• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.11 no.5
• /
• pp.1685-1692
• /
• 2010

The Laplacian operator is usually used as a regularization operator which may be used as any differential operator in the regularization iterative processing. In this paper, several kinds of differential operator and proposed operator as a regularization operator were compared with each other performance. For noisy gaussian-blurred images, proposed operator worked better in the edge, while in flat region the conventional operator resulted better. In regularization, smoothing the noise and restoring 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.

• Journal of Korea Multimedia Society
• /
• v.2 no.3
• /
• pp.320-328
• /
• 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 applied mathematics & informatics
• /
• v.35 no.3_4
• /
• pp.399-411
• /
• 2017

We first provide the linear operator equations corresponding to the Tikhonov regularization image denoising problems with different regularization terms, and then we propose how to choose Kronecker product preconditioners which are required for accelerating the $G{\ell}$-PCG method. Next, we provide how to apply the $G{\ell}$-PCG method with Kronecker product preconditioner to the linear operator equations. Lastly, we provide numerical experiments for image denoisng problems to evaluate the effectiveness of the $G{\ell}$-PCG with Kronecker product preconditioner.

• Journal of KIISE:Software and Applications
• /
• v.33 no.10
• /
• pp.862-867
• /
• 2006

To restore image degraded by blur and additive noise in the optical and electrical system, a regularized iterative restoration is used. A regularization operator is usually applied to all over the image without considering the local characteristics of image in conventional method. As a result, ringing artifacts appear in edge regions and the noise is amplified in flat regions. To solve these problems we propose an adaptive regularization iterative restoration considering the characteristic of edge and flat regions using directional regularization operator. Experimental results show that the proposed method suppresses the noise amplification in flat regions, and restores the edge more sharply in edge regions.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.25 no.9B
• /
• pp.1588-1595
• /
• 2000

To restore image degraded by out-of-focus blur and additivie noise a regularized iterative restoration is used. In concentional method, regularization is usually applied to all over the image without considering the local characteristics of image. As a result, ringing artifacts appear in edge regions and the noise amplification is introduced in flat regions. To solve this problem we propose an adaptive regularization iterative restoration using directional regularization operator considering edges in four directions and the regularization operator with on direction for flat regions. We verified that the proposed method show better results in the suppression of the noise amplification in flat regions, and introduced less ringing artifacts in edge regions. As a result it showed visually better image and improved better ISNR further than the conventional methods.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.11 no.3
• /
• pp.965-970
• /
• 2010

In this paper, a iterative image restoration method is proposed to restore for noisy-blurred images. In conventional method, regularization is usually applied to all over the without considering the local characteristics of image. As a result, ringing artifacts appear in edge regions and the noise amplification is introduced in flat regions. To solvethis problem we proposed an adaptive regularization iterative restoration using directional regularization operator considering edges in four directions and the regularization operator with no direction for flat regions. We verified that the proposed methods showed better results in the suppression of the noise amplification in flat regions, and introduced less ringing artifacts in edge regions. As a result it showed visually better image and improved better ISNR further than the conventional methods.

• Journal of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.849-875
• /
• 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 the Korean Mathematical Society
• /
• v.22 no.1
• /
• pp.35-42
• /
• 1985

• The KIPS Transactions:PartB
• /
• v.16B no.1
• /
• pp.1-6
• /
• 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
• /
• v.25 no.1B
• /
• pp.141-147
• /
• 2000

In the restoration of degraded noisy motion blurred image, we have trade-off problem between smoothing the noise and restoration of the edge region. While the noise is smoothed, die edge or details will be corrupted. On the other hand, restoring the edge will amplify the noise. To solve this problem we propose an adaptive algorithm which uses I- H regularization operator for flat region and Laplacian regularization operator for edge region. Through the experiments, we verify that the proposed method shows better results in the suppression of the noise amplification in flat region, introducing less ringing artifacts in edge region and better ISNR than those of the conventional ones.