• 제목/요약/키워드: $l_1$-norm

검색결과 190건 처리시간 0.021초

강인한 역산으로서의 하이브리드 $l^1/l^2$ norm IRLS 방법의 효율적 구현기법 (An Efficient Implementation of Hybrid $l^1/l^2$ Norm IRLS Method as a Robust Inversion)

  • 지준
    • 지구물리와물리탐사
    • /
    • 제10권2호
    • /
    • pp.124-130
    • /
    • 2007
  • 탄성파 역산에 있어서 가장 널리 사용되는 최소자승($l^2$ norm)해는 이상치(outlier)에 매우 민감하게 반응하는 경향이 있다. 이에 반해서 $l^1$ norm을 최소화하는 해는 이상치에 강인한 면을 보이나 일반적으로 좀 더 많은 계산이 필요하다. 반복적가중의 최소자승법(Iteratively reweighted least squares [IRLS] method)을 이용하면 이러한 $l^1$ norm 문제의 근사해(approximate solution)를 효율적으로 구할 수 있다. 본 논문에서는 작은 크기의 잔여분은 $l^2$ norm으로 처리하며, 큰 크기의 잔여분은 $l^1$ norm으로 처리하는 하이브리드 $l^1/l^2$ norm 최소화를 IRLS 방법에 쉽게 적용하는 구현 기법을 소개한다. 소개된 알고리즘은 특이치(singularity)처리를 위한 임계값의 결정에 민감하게 반응하는 기존의 $l^1$ norm IRLS 방법과는 달리 임계값 결정에 상관없이 늘 강인한 역산의 특성을 보여준다.

lp-norm regularization for impact force identification from highly incomplete measurements

  • Yanan Wang;Baijie Qiao;Jinxin Liu;Junjiang Liu;Xuefeng Chen
    • Smart Structures and Systems
    • /
    • 제34권2호
    • /
    • pp.97-116
    • /
    • 2024
  • The standard l1-norm regularization is recently introduced for impact force identification, but generally underestimates the peak force. Compared to l1-norm regularization, lp-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 lp-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 lp-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 lp-norm (0 ≤ p < 1) regularization. Both numerical and experimental results demonstrate that the proposed lp-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, lp-norm (0 ≤ p < 1) regularization procures sufficiently sparse and more accurate estimates; although the peak relative error of the identified impact force using lp-norm regularization has a decreasing tendency as p is approaching 0, the results of lp-norm regularization with 0 ≤ p ≤ 1/2 have no significant differences.

THE GROUP OF HAMILTONIAN HOMEOMORPHISMS IN THE L-NORM

  • Muller, Stefan
    • 대한수학회지
    • /
    • 제45권6호
    • /
    • pp.1769-1784
    • /
    • 2008
  • The group Hameo (M, $\omega$) of Hamiltonian homeomorphisms of a connected symplectic manifold (M, $\omega$) was defined and studied in [7] and further in [6]. In these papers, the authors consistently used the $L^{(1,{\infty})}$-Hofer norm (and not the $L^{\infty}$-Hofer norm) on the space of Hamiltonian paths (see below for the definitions). A justification for this choice was given in [7]. In this article we study the $L^{\infty}$-case. In view of the fact that the Hofer norm on the group Ham (M, $\omega$) of Hamiltonian diffeomorphisms does not depend on the choice of the $L^{(1,{\infty})}$-norm vs. the $L^{\infty}$-norm [9], Y.-G. Oh and D. McDuff (private communications) asked whether the two notions of Hamiltonian homeomorphisms arising from the different norms coincide. We will give an affirmative answer to this question in this paper.

L0 Norm 기반의 LE(Local Effect) 연산자를 이용한 디지털 이미지 위변조 검출 기술 개발 (Development of Digital Image Forgery Detection Method Utilizing LE(Local Effect) Operator based on L0 Norm)

  • 최용수
    • 한국소프트웨어감정평가학회 논문지
    • /
    • 제16권2호
    • /
    • pp.153-162
    • /
    • 2020
  • 디지털 이미지 위조 탐지는 디지털 포렌식 분야에서 매우 중요한 분야 중 하나이다. 기술의 발전을 통해 위조된 이미지가 자연스럽게 바뀜에 따라 이미지 위조를 감지하기 어렵게 만들었다. 본 논문에서는 디지털 이미지에서 복사 붙여넣기 위조에 대한 수동적 위조 검출을 이용한다. 또한, L0 Norm 기반 LE 연산자를 사용해 복사 붙여넣기 위조를 검출함과 동시에 기존에 존재하던 L2, L1 Norm 기반 LE 연산자를 이용한 위조 검출 정확도를 비교하였다. 제안한 하삼각 윈도우를 적용하고 L2, L1 및 L0 Norm 기반 LE 연산자를 통해 BAG 불일치를 검출하고 위조 검출률을 측정하였다. 검출률의 비교에서 제안한 하삼각 윈도우는 기존의 윈도우 필터보다 BAG 불일치 검출에 강인함을 볼 수 있었다. 또한, 하삼각 윈도우를 쓰는 경우 L2, L1, L0 Norm LE 연산으로 갈수록 이미지 위조 검출의 성능이 점점 높게 측정되었다.

Two Dimensional Slow Feature Discriminant Analysis via L2,1 Norm Minimization for Feature Extraction

  • Gu, Xingjian;Shu, Xiangbo;Ren, Shougang;Xu, Huanliang
    • KSII Transactions on Internet and Information Systems (TIIS)
    • /
    • 제12권7호
    • /
    • pp.3194-3216
    • /
    • 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.

The strong consistency of the $L_1$-norm estimators in censored nonlinear regression models

  • Park, Seung-Hoe;Kim, Hae-Kyung
    • 대한수학회보
    • /
    • 제34권4호
    • /
    • pp.573-581
    • /
    • 1997
  • This paper is concerned with the strong consistency of the $L_1$-norm estimators for the nonlinear regression models when dependent variables are subject to censoring, and provides the sufficient conditions which ensure the strong consistency of $L_1$-norm estimators of the censored regression models.

  • PDF

L1-norm Minimization based Sparse Approximation Method of EEG for Epileptic Seizure Detection

  • Shin, Younghak;Seong, Jin-Taek
    • 한국정보전자통신기술학회논문지
    • /
    • 제12권5호
    • /
    • pp.521-528
    • /
    • 2019
  • Epilepsy is one of the most prevalent neurological diseases. Electroencephalogram (EEG) signals are widely used for monitoring and diagnosis tool for epileptic seizure. Typically, a huge amount of EEG signals is needed, where they are visually examined by experienced clinicians. In this study, we propose a simple automatic seizure detection framework using intracranial EEG signals. We suggest a sparse approximation based classification (SAC) scheme by solving overdetermined system. L1-norm minimization algorithms are utilized for efficient sparse signal recovery. For evaluation of the proposed scheme, the public EEG dataset obtained by five healthy subjects and five epileptic patients is utilized. The results show that the proposed fast L1-norm minimization based SAC methods achieve the 99.5% classification accuracy which is 1% improved result than the conventional L2 norm based method with negligibly increased execution time (42msec).

ROBUST $L_{p}$-NORM ESTIMATORS OF MULTIVARIATE LOCATION IN MODELS WITH A BOUNDED VARIANCE

  • Georgly L. Shevlyakov;Lee, Jae-Won
    • 한국수학교육학회지시리즈B:순수및응용수학
    • /
    • 제9권1호
    • /
    • pp.81-90
    • /
    • 2002
  • The least informative (favorable) distributions, minimizing Fisher information for a multivariate location parameter, are derived in the parametric class of the exponential-power spherically symmetric distributions under the following characterizing restrictions; (i) a bounded variance, (ii) a bounded value of a density at the center of symmetry, and (iii) the intersection of these restrictions. In the first two cases, (i) and (ii) respectively, the least informative distributions are the Gaussian and Laplace, respectively. In the latter case (iii) the optimal solution has three branches, with relatively small variances it is the Gaussian, them with intermediate variances. The corresponding robust minimax M-estimators of location are given by the $L_2$-norm, the $L_1$-norm and the $L_{p}$ -norm methods. The properties of the proposed estimators and their adaptive versions ar studied in asymptotics and on finite samples by Monte Carlo.

  • PDF

전기 저항 단층촬영법에서의 조정기법 성능비교 (Performance Comparison of Regularization Methods in Electrical Resistance Tomography)

  • 강숙인;김경연
    • 전기전자학회논문지
    • /
    • 제20권3호
    • /
    • pp.226-234
    • /
    • 2016
  • 전기 저항 단층촬영법(ERT)은 대상체 내부 단면의 저항률 분포를 추정하고 이를 영상화하는 기술이다. ERT의 영상복원은 매우 비정치성이 강한 역문제의 일종으로 의미있는 영상을 얻기 위해서는 조정기법이 사용된다. 대표적으로 l2-norm 조정기법, l1-norm 조정기법, Total Variation 조정기법이 사용되며, 조정기법에 따라 ERT의 영상복원 성능이 달라진다. 즉, 상황에 맞는 적절한 조정기법의 사용은 ERT 영상 복원을 개선할 수 있다. 따라서, 본 논문에서는 모의실험을 통하여 상황에 따른 세 가지 조정기법의 영상복원 성능을 비교하였다.

로버스트추정에 의한 지구물리자료의 역산 (Inversion of Geophysical Data with Robust Estimation)

  • 김희준
    • 자원환경지질
    • /
    • 제28권4호
    • /
    • 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.

  • PDF