• Journal of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.495-505
• /
• 1996

Let $\Omega$ be a bounded domain in $R^d, d \geq 1$, with smooth boundary $\partial\Omega$, and let $0 < T < \infty$ be given.

• Journal of applied mathematics & informatics
• /
• v.7 no.1
• /
• pp.61-82
• /
• 2000

In this paper two so-called regularized Green's functions are introduced to derive the optimal maximum norm error estimates for the unknown function and the adjoint vector-valued function for mixed finite element methods of Laplacian operator. One contribution of the paper is a demonstration of how the boundedness of $L^1$-norm estimate for the second Green's function ${\lambda}_2$ and the optimal maximum norm error estimate for the adjoint vector-valued function are proved. These results are seemed to be to be new in the literature of the mixed finite element methods.

• Economic and Environmental Geology
• /
• v.28 no.4
• /
• pp.433-438
• /
• 1995

The most popular minimization method is based on the least-squares criterion, which uses the $L_2$ norm to quantify the misfit between observed and synthetic data. The solution of the least-squares problem is the maximum likelihood point of a probability density containing data with Gaussian uncertainties. The distribution of errors in the geophysical data is, however, seldom Gaussian. Using the $L_2$ norm, large and sparsely distributed errors adversely affect the solution, and the estimated model parameters may even be completely unphysical. On the other hand, the least-absolute-deviation optimization, which is based on the $L_1$ norm, has much more robust statistical properties in the presence of noise. The solution of the $L_1$ problem is the maximum likelihood point of a probability density containing data with longer-tailed errors than the Gaussian distribution. Thus, the $L_1$ norm gives more reliable estimates when a small number of large errors contaminate the data. The effect of outliers is further reduced by M-fitting method with Cauchy error criterion, which can be performed by iteratively reweighted least-squares method.

• Journal of the Institute of Electronics Engineers of Korea SP
• /
• v.44 no.6
• /
• pp.93-99
• /
• 2007

Robust nonlinear image denoising algorithms for the class of ${\alpha}$-stable distribution are introduced. The proposed amplitude-limited sample average filter(ALSAF) proves to be the maximum likelihood estimator under the heavy-tailed Gaussian noise environments. The error norm for this estimator is equivalent to Huber#s minimax norm. It is optimal in the respect of maximizing the efficacy under the above noise environment. It is mired with the myriad filter to propose an amplitude-limited myriad filter(ALMF). The behavior and performance of the ALSAF and ALMF in ${\alpha}$-stable noise environment are illustrated and analyzed through simulation.

• Proceedings of the KIEE Conference
• /
• 2006.04a
• /
• pp.18-20
• /
• 2006

The statistics for the neighbor differences between the particular pixels and their neighbors are introduced. They are incorporated into the filter to remove additive Gaussian noise contaminating images. The derived denoising method corresponds to the maximum likelihood estimator for the heavy-tailed Gaussian distribution. The error norm corresponding to our estimator from the robust statistics is equivalent to Huber's minimax norm. Our estimator is also optimal in the respect of maximizing the efficacy under the above noise environment.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.21 no.6
• /
• pp.1522-1532
• /
• 1996

In this paper, we compare the performance of channel estimators with the L$_{1}$-norm and L$_{2}$-norm criteria in impulaive noise environment, and show than the L$_{1}$-norm criterion is appropriate for that situation. Also, it is shown that the performance of the conventional maximum likelihood sequence detector(MLSD) can be improved by applying the same principle to mobile channels. That is, the performance of the conventional MLSD, which is known to be optimal under the Gaussian noise assumption, degrades in the impulsive noise of radio mobile communication channels. So, we proposed the MLSD which can reduce the effect of impulsive noise effectively by applying the results of channel estimators. Finally, it is confirmed by computer simulation that the performance of MLSD is significantly affected depending on the types of branch metrics, and that, in the impulsive noise environments, the proposed one with new branch metrics performs better thatn the conventional branch metric, l y(k)-s(k) l$^{[-992]}$ .

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.46 no.5
• /
• pp.39-48
• /
• 2009

Many super-resolution reconstruction algorithms have been proposed since it was the first proposed in 1984. The spatial domain approach of the super-resolution reconstruction methods is accomplished by mapping the low resolution image pixels into the high resolution image pixels. Generally, a super-resolution reconstruction algorithm by using the spatial domain approach has the noise problem because the low resolution images have different noise component, different PSF, and distortion, etc. In this paper, we proposed the new super-resolution reconstruction method that uses the L1 norm to minimize noise source and also uses the Huber norm to preserve edges of image. The proposed algorithm obtained the higher image quality of the result high resolution image comparing with other algorithms by experiment.

• Journal of the Korean Society for Precision Engineering
• /
• v.26 no.3
• /
• pp.32-39
• /
• 2009

A new discrete time gain-scheduled control design is proposed to improve disturbance attenuation for systems with bounded control input under known disturbance maximum norm. The state feedback gains are scheduled according to the proximity of the state of the plant to the origin. The controllers are derived in the framework of linear matrix inequality(LMI) optimization. This procedure yields a linear time varying control structure that allows higher gain and hence higher performance controllers as the state moves closer to the origin. The main results give sufficient conditions for the satisfaction of a parameter-dependent performance measure, without violating the bounded control input condition under the given disturbance maximum norm.

• Journal of applied mathematics & informatics
• /
• v.37 no.5_6
• /
• pp.357-382
• /
• 2019

In this paper, we consider boundary value problem for a weakly coupled system of two singularly perturbed differential equations of convection diffusion type with discontinuous source term. In general, solution of this type of problems exhibits interior and boundary layers. A numerical method based on streamline diffusiom finite element and Shishkin meshes is presented. We derive an error estimate of order $O(N^{-2}\;{\ln}^2\;N$) in the maximum norm with respect to the perturbation parameters. Numerical experiments are also presented to support our theoritical results.

• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10b
• /
• pp.562-565
• /
• 1993

It is well known that H$_{\infty}$ control problem involves solving an algebraic Riccati equation which includes a pair of parameters (.gamma., .epsilon.). Focusing on .epsilon. the maximum of .epsilon.. We discuss in this paper about the properties between the H$_{\infty}$ norm of a trnsfer function matrix and the parameters(.gamma., .epsilon.). We can change the algebraic relattion between .gamma. and .epsilon. by the similarity transformation of a considered system and we can find a proper transformation to get a simple quadratic algebraic equation between .gamma. and .epsilon.. This relation provide the H$_{\infty}$ norm of a transfer function.on.