• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.9
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.7
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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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• v.16 no.1E
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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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• v.45 no.1
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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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• v.46 no.3
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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.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.2
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.7A
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• pp.794-806
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• 2004

This paper deals with correction of frequency offset and analysis of quantization angle noise in the IEEE 802.1la OFDM system. The rotation phase per symbol due to the carrier frequency offset is estimated from auto-correlation of the short Preambles, which are over-sampled for the reduction of noise in OFDM signals. The pilot signals are introduced to estimate the rotation phase per OFDM symbol due to estimation error of the carrier frequency offset and the sampling frequency onset. During the estimation and correction of the frequency onsets, a CORDIC processor and a look-up table are used for the conversion between a rotation phase and its complex number. Being calculated by a limited number of bits in the CORDIC processor and the look-up table, the rotation phase and its complex number have quantization angle errors. The quantization errors are analyzed as SNR (signal to noise ratio) due to the quantization bit numbers. The minimum bit number is suggested to meet the specification of IEEE 802.1la properly. Finally, the quantization errors are evaluated through simulations on number of quantization bits and SNR of received signals.

• IEIE Transactions on Smart Processing and Computing
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• v.4 no.6
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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.

• Proceedings of the KIEE Conference
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• 2003.07d
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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.

• Journal of the Korea Society of Computer and Information
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• v.19 no.6
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• pp.11-17
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• 2014

While safe and convenient, ultrasound imaging analysis is often criticized by its subjective decision making nature by field experts in analyzing musculoskeletal system. In this paper, we propose a new automatic method to extract muscle area using ART2 neural network based quantization. A series of image processing algorithms such as histogram smoothing and End-in search stretching are applied in pre-processing phase to remove noises effectively. Muscle areas are extracted by considering various morphological features and corresponding analysis. In experiment, our ART2 based Quantization is verified as more effective than other general quantization methods.