• 전자공학회논문지B
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• 제30B권9호
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• pp.54-63
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• 1993

Quantization error, generated by the quantization process of an image, is inherent in computer vision. Because, especially in stereo vision, the quantization error in a 2-D image results in position errors in the reconstructed 3-D scene, it is necessary to analyze it mathematically. In this paper, the analysis of the probability density function (pdf) of quantization error for a line-based stereo matching scheme is presented. We show that the theoretical pdf of quantization error in the reconstructed 3-D position information has more general form than the conventional analysis for pixel-based stereo matching schemes. Computer simulation is observed to surpport the theoretical distribution.

• 한국통신학회논문지
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• 제21권7호
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• pp.1685-1695
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• 1996

The postprocessing of compressed images based on the projections onto convex sets and the constrained minimization imposes several constraints on the procesed data. The quantization constraint has been commonly used in various algorithms. Quantization is many-to-one mapping, by which all the dat in a quantization region are mapped to the corresponding representative level. The basic idea behind the projection onto the QCS(quantization constraint set) is to prevent the processed data from diverging from the original quantization region in order to redue the artifacts caused by filtering in postprocessing. However, there have been few efforts to analye the POQCS(projection onto the QCS). This paper analyzed mathematically the POQCS of filtered data from the viewpoint of minimizing the mean square error. Our analysis shows that a proper filtering technique followed by the POQCS can reduce the quantization distortion. In the conventional POQCS, the outside data of each quantization region are mapped into the corresponding boundary. Our analysis also shows that mappingthe outside data to the boundary of a subregion of the quantization region yields lower distortion than does the mapping to the boundary of the original region. In addition, several examples and discussions on the theory are introduced.

• The Journal of the Acoustical Society of Korea
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• 제16권1E호
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• pp.41-48
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• 1997

The very purpose of subband codec is the attainment of data rate compression through the use of quantizer and optimum bit allocation for each decimated signal. Yet the question of floating-point quantization effects in subband codec has received scant attention. There has been no direct focus on the analysis of quantization errors, nor on design with quantization errors embedded explicitly in the criterion. This paper provides a rigorous theory for the modelling, analysis and optimum design of the general M-band subband codec in the presence of the floating-point quantization noise. The floating-point quantizers are embedded into the codec structure by its equivalent multiplicative noise model. We then decompose the analysis and synthesis subband filter banks of the codec into the polyphase form and construct an equivalent time-invariant structure to compute exact expression for the mean square quantization error in the reconstructed an equivalent time-invariant structure to compute exact expression for the mean square quantization error in the reconstructed output. The optimum design criteria of the subband codec is given to the design of the analysis/synthesis filter bank and the floating-point quantizer to minimize the output mean square error. Specific optimum design examples are developed with two types of filter of filter banks-orthonormal and biorthogonal filter bank, along with their perpormance analysis.

• ETRI Journal
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• 제45권1호
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• pp.119-130
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• 2023

We propose a quantized gradient search algorithm that can achieve global optimization by monotonically reducing the quantization step with respect to time when quantization is composed of integer or fixed-point fractional values applied to an optimization algorithm. According to the white noise hypothesis states, a quantization step is sufficiently small and the quantization is well defined, the round-off error caused by quantization can be regarded as a random variable with identically independent distribution. Thus, we rewrite the searching equation based on a gradient descent as a stochastic differential equation and obtain the monotonically decreasing rate of the quantization step, enabling the global optimization by stochastic analysis for deriving an objective function. Consequently, when the search equation is quantized by a monotonically decreasing quantization step, which suitably reduces the round-off error, we can derive the searching algorithm evolving from an optimization algorithm. Numerical simulations indicate that due to the property of quantization-based global optimization, the proposed algorithm shows better optimization performance on a search space to each iteration than the conventional algorithm with a higher success rate and fewer iterations.

• ETRI Journal
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• 제46권3호
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• pp.367-378
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• 2024

We propose a number-theory-based quantized mathematical optimization scheme for various NP-hard and similar problems. Conventional global optimization schemes, such as simulated and quantum annealing, assume stochastic properties that require multiple attempts. Although our quantization-based optimization proposal also depends on stochastic features (i.e., the white-noise hypothesis), it provides a more reliable optimization performance. Our numerical analysis equates quantization-based optimization to quantum annealing, and its quantization property effectively provides global optimization by decreasing the measure of the level sets associated with the objective function. Consequently, the proposed combinatorial optimization method allows the removal of the acceptance probability used in conventional heuristic algorithms to provide a more effective optimization. Numerical experiments show that the proposed algorithm determines the global optimum in less operational time than conventional schemes.

• 대한전기학회논문지
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• 제43권2호
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• pp.318-329
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• 1994

This paper deals with the finite wordlength effect on the performance of digital PID controllers. The finite wordlength, one of the major limitation factors in digital controllers, results on two kinds of quantization error : the signal quantization error and the coefficient quantization error. This paper derives the variance of the plant output due to the signal quantization error. Using stability margins as performance criterion, the statistical wordlength concept is adopted for coefficient wordlength selection. Finally, the experimental results exhibit satisfactory performance of the digital PID controller with statistical coefficient wordlength.

• 한국통신학회논문지
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• 제29권7A호
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• pp.794-806
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• 2004

본 논문에서는 IEEE 802.11a의 OFDM 통신시스템에 대한 송수신 주파수편차의 교정기법을 연구하고 편차주파 수들의 교정오차에 의한 잡음을 분석한다. 반송주파수편차에 의한 심볼당 회전위상을 짧은 훈련신호(short preamble)의 자기상관에서 추정한다. 잡음의 영향을 줄이기 위하여 짧은 훈련신호(short preamble)를 과도표본화 (over-sampling)한다. 파일롯(pilot) 신호를 도입하여 추정된 반송주파수편차의 오차와 표본화 주파수편차에 의한 OFDM 심볼당 회전위상을 추정한다. 이러한 회전위상의 추정과 교정에 CORDIC(Coordinated Rotational Digital Computer) 프로세서 또는 각도와 복소수의 환산표를 사용하고 이것들의 구현기법과 장단점을 비교한다. 복소수와 위상은 CORDIC 프로세서와 환산표에서 한정된 비트(bit) 개수로 계산되므로 각도양자화 오차가 있게 된다. 비트개수에 따른 각도양자화 오차를 OFDM 신호의 SNR로 나타내고 IEEE 802.11a의 편차주파수 교정에서 요구되는 최소한의 비트 개수를 제시한다. 끝으로, 모의실험을 통하여 짧은 훈련신호로 반송주파수편차를 추정하고 CORDIC 프로세서와 환산표에서 사용된 비트 개수에 따른 양자화 잡음을 검증한다.

• IEIE Transactions on Smart Processing and Computing
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• 제4권6호
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• pp.391-402
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• 2015

In this paper, we present implementation of backward movement control of truck-trailer vehicles using a fuzzy mode-based control scheme considering practical constraints and computational overhead. We propose a fuzzy feedback controller where output is predicted with the delay of a unit sampling period. Analysis and design of the proposed controller is very easy, because it is synchronized with sampling time. Stability analysis is also possible when quantization exists in the implementation of fuzzy control architectures, and we show that if the trivial solution of the fuzzy control system without quantization is asymptotically stable, then the solutions of the fuzzy control system with quantization are uniformly ultimately bounded. Experimental results using a toy truck show that the proposed control system outperforms a conventional system.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 하계학술대회 논문집 D
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• pp.2783-2785
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• 2003

In multi-dimensional magnetic resonance imaging, data is obtained in the spatial frequency domain. Since the signal variation in the spatial frequency domain is much larger than that in the spatial domain, analog-to-digital converts with wide conversion bits are required. In this paper, the quantization noise in magnetic resonance imaging is analyzed. The signal-to-quantization noise ratio(SQNR) in the reconstructed image is derived from the level of quantization in the data acquisition. Since the quantization noise is proportional to the signal amplitude, it becomes more dominant in high field imaging. Using the derived formula the SQNR for several MRI systems are evaluated, and it is shown that the quantization noise can be a limiting factor in high field imaging, especially in three dimensional imaging in magnetic resonance imaging.

• 한국컴퓨터정보학회논문지
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• 제19권6호
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• pp.11-17
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• 2014

초음파 영상은 미세한 명암도 차이 등에 의해 분석 과정에서 근육 영역의 위치와 크기를 판단하는데 어려움이 발생하고 이로 인해 근육 영역을 파악하는데 주관성이 개입된다. 본 논문에서는 근육 영역을 객관적으로 분석하기 위해ART2 신경망을 적용하여 양자화를 수행한 후, 국부적 영역에서 근육 영역을 추출한다. 초음파 영상에서 히스토그램 평활화와 엔드인 탐색 알고리즘을 적용하여 명암도의 분포와 밝기 값을 보정한 후, ART2 신경망을 이용하여 유사한 영역을 클러스터링 한다. 클러스터링 된 각 영역의 크기, 위치 및 명암도 정보를 분석하여 피하지방, 근막, 기타 배경 영역으로 분류한다. 최종적인 근육 영역은 근막 내부 객체들 간의 거리, 각도를 이용하여 추출된다. 실제 초음파 영상 대상 실험 결과, 일반적인 클러스터링 기법을 적용한 방법 보다 ART2 기반 양자화와 제안된 영역 확장 기법으로 근육 영역을 추출하고 분석하는 것이 효율적임을 확인하였다.