• Communications for Statistical Applications and Methods
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• v.23 no.1
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• pp.71-83
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• 2016

In this paper we discuss a deconvolution density estimator obtained using the support vector machines (SVM) and Tikhonov's regularization method solving ill-posed problems in reproducing kernel Hilbert space (RKHS). A remarkable property of SVM is that the SVM leads to sparse solutions, but the support vector deconvolution density estimator does not preserve sparsity as well as we expected. Thus, in section 3, we propose another support vector deconvolution estimator (method II) which leads to a very sparse solution. The performance of the deconvolution density estimators based on the support vector method is compared with the classical kernel deconvolution density estimator for important cases of Gaussian and Laplacian measurement error by means of a simulation study. In the case of Gaussian error, the proposed support vector deconvolution estimator shows the same performance as the classical kernel deconvolution density estimator.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.951-959
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• 2014

Recently Hazelton and Turlach (2009) proposed a weighted kernel density estimator for the deconvolution problem. In the case of Gaussian kernels and measurement error, they argued that the weighted kernel density estimator is a competitive estimator over the classical deconvolution kernel estimator. In this paper we consider weighted kernel density estimators when sample observations are contaminated by double exponentially distributed errors. The performance of the weighted kernel density estimators is compared over the classical deconvolution kernel estimator and the kernel density estimator based on the support vector regression method by means of a simulation study. The weighted density estimator with the Gaussian kernel shows numerical instability in practical implementation of optimization function. However the weighted density estimates with the double exponential kernel has very similar patterns to the classical kernel density estimates in the simulations, but the shape is less satisfactory than the classical kernel density estimator with the Gaussian kernel.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.265-276
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• 1996

The nonparametric deconvolution problems are studied to recover an unknown density when the data are contaminated with Gaussian error. We propose the estimator which is a linear combination of kernel type estimates of derivertives of the observed density function. We show that this estimator is consistent and also consider the properties of estimator at small sample by simulation.

• Communications for Statistical Applications and Methods
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• v.19 no.4
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• pp.517-526
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• 2012

In this paper a support vector method is proposed for use when the sample observations are contaminated by a normally distributed measurement error. The performance of deconvolution density estimators based on the support vector method is explored and compared with kernel density estimators by means of a simulation study. An interesting result was that for the estimation of kurtotic density, the support vector deconvolution estimator with a Gaussian kernel showed a better performance than the classical deconvolution kernel estimator.

• Journal of radiological science and technology
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• v.45 no.2
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• pp.145-150
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• 2022

The main purpose of this work was to restore the blurry chest CT images by applying a blind deconvolution algorithm. In general, image restoration is the procedure of improving the degraded image to get the true or original image. In this regard, we focused on a blind deblurring approach with chest CT imaging by using digital image processing in MATLAB, which the blind deconvolution technique performed without any whole knowledge or information as to the fundamental point spread function (PSF). For our approach, we acquired 30 chest CT images from the public source and applied three type's PSFs for finding the true image and the original PSF. The observed image might be convolved with an isotropic gaussian PSF or motion blurring PSF and the original image. The PSFs are assumed as a black box, hence restoring the image is called blind deconvolution. For the 30 iteration times, we analyzed diverse sizes of the PSF and tried to approximate the true PSF and the original image. For improving the ringing effect, we employed the weighted function by using the sobel filter. The results was compared with the three criteria including mean squared error (MSE), root mean squared error (RMSE) and peak signal-to-noise ratio (PSNR), which all values of the optimal-sized image outperformed those that the other reconstructed two-sized images. Therefore, we improved the blurring chest CT image by using the blind deconvolutin algorithm for optimal approach.

• Communications for Statistical Applications and Methods
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• v.29 no.2
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• pp.277-286
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• 2022

Due to the uniquely slow convergence speed of the EM algorithm, it suffers form a lot of processing time until the desired deconvolution image is obtained when the image is large. To cope with the problem, in this paper, an immediate solution of the EM algorithm is provided under the Gaussian image model. It is derived by finding the recurrent formular of the EM algorithm and then substituting the results repeatedly. In this paper, two types of immediate soultion of image deconboution by EM algorithm are provided, and both methods have been shown to work well. It is expected that it free the processing time of image deconvolution because it no longer requires an iterative process. Based on this, we can find the statistical properties of the restored image at specific iterates. We demonstrate the effectiveness of the proposed method through a simple experiment, and discuss future concerns.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10c
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• pp.336-338
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• 1998

This paper presents a novel neural network structure to the blind deconvolution task where the input (source) to a system is not available and the source has any type of distribution including sparse distribution. We employ multiple sensors so that spatial information plays a important role. The resulting learning algorithm is linear so that it works for both sub-and super-Gaussian source. Moreover, we can successfully deconvolve the mixture of a sparse source, while most existing algorithms [5] have difficulties in this task. Computer simulations confirm the validity and high performance of the proposed algorithm.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.35 no.2
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• pp.101-107
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• 2022

This study proposes the deconvolution method for the nanoindentation test results of geopolymer employing the Gaussian mixture model. Geopolymer has been studied extensively as an alternative construction material because it emits relatively lower CO₂ compared to ordinary Portland cement. Geopolymer is made of aluminosilicate and alkaline solution, and the Si/Al molar ratio affects its mechanical properties. Previous studies revealed that the Si/Al molar ratio of 1.8~2.0 results in the highest compressive strength, and the Si/Al molar ratio over 1.8 degrades the compressive strength of geopolymer severely; however the reason for the compressive strength degradation is still unclear. To understand the effect of the Si/Al molar ratio on the geopolymer structure, this study exploits the nanoindentation. The phase deconvolution of the indent modulus data is successful using the Gaussian mixture model, and it is observed that the Si/Al molar ratio alters the homogeneity of the geopolymer. Geopolymer becomes more homogeneous up to an Si/Al molar ratio of 1.8 at which geopolymer exhibits the highest compressive strength. The examination of this study is assumed to be adopted as evidence of strength degradation by the Si/Al ratio higher than the optimum value.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.1
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• pp.13-20
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• 2005

This paper addresses a new blind channel equalization method using fourth-order cumulants of channel inputs and a three-layer neural network equalizer. The proposed algorithm is robust with respect to the existence of heavy Gaussian noise in a channel and does not require the minimum-phase characteristic of the channel. The transmitted signals at the receiver are over-sampled to ensure the channel described by a full-column rank matrix. It changes a single-input/single-output (SISO) finite-impulse response (FIR) channel to a single-input/multi-output (SIMO) channel. Based on the properties of the fourth-order cumulants of the over-sampled channel inputs, the iterative algorithm is derived to estimate the deconvolution matrix which makes the overall transfer matrix transparent, i.e., it can be reduced to the identity matrix by simple recordering and scaling. By using this estimated deconvolution matrix, which is the inverse of the over-sampled unknown channel, a three-layer neural network equalizer is implemented at the receiver. In simulation studies, the stochastic version of the proposed algorithm is tested with three-ray multi-path channels for on-line operation, and its performance is compared with a method based on conventional second-order statistics. Relatively good results, withe fast convergence speed, are achieved, even when the transmitted symbols are significantly corrupted with Gaussian noise.

• Journal of Astronomy and Space Sciences
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• v.39 no.4
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• pp.127-139
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• 2022

Irregular mare patches (IMPs), recently discovered on the Moon, are eruptions of magma on the lunar surface, and their origins are still in question. While prior studies on IMPs have mainly focused on optical image analysis, in this study, an analysis of the characteristics of minerals is performed exemplary for the first time. Modified Gaussian model (MGM) deconvolution was applied to the infrared spectrum to confirm the properties of the mafic mineral. Mafic minerals were analyzed for 6 olivine-rich (Ol-rich) IMPs out of 91 currently reported, and only 4 of them yielded results of significance. All four sites showed more abundance of Fe than Mg, and manifested a weak relationship with Mg-suite rock. However, a problem was discovered during the MGM application process due to pilot implementation. In order to solve this problem, it is required to adjust the MGM initial condition settings more precisely and to increase the signal to noise ratio of the observation data. Moreover, it is necessary to analyze the mineral properties for all IMPs considering minerals other than Ol and utilize them to deduce the origin of the IMPs.