• Proceedings of the KSMRM Conference
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• 2002.11a
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• pp.96-96
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• 2002

목적： MRI 시스템의 비약적인 발전으로 인하여, 시스템에서 발생되는 noise가 상당히 줄었다. 따라서 시스템에서 발생되는 random noise뿐만 아니라 sampling 과정에서 발생되는 quantization noise도 중요하게 고려하여야 할 요소가 되었다. 특히, MRI 신호의 경우 dynamic range가 크기 때문에 bit 수가 큰 ADC를 이용하여 데이터를 얻어야 한다. 그러나, bit 수가 크고 높은 sampling rate를 갖는 ADC의 경우 가격이 높을 뿐만 아니라, 기존의 장비를 교체해야하는 어려움이 있다. 본 연구는 oversampling과 quantization noise와의 관계를 컴퓨터 시뮬레이션을 통하여 알아보고, MRI영상에서 oversampling을 통하여 quantization noise를 줄임으로써 영상의 질을 개선하고자 한다.

• Proceedings of the KSMRM Conference
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• 2002.11a
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• pp.75-75
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• 2002

목적： 고자장 자기공명영상 시스템 등으로 신호대잡음비가 향상됨에 따라 데이터 측정에서 analog-to-digital converter (ADC)의 quantization noise 가 중요한 시스템 사양으로 부각되고 있다. 특히 자기공명영상은 공간주파수 영역에서 데이터를 측정하기 때문에 dc와 ac간의 신호 차이가 매우 크며, 이러한 dynmic range는 3-D 영상에서 더욱 커진다. 본 연구에서는 다양한 자기총명 영상기법 및 실험 파라미터에 따른 신호의 dynamic range와 ADC의 bit 수에 따른 quantization noise를 살펴봄으로써, 주어진 시스템에 적합한 ADC의 bit 수를 분석하고자 한다. 대상 및 방법： 펄스 시퀀스의 종류, 파라미터, 2D/3D 등에 따른 각 신호의 크기를 수학적으로 모델링하여 신호의 크기를 예측하였다. 또한 whole body MRI 시스템에서 실험을 통하여 신호의 크기를 비교하였다. ADC의 quantization noise를 실험과 시뮬레이션을 통하여 살펴보았다. 시뮬레이션은 test 영상을 Inverse FFT 하여 spatial frequency domain data를 만든 후, 다양한 bit 수의 ADC로 quantization을 한 후 다시 영상을 재구성하였다. 재구성된 영상과 원영상 간의 error가 quantization noise가 된다. 또한 이러한 error가 주파수 영역에서의 error 값과 일치하는지를 확인하였다.

• Proceedings of the IEEK Conference
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• 2000.11d
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• pp.155-158
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• 2000

In this paper, the quantization noise in block-based video coding is analyzed, and a post-processing method based on the analysis is presented for reducing the quantization noise by using a wavelet transform(WT). In the proposed method, the quantization noise is considered as the sum of a blocking noise expressed as a deterministic profile and the random remainder noise. Each noise is removed in a viewpoint of image restoration using a 1-D WT, which yields a regularized differentiation. The blocking noise first is reduced by weakening the strength of each blocking noise component that appears as an impulse in the first scale wavelet domain. The impulse strength estimation is performed using median filter, quantization parameter(QP), and local activity. The remainder noise, which is considered as a white noise at non-edge pixels, then is reduced by soft-thresholding. The experimental results show that the proposed method yields better performance in terms if subjective quality as well as PSNR performance over VM post-filter in MPEG-4 for all test sequences of various compression ratios. We also present a fast post-processing in spatial domain equivalent to that in wavelet domain for real-time application.

• Investigative Magnetic Resonance Imaging
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• v.8 no.1
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• pp.42-49
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• 2004

Purpose : The quantization noise in magnetic resonance imaging (MRI) systems is analyzed. The signal-to-quantization noise ratio (SQNR) in the reconstructed image is derived from the level of quantization in the signal in spatial frequency domain. Based on the derived formula, the SQNRs in various main magnetic fields with different receiver systems are evaluated. From the evaluation, the quantization noise could be a major noise source determining overall system signal-to-noise ratio (SNR) in high field MRI system. A few methods to reduce the quantization noise are suggested. Materials and methods : In Fourier imaging methods, spin density distribution is encoded by phase and frequency encoding gradients in such a way that it becomes a distribution in the spatial frequency domain. Thus the quantization noise in the spatial frequency domain is expressed in terms of the SQNR in the reconstructed image. The validity of the derived formula is confirmed by experiments and computer simulation. Results : Using the derived formula, the SQNRs in various main magnetic fields with various receiver systems are evaluated. Since the quantization noise is proportional to the signal amplitude, yet it cannot be reduced by simple signal averaging, it could be a serious problem in high field imaging. In many receiver systems employing analog-to-digital converters (ADC) of 16 bits/sample, the quantization noise could be a major noise source limiting overall system SNR, especially in a high field imaging. Conclusion : The field strength of MRI system keeps going higher for functional imaging and spectroscopy. In high field MRI system, signal amplitude becomes larger with more susceptibility effect and wider spectral separation. Since the quantization noise is proportional to the signal amplitude, if the conversion bits of the ADCs in the receiver system are not large enough, the increase of signal amplitude may not be fully utilized for the SNR enhancement due to the increase of the quantization noise. Evaluation of the SQNR for various systems using the formula shows that the quantization noise could be a major noise source limiting overall system SNR, especially in three dimensional imaging in a high field imaging. Oversampling and off-center sampling would be an alternative solution to reduce the quantization noise without replacement of the receiver 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.11 no.6
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• pp.411-420
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• 1986

Quantization noise of nonadaptive Linear Delta Modulation(LDM) and adaptive Constant Factor Delta Modulation(CFDM) systems is studied. The formulas for quantization noise of CFDM system are derived on the basis of the rusults of LDM. And the output signal-to-quantization noise ratios(SNR) in LDM and CFDM systems are calculated in the range of bit rates from 16[Kb/s] to 96[Kb/s]. By comparing LDM and CFDM, it is known that the adaptive DM is superior to non-adaptive DM by 8[dB] when bit rate is 20[Kb/s] and SNR advantage increases to 14[dB] when bit rate is 56[Kb/s]. All the theoretical results agree well with the experimental results.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.12A
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• pp.2085-2091
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• 2001

In lossy compression method, the transformed coefficients are quantized. This results in the quantization noise. The video image quality and bit rate is closely related with the quantization step. In this paper, we proposed a new quantization function for the improved performance. The DC value of each macroblock is compensated depending on the magnitude of DC quantization error. It is implemented very low bit-rate video coding, i.e., H.26L. The experimental result is useful when the object motion is not severe.

• 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.

• 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.