• Geophysics and Geophysical Exploration
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• v.10 no.2
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• pp.124-130
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• 2007

Least squares ($l^2$ norm) solutions of seismic inversion tend to be very sensitive to data points with large errors. The $l^1$ norm minimization gives more robust solutions, but usually with higher computational cost. Iteratively reweighted least squares (IRLS) method gives efficient approximate solutions of these $l^1$ norm problems. I propose an efficient implementation of the IRLS method for a hybrid $l^1/l^2$ minimization problem that behaves as $l^2$ norm fit for small residual and $l^1$ norm fit for large residuals. The proposed algorithm shows more robust characteristics to the decision of the threshold value than the l1 norm IRLS inversion does with respect to the threshold value to avoid singularity.

• 한국지구물리탐사학회:학술대회논문집
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• 2005.05a
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• pp.227-232
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• 2005

Least squares (${\ell}^2-norm$) solutions of seismic inversion tend to be very sensitive to data points with large errors. The ${\ell}^p-norm$ minimization for $1{\le}p<2$ gives more robust solutions, but usually with higher computational cost. Iteratively reweighted least squares (IRLS) gives efficient approximate solutions of these ${\ell}^p-norm$ problems. I propose a simple way to implement the IRLS method for a hybrid ${\ell}^1/{\ell}^2$ minimization problem that behaves as ${\ell}^2$ fit for small residual and ${\ell}^1$ fit for large residuals. Synthetic and a field-data examples demonstrates the improvement of the hybrid method over least squares when there are outliers in the data.

• Journal of Software Assessment and Valuation
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• v.16 no.2
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• pp.153-162
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• 2020

Digital image forgery detection is one of very important fields in the field of digital forensics. As the forged images change naturally through the advancement of technology, it has made it difficult to detect forged images. In this paper, we use passive forgery detection for copy paste forgery in digital images. In addition, it detects copy-paste forgery using the L₀ Norm-based LE operator, and compares the detection accuracy with the forgery detection using the existing L₂, L₁ Norm-based LE operator. In comparison of detection rates, the proposed lower triangular(Ayalneh and Choi) window was more robust to BAG mismatch detection than the conventional window filter. In addition, in the case of using the lower triangular window, the performance of image forgery detection was measured increasingly higher as the L₂, L₁ and L₀ Norm LE operator was performed.

• Smart Structures and Systems
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• v.34 no.2
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• pp.97-116
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• 2024

The standard l₁-norm regularization is recently introduced for impact force identification, but generally underestimates the peak force. Compared to l₁-norm regularization, l_p-norm (0 ≤ p < 1) regularization, with a nonconvex penalty function, has some promising properties such as enforcing sparsity. In the framework of sparse regularization, if the desired solution is sparse in the time domain or other domains, the under-determined problem with fewer measurements than candidate excitations may obtain the unique solution, i.e., the sparsest solution. Considering the joint sparse structure of impact force in temporal and spatial domains, we propose a general l_p-norm (0 ≤ p < 1) regularization methodology for simultaneous identification of the impact location and force time-history from highly incomplete measurements. Firstly, a nonconvex optimization model based on l_p-norm penalty is developed for regularizing the highly under-determined problem of impact force identification. Secondly, an iteratively reweighed l₁-norm algorithm is introduced to solve such an under-determined and unconditioned regularization model through transforming it into a series of l₁-norm regularization problems. Finally, numerical simulation and experimental validation including single-source and two-source cases of impact force identification are conducted on plate structures to evaluate the performance of l_p-norm (0 ≤ p < 1) regularization. Both numerical and experimental results demonstrate that the proposed l_p-norm regularization method, merely using a single accelerometer, can locate the actual impacts from nine fixed candidate sources and simultaneously reconstruct the impact force time-history; compared to the state-of-the-art l₁-norm regularization, l_p-norm (0 ≤ p < 1) regularization procures sufficiently sparse and more accurate estimates; although the peak relative error of the identified impact force using l_p-norm regularization has a decreasing tendency as p is approaching 0, the results of l_p-norm regularization with 0 ≤ p ≤ 1/2 have no significant differences.

• Journal of the Korean housing association
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• v.2 no.1
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• pp.13-34
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• 1991

The main purpose of this study is to examine housing norm of the middle classes, housing norm and normative housing deficits by independent variables(socio - economic variables, family characteristic variable sand housing characteristic variables).There are two major findings of this study as follows :1. In the housing norm, housing space is 99.Om2, the number of rooms is 3.0, housing structure type is apartment, the maintenance cost is 13 thousand won, and housing tenure is home ownership. And housing qualify is classified into 5 dimensions, and neighborhood environment is classified into 3 dimensions.2. This thesis is to conform Morris et aL.(1984)`s hypotheses that cultural norm is homogeneous in culturally unified society and if it appears heterogeneously, It is the subject`s reporting error of the subjects confusing cultural norm with family norm.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.7
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• pp.3194-3216
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• 2018

Slow Feature Discriminant Analysis (SFDA) is a supervised feature extraction method inspired by biological mechanism. In this paper, a novel method called Two Dimensional Slow Feature Discriminant Analysis via $L_{2,1}$ norm minimization ($2DSFDA-L_{2,1}$) is proposed. $2DSFDA-L_{2,1}$ integrates $L_{2,1}$ norm regularization and 2D statically uncorrelated constraint to extract discriminant feature. First, $L_{2,1}$ norm regularization can promote the projection matrix row-sparsity, which makes the feature selection and subspace learning simultaneously. Second, uncorrelated features of minimum redundancy are effective for classification. We define 2D statistically uncorrelated model that each row (or column) are independent. Third, we provide a feasible solution by transforming the proposed $L_{2,1}$ nonlinear model into a linear regression type. Additionally, $2DSFDA-L_{2,1}$ is extended to a bilateral projection version called $BSFDA-L_{2,1}$. The advantage of $BSFDA-L_{2,1}$ is that an image can be represented with much less coefficients. Experimental results on three face databases demonstrate that the proposed $2DSFDA-L_{2,1}/BSFDA-L_{2,1}$ can obtain competitive performance.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.165-173
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• 2019

In this paper, the definition b-numerical radius and b-norm is introduced and we present several b-numerical radius inequalities. Some applications of these inequalities are considered as well.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.735-748
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• 1998

We analyze the error in the p version of the of the finite element method when the effect of the quadrature error is taken in the load vector. We briefly study some results on the $H^{1}$ norm error and present some new results for the error in the $L^{2}$ norm. We inves-tigate the quadrature error due to the numerical integration of the right hand side We present theoretical and computational examples showing the sharpness of our results.

• Journal of Information Technology Services
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• v.12 no.2
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• pp.1-12
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• 2013

A new form of software piracy known as digital piracy has taken the spotlight. Lost revenues due to digital piracy could reach 2,500 billion won in year 2010 alone. This paper examines the causal relationships among the attitude toward digital piracy, subjective norm, economic gain, political efficacy, school policy, etc, in a university setting. Results from survey responses indicate that the social norm and economic gain affect the attitude toward digital piracy, and that school policy influences the subjective norm as well as political efficacy. But, contrary to our expectation, political efficacy has been found to have no impact on the social norm and economic gain. Prior learning experiences have been shown to affect economic gain, but not the subjective norm. As a conclusion, the academic and practical implications of these findings are discussed.

• Journal of Oriental Neuropsychiatry
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• v.15 no.1
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• pp.197-209
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• 2004

Objectives : The purpose of this case-control research was to investigate the effects of acupuncture stimulation on autonomic nervous system for patients with HRV and to find out relationship with anti-stress effects. Methods : The study group consists of 24 patients with self-recognition of stress as the case group, and 20 normal person as the control group by similar age. We measured HRV of case and control groups before acupuncture stimulation, prick acupuncture in Hegu(LI4), Taichong(Liv3), Shenme(H7), Neiguan(P6), Zusanli(S36). After treating for 20 minutes, measurement values of HRV and PSV were compared for pre-acupuncture and post-acupuncture. Results : 1. LF norm, HF norm, LF/HF between the case and control groups were significant different in HRV before acupuncture stimulation in the 1st experiment. 2. HRT, SDNN, SDSD, LF norm, HF norm, and LF/HF of the case group were significant different in HRV after acupuncture stimulation in the 1st experiment. HRT of the case group was significantly different in HRV after acupuncture stimulation in the 1st experiment. 3. LF norm, HF norm, LF/HF of the case group were significant different between the 1st and 2nd experiment in HRV before acupuncture stimulation. 4. LF norm, HF norm, and LF/HF were significant different between the 1st and 2nd experiment in HRV of patients whose symptoms improved. But HRV of patients whose symptoms unimproved didn't show significant difference. Conclusion : The results suggest that acupuncture stimulation is associated with changed activity in the sympathetic and parasympathetic nervous system. Measurement values of HRV is suitable to estimate the activity of automatic nervous system.