• Communications of the Korean Mathematical Society
• /
• v.16 no.3
• /
• pp.487-508
• /
• 2001

We consider the Cauchy problem for Laplacian. Using the single layer representation, we obtain an equivalent system of boundary integral equations. We show the singular values of the ill-posed Cauchy operator decay exponentially, which means that a small error is exponentially amplified in the solution of the Cauchy problem. We show the decaying rate is dependent on the geometry of he domain, which provides the information on the choice of numerically meaningful modes. We suggest a pseudo-inverse regularization method based on singular value decomposition and present various numerical simulations.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.1
• /
• pp.149-156
• /
• 2019

This paper present the global generalized cross validation as the appropriate choice of the regularization parameter in the preconditioned Gl-LSQR method in solving image deblurring problems. The regularization parameter, chosen from the global generalized cross validation, with preconditioned Gl-LSQR method can give better reconstructions of the true image than other parameters considered in this study.

• East Asian mathematical journal
• /
• v.40 no.5
• /
• pp.527-549
• /
• 2024

In this paper we study the semilinear first order evolution problems of Volterra type with Lipschitz continuous nonlinearities. Using the variational formulation of problems due to Dautray and Lions [6], we have proved the fundamental results on existence, uniqueness and continuous dependence of solutions. Especially in the proof of the regularity we have used the double regularization method. Applications to nonlinear partial integro-differential equations are given.

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

• Structural Engineering and Mechanics
• /
• v.75 no.4
• /
• pp.415-424
• /
• 2020

Recently, many structural damage detection (SDD) methods have been proposed to monitor the safety of structures. As an important modal parameter, mode shape has been widely used in SDD, and the difference of vectors was adopted based on sensitivity analysis and mode shapes in the existing studies. However, amplitudes of mode shapes in different measured points are relative values. Therefore, the difference of mode shapes will be influenced by their amplitudes, and the SDD results may be inaccurate. Focus on this deficiency, a multi-strategy SDD method is proposed based on the included angle of vectors and sparse regularization in this study. Firstly, inspired by modal assurance criterion (MAC), a relationship between mode shapes and changes in damage coefficients is established based on the included angle of vectors. Then, frequencies are introduced for multi-strategy SDD by a weighted coefficient. Meanwhile, sparse regularization is applied to improve the ill-posedness of the SDD problem. As a result, a novel convex optimization problem is proposed for effective SDD. To evaluate the effectiveness of the proposed method, numerical simulations in a planar truss and experimental studies in a six-story aluminum alloy frame in laboratory are conducted. The identified results indicate that the proposed method can effectively reduce the influence of noises, and it has good ability in locating structural damages and quantifying damage degrees.

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

• Journal of Broadcast Engineering
• /
• v.10 no.2
• /
• pp.238-246
• /
• 2005

This paper proposes an iterative high-resolution image interpolation algorithm using spatially adaptive constraints and regularization functional. The proposed algorithm adapts adaptive constraints according to the direction of..edges in an image, and can restore high-resolution image by optimizing regularization functional at each iteration, which is suitable for edge directional regularization. The proposed algorithm outperforms the conventional adaptive interpolation methods as well as non-adaptive ones, which not only can restore high frequency components, but also effectively reduce undesirable effects such as noise. Finally, in order to evaluate the performance of the proposed algorithm, various experiments are performed so that the proposed algorithm can provide good results in the sense of subjective and objective views.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.21 no.1
• /
• pp.6-11
• /
• 2011

In this paper, we propose a gait-based human identification system using eigenfeature regularization and extraction (ERE). First, a gait feature for human identification which is called gait energy image (GEI) is generated from walking sequences acquired from a camera sensor. In training phase, regularized transformation matrix is obtained by applying ERE to the gallery GEI dataset, and the gallery GEI dataset is projected onto the eigenspace to obtain galley features. In testing phase, the probe GEI dataset is projected onto the eigenspace created in training phase and determine the identity by using a nearest neighbor classifier. Experiments are carried out on the CASIA gait dataset A to evaluate the performance of the proposed system. Experimental results show that the proposed system is better than previous works in terms of correct classification rate.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.21 no.1
• /
• pp.73-82
• /
• 2008

In this paper, a new regularization method by parameter subset selection method is proposed based on the residual force vector for damage localization. Although subset selection using the fundamental modal characteristics as a residual function has been successful in detecting a single damage location, this method seems to have limited capabilities in the detection of multiple damage locations and typically requires cumbersome weighting values. The method is presented herein and considers cases in which damage detection must be achieved using incomplete measurements of the structural responses. Model expansion is incorporated to deal with this challenge. The unique advantage of employing the new regularization method is that it can reliably identify multiple damage locations. Through an illustrative example, the proposed damage detection method is demonstrated to be a reliable tool for identifying multiple damage locations for a planar truss structure.

• Journal of the Institute of Electronics and Information Engineers
• /
• v.54 no.4
• /
• pp.91-98
• /
• 2017

Electrical impedance tomography is a nondestructive imaging technique to reconstruct unknown conductivity distribution based on applied current data and measured voltage data through an array of electrodes attached on the periphery of a domain. In this paper, an inverse method based on truncated singular value decomposition is proposed to solve the inverse problem with the generalized Tikhonov regularization and to reconstruct the conductivity distribution. In order to reduce the inverse computational time, truncated singular value decomposition is applied to the inverse term after the generalized regularization matrix is taken out from the inverse matrix term. Numerical experiments and phantom experiments have been performed to verify the performance of the proposed method.