• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.12 no.5
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• pp.521-528
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• 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).

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2010.07a
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• pp.50-52
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• 2010

통신 시스템의 성능을 향상시키는 핵심 문제 중에 하나인 채널을 추정하는 문제는 다양한 분야에서 연구되고 있다. 채널의 sparse한 특징으로 인해 기존의 linear square나 minimum mean square error보다 발전된 $l_1$-norm minimization 방법 등이 많이 연구되고 있다. 이에 본 논문은 sparse한 채널의 특징과 천천히 변화하는 채널환경 특징을 이용하여 기존의 방법에 비해 더 높은 성능의 채널 추정 기법을 연구한다. 천천히 변화하는 채널환경의 특징으로 인해 이전 채널 정보를 현재 채널 추정에 사용할 수 있고 sparse한 채널의 특징으로 $l_1$-norm minimization을 사용할 수 있다. 이러한 두 가지의 정보를 이용하여 weighted $l_1$-norm minimization 이용한 support detection후 MMSE를 이용한 채널 추정기법을 연구한다.

• 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.

• 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.

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

• IEIE Transactions on Smart Processing and Computing
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• v.4 no.6
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• pp.413-421
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• 2015

Regularized Blind Deconvolution is a problem applicable in degraded images in order to bring the original image out of blur. Multichannel blind Deconvolution considered as an optimization problem. Each step in the optimization is considered as variable splitting problem using an algorithm called Alternating Minimization Algorithm. Each Step in the Variable splitting undergoes Augmented Lagrangian method (ALM) / Bregman Iterative method. Regularization is used where an ill posed problem converted into a well posed problem. Two well known regularizers are Tikhonov class and Total Variation (TV) / L2 model. TV can be isotropic and anisotropic, where isotropic for L2 norm and anisotropic for L1 norm. Based on many probabilistic model and Fourier Transforms Image deblurring can be solved. Here in this paper to improve the performance, we have used an adaptive regularization filtering and isotropic TV model Lp norm. Image deblurring is applicable in the areas such as medical image sensing, astrophotography, traffic signal monitoring, remote sensors, case investigation and even images that are taken using a digital camera / mobile cameras.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.10
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• pp.1859-1864
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• 2007

Existing barcode signal restoration algorithms are not robust to unmodeled outliers that may exist in scanned barcode images due to scratches, dirts, etc. In this paper, we describe a robust barcode signal restoration algorithm that uses the hybrid $L_1-L_2$ norm as a similarity measure. To optimze the similarity measure, we propose a modified iterative reweighted least squares algorithm based on the one step minimization of a quadratic surrogate function. In the simulations and experiments with barcode images, the proposed method showed better robustness than the conventional MSE based method. In addition, the proposed method converged quickly during optimization process.

• Journal of electromagnetic engineering and science
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• v.17 no.3
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• pp.113-119
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• 2017

The application of compressive sensing (CS) to a radar imaging system based on a frequency-scanned microstrip leaky wave antenna is investigated. First, an analytical model of the system matrix is formulated as the basis for the inversion algorithm. Then, $L_1-norm$ minimization is applied to the inverse problem to generate a range-azimuth image of the scene. Because of the antenna length, the near-field effect is considered in the CS formulation to properly image close-in targets. The resolving capability of the combined frequency-scanned antenna and CS processing is examined and compared to results based on the short-time Fourier transform and the pseudo-inverse. Both simulation and measurement data are tested to show the system performance in terms of image resolution.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38C no.6
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• pp.497-502
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• 2013

In this paper, we aim to evaluate the performance of the digital signal processing (DSP) algorithm used in [8] in order to improve the resolution of spectrometers with fixed number of low-cost, non-ideal filters. In such spectrometers, the resolution is limited by the number of filters. We aim to demonstrate via new experiments that the resolution improvement by six times over the conventional limit is possible by using the DSP algorithm as claimed by [8].

• Journal of the Optical Society of Korea
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• v.20 no.6
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• pp.752-761
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• 2016

Hyperspectral images are often contaminated with stripe noise, which severely degrades the imaging quality and the precision of the subsequent processing. In this paper, a variational model is proposed by employing spectral-spatial adaptive unidirectional variation and a sparse representation. Unlike traditional methods, we exploit the spectral correction and remove stripes in different bands and different regions adaptively, instead of selecting parameters band by band. The regularization strength adapts to the spectrally varying stripe intensities and the spatially varying texture information. Spectral correlation is exploited via dictionary learning in the sparse representation framework to prevent spectral distortion. Moreover, the minimization problem, which contains two unsmooth and inseparable $l_1$-norm terms, is optimized by the split Bregman approach. Experimental results, on datasets from several imaging systems, demonstrate that the proposed method can remove stripe noise effectively and adaptively, as well as preserve original detail information.