction performance is compared with traditional methods. From numerical results, improved performance of proposed method is seen as compared to conventional methods.

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.489-492
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• 2003

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$_4$ functional is proposed. 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$_2$ functional and the regularized l$_4$ functional. An iterative algorithm is utilized for obtaining a solution and its convergence is analyzed.

• Steel and Composite Structures
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• v.39 no.5
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• pp.511-528
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• 2021

There are recently some advances in solving numerically topology optimization problems for large-scaled trusses based on ground structure approach. A disadvantage of this approach is that the final design usually includes many bars, which is difficult to be produced in practice. One of efficient tools is a so-called filter scheme for the ground structure to reduce this difficulty and determine several distinct bars. In detail, this technique is valuable for practical uses because unnecessary bars are filtered out from the ground structure to obtain a well-defined structure during the topology optimization process, while it still guarantees the global equilibrium condition. This process, however, leads to a singular system of equilibrium equations. In this case, the minimization of least squares with Tikhonov regularization is adopted. In this paper, a proposed algorithm in controlling optimal Tikhonov parameter is considered in combination with the filter scheme due to its crucial role in obtaining solution to remove numerical singularity and saving computational time by using sparse matrix, which means that the discrete optimal topology solutions depend on choosing the Tikhonov parameter efficiently. Several numerical examples are investigated to demonstrate the efficiency of the filter parameter control algorithm in terms of the large-scaled optimal topology designs.

• Journal of IKEEE
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• v.18 no.2
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• pp.272-281
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• 2014

In electrical impedance tomography (EIT), modified Newton Raphson (mNR) method is widely used inverse algorithm for static image reconstruction due to its convergence speed and estimation accuracy. The unknown conductivity distribution is estimated iteratively by minimizing a cost functional such that the residual error namely the difference in measured and calculated voltages is reduced. Although, mNR method has good estimation performance, EIT inverse problem still suffers from ill-conditioned and ill-posedness nature. To mitigate the ill-posedness, generally, regularization methods are adopted. The inverse solution is highly dependent on the choice of regularization parameter. In most cases, the regularization parameter has a constant value and is chosen based on experience or trail and error approach. In situations, when the internal distribution changes or with high measurement noise, the solution does not get converged with the use of constant regularization parameter. Therefore, in this paper, in order to improve the image reconstruction performance, we propose a new scheme to determine the regularization parameter. The regularization parameter is computed based on residual error and updated every iteration. The proposed scheme is tested with numerical simulations and laboratory phantom experiments. The results show an improved reconstruction performance when using the proposed regularization scheme as compared to constant regularization scheme.

• 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 Korean Society of Radiology
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• v.11 no.7
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• pp.679-685
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• 2017

Computed tomography has widely been used to diagnose patient disease, and patient dose also increase rapidly. To reduce the patient dose by CT, various techniques have been applied. The iterative reconstruction is used in view of image reconstruction. Image quality of the reconstructed section image through algebraic reconstruction technique, one of iterative reconstruction methods, was examined by the normalized root mean square error. The computer program was written with the Visual C++ under the parallel beam geometry, Shepp-Logan head phantom of $512{\times}512$ size, projections of 360, and detector-pixels of 1,024. The forward and backward projection was realized by Joseph method. The minimum NRMS of 0.108 was obtained after 10 iterations in the regularization parameter of 0.09-0.12, and the optimum image was obtained after 8 and 6 iterations for 0.1% and 0.2% noise. Variation of optimum value of the regularization parameter was observed according to the phantom used. If the ART was used in the reconstruction, the optimal value of the regularization parameter should be found in the case-by-case. By finding the optimal regularization parameter in the algebraic reconstruction technique, the reconstruction time can be reduced.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.849-875
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• 2018

The purpose of this paper is to present an operator method of regularization for the problem of finding a solution of a system of nonlinear ill-posed equations with a monotone hemicontinuous mapping and N inverse-strongly monotone mappings in Banach spaces. A regularization parameter choice is given and convergence rate of the regularized solutions is estimated. We also give the convergence and convergence rate for regularized solutions in connection with the finite-dimensional approximation. An iterative regularization method of zero order in a real Hilbert space and two examples of numerical expressions are also given to illustrate the effectiveness of the proposed methods.

• Journal of Ocean Engineering and Technology
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• v.22 no.4
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• pp.1-7
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• 2008

The primary aim of the paper is to solve an unstable axisymmetric initial value problem of wave propagation when given initial data that is deteriorated by noise such as measurement error. To overcome the instability of the problem, Tikhonov's regularization, known as a non-iterative numerical regularization method, is introduced to solve the problem. The L-curvecriterion is introduced to find the optimal regularization parameter for the solution. It is confirmed that fairly stable solutions are realized and that they are accurate when compared to the exact solution.

• Smart Structures and Systems
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• v.31 no.3
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• pp.229-245
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• 2023

The absence of excitation measurements may pose a big challenge in the application of structural damage identification owing to the fact that substantial effort is needed to reconstruct or identify unknown input force. To address this issue, in this paper, an iterative strategy, a synergy of Tikhonov regularization method for force identification and modified Jaya algorithm (M-Jaya) for stiffness parameter identification, is developed for damage identification with partial output-only responses. On the one hand, the probabilistic clustering learning technique and nonlinear updating equation are introduced to improve the performance of standard Jaya algorithm. On the other hand, to deal with the difficulty of selection the appropriate regularization parameters in traditional Tikhonov regularization, an improved L-curve method based on B-spline interpolation function is presented. The applicability and effectiveness of the iterative strategy for simultaneous identification of structural damages and unknown input excitation is validated by numerical simulation on a 21-bar truss structure subjected to ambient excitation under noise free and contaminated measurements cases, as well as a series of experimental tests on a five-floor steel frame structure excited by sinusoidal force. The results from these numerical and experimental studies demonstrate that the proposed identification strategy can accurately and effectively identify damage locations and extents without the requirement of force measurements. The proposed M-Jaya algorithm provides more satisfactory performance than genetic algorithm, Gaussian bare-bones artificial bee colony and Jaya algorithm.