• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.93-100
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• 2012

In this paper, we present a strongly convergent parallel projection algorithm by introducing some parameter sequences for convex feasibility problem. To prove the strong convergence in a simple way, we transmit the parallel algorithm in the original space to an alternating one in a newly constructed product space. Thus, the strong convergence of the parallel projection algorithm is derived with the help of the alternating one under some parametric controlling conditions.

• Journal of information and communication convergence engineering
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• v.16 no.1
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• pp.17-22
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• 2018

In massive multiple-input multiple-output (MIMO) systems, linear channel estimation algorithms are widely applied owing to their simple structures. However, they may cause pilot contamination, which affects the subsequent data detection performance. Therefore, herein, for an uplink multicell massive multiuser MIMO system, we consider using an alternating projection (AP) for channel estimation to eliminate the effect of pilot contamination and improve the performance of data detection in terms of the bit error rates as well. Even though the AP is nonlinear, it iteratively searches the best solution in only one dimension, and the computational complexity is thus modest. We have analyzed the mean square error with respect to the signal-to-interference ratios for both the cooperative and non-cooperative multicell scenarios. From the simulation results, we observed that the channel estimation results via the AP benefit the following signal detection more than that via the least squares for both the cooperative and non-cooperative multicell scenarios.

• Journal of the Korea Institute of Military Science and Technology
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• v.12 no.1
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• pp.97-105
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• 2009

In this paper, the performance of AP(Alternating Projection) and EM(Expectation Maximization) algorithms is investigated in terms of detection of multiple signals, resolvability of coherent signals and the efficiency of sensor array processing. The basic idea of these algorithms is utilization of relaxation technique of successive 1D maximization to solve a direction finding problem by maximizing the multidimensional likelihood function. It means that the function is maximized over only for a single parameter while the other parameters are fixed at each step of the iteration. According to simulation results, the algorithms showed good performance for both incoherent and coherent multiple signals. Moreover, some advantages are identified for direction finding with very small samples and fast convergence. The performance of AP algorithm is compared with that of EM using multiple criteria such as the number of sensor, SNR, the number of samples, and convergence speed over uniform circular array. It is resulted AP algorithm is superior to EM overally except for one criterion, convergence speed. Especially, for EM algorithm there is no performance difference between incoherent and coherent case. In conclusion, AP and EM are viable and practical alternatives, which can be applied to a direction under due to the resolvability of multi-path signals, reliable performance and no troublesome eigen-decomposition of the sample-covariance matrix.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.11
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• pp.1-11
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• 1998

We present somple block methods for blind maximal ratio combining (MRC) based on a maximum likelihood (ML) principle and finite alphabet properties (FAP) inherent in digital communication systems. The methods can provide accurate estimates of channel parameters even with a small subset of data, thus realizing nearly perfect combining. The channel parameters of diversity branches and the data sequence are estimated simultaneously by using an alternating projection technique. Two different methods, that is, (1) Joint combining and data sequence estimation(JC-DSE) method and (2) Pre-combining and blind phase estimation (PC-BPE) method are presented. Efficient initiallization schemes that can assure the convergence to the global optimum are also presented. Simulation results demonstrate the performance of two methods on the symbol error rate (SER) and the estimated accuracy of the channel parameters.

• Journal of the Korea Society of Computer and Information
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• v.22 no.11
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• pp.25-30
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• 2017

In this paper, We proposed an effective demosaicking method for single chip RGB-NIR sensors to recover RGB and NIR images. As the method operates in the spatial frequency domain, the frequency domain characteristics of the sampled CFA data are investigated. Using the luminance signal in the frequency domain and the chrominance signals are processed separately with different filters. The simulated images using the real images are compared with other state-of-art methods. As a result, the proposed demosaicking method resulted an effective calculation by a single processing which the existing alternating projection method requires repeated calculation.

• The Journal of the Acoustical Society of Korea
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• v.38 no.5
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• pp.522-533
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• 2019

The compressive sensing model for range-Doppler estimation can be expressed as an under-determined linear system y = Ax. To find the solution of the linear system with the compressive sensing method, matrix A should be sufficiently incoherent and x to be sparse. In this paper, we propose a transmission waveform design method that maintains the bandwidth required by the sonar system while lowering the mutual coherence of the matrix A so that the matrix A is incoherent. The proposed method combines two methods of optimizing the sensing matrix with the alternating projection and suppressing unwanted frequency bands using the DFT (Discrete Fourier Transform) matrix. We compare range-Doppler estimation performance of existing waveform LFM(Linear Frequency Modulated) and designed waveform using the matched filter and the compressive sensing method. Simulation shows that the designed transmission waveform has better detection performance than the existing waveform LFM.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.131-164
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• 2024

In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite family of τ-demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertial extrapolation steps and adaptive non-monotonic step sizes. Under some appropriate conditions that are imposed on the parameters, the weak and linear convergence results of the proposed iterative scheme are established. Furthermore, we present some numerical examples and application of our proposed methods in comparison with other existing iterative methods. In order to show the practical applicability of our method to real word problems, we show that our algorithm has better restoration efficiency than many well known methods in image restoration problem. Our proposed iterative method generalizes and extends many existing methods in the literature.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.12B
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• pp.2369-2381
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• 1999

In this paper, we propose an iterative algorithm for reducing the blocking artifact in block transform-coded images by using a wavelet transform. In the proposed method, an image is considered as a set of one-dimensional horizontal and vertical signals and one-dimensional wavelet transform is utilized in which the mother wavelet is the first order derivative of a Gaussian like function. The blocking artifact is reduced by removing the blocking component, that causes the variance at the block boundary position in the first scale wavelet domain to be abnormally higher than those at the other positions, using a minimum mean square error (MMSE) filter in the wavelet domain. This filter minimizes the MSE between the ideal blocking component-free signal and the restored signal in the neighborhood of block boundaries in the wavelet domain. It also uses local variance in the wavelet domain for pixel adaptive processing. The filtering and the projection onto a convex set of quantization constraint are iteratively performed in alternating fashion. Experimental results show that the proposed method yields not only a PSNR improvement of about 0.56-1.07 dB, but also subjective quality nearly free of the blocking artifact and edge blur.