• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.31 no.10C
• /
• pp.991-999
• /
• 2006

This paper shows that the support growth of an optimum (minimum mean square-error) scalar quantizer for a Laplacian density is logarithmic with the number of quantization points. Specifically, it is shown that, for a unit-variance Laplacian density, the ratio of the support-determining threshold of an optimum quantizer to $\frac 3{\sqrt{2}}1n\frac N 2$ converges to 1, as the number of quantization points grows. Also derived is a limiting upper bound that says that the optimum support cannot exceed the logarithmic growth by more than a constant. These results confirm the logarithmic growth of the optimum support that has previously been derived heuristically.

• Journal of the Institute of Electronics Engineers of Korea SP
• /
• v.49 no.2
• /
• pp.18-27
• /
• 2012

Optimal quantizers in conducting the entropy-constrained quantization for high bit rates have the lattice structure. The quantization process is simple due to the regular structure and various quantization algorithms are proposed depending on the lattice. In this paper, such a lattice vector quantization is implemented by using the sample-adaptive product quantizer (SAPQ). It is shown that several important lattices can be implemented by SAPQ and the lattice vector quantization can be performed by using a simple integer-transform function of scalar values within SAPQ. The performance of the proposed lattice SAPQ is compared to the entropy-constrained scalar quantizer and the entropy-constrained SAPQ (ECSAPQ) at a similar encoding complexity. Even though ECSAPQ shows a good performance at low bit-rates, lattice SAPQ shows better performance than the ECSAPQ case for a wide range of bit rates.

• Proceedings of the Korean Society of Broadcast Engineers Conference
• /
• 2019.06a
• /
• pp.114-115
• /
• 2019

This paper introduces an adaptive scalar quantization scheme for video coding technology. The method utilizes the property of the coefficient groups (CG) inside each transform block so that the dead-zone interval of the scalar quantizer is adaptively set up for different CGs. Its experimental results show that our proposed quantization scheme can achieve BDBR reduction of 4.75%, 5.93, and 5.16% for Y, Cb, and Cr channel respectively when encoding with HEVC.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.17 no.1
• /
• pp.107-113
• /
• 2017

This paper provides a new approach for modeling of vector quantizer(VQ) followed by analysis and design of subband codecs with imbedded VQ's. We compute the mean squared reconstruction error(MSE) which depend on N the number of entries in each codebook, k the length of each codeword, and on the filter bank(FB) coefficients in subband codecs. We show that the optimum M-band filter bank structure in presence of pdf-optimized vector quantizer can be designed by a suitable choice of equivalent scalar quantizer parameters. Specific design examples have been developed for two different classes of filter banks, paraunitary and the biorthogonal FB and the 2 channel case. These theoretical results are confirmed by Monte Carlo simulation.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.37 no.5A
• /
• pp.279-289
• /
• 2012

Characteristics, such as the support limit and distortions, of minimum mean-squared error (MSE) N-level uniform and nonuniform scalar quantizers are studied for the family of the generalized gamma density functions as N increases. For the study, MSE-optimal scalar quantizers are designed at integer rates from 1 to 16 bits/sample, and their characteristics are compared with corresponding asymptotic formulas. The results show that the support limit formulas are generally accurate. They also show that the distortion of nonuniform quantizers is observed to converge to the Panter-Dite asymptotic constant, whereas the distortion of uniform quantizers exhibits slow or even stagnant convergence to its corresponding Hui-Neuhoff asymptotic constant at the studied rate range, though it may stay at a close proximity to the asymptotic constant for the Rayleigh and Laplacian pdfs. Additional terms in the asymptote result in quite considerable accuracy improvement, making the formulas useful especially when rate is 8 or greater.

• Proceedings of the IEEK Conference
• /
• 2000.09a
• /
• pp.667-670
• /
• 2000

This paper provides a heuristic theory for modeling and analysis of vector quantization effects in 2-dimensional subband filter banks. This model is used as the basis for optimal filter bank design. The scalar non-linear gain-plus-additive noise quantization model can be used to represent each vector quantizer in 2-band subband codec. The validity and accuracy and of this analytic model is confirmed by comparing the calculated model quantization errors with actual simulation of the optimum LBG vector quantizer. Numerical design examples for the optimum separable paraunitary filter banks are suggested in this paper.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.29 no.1C
• /
• pp.129-139
• /
• 2004

This paper studies the support region of an optimum (minimum mean-squre error) fixed-rate scalar quantizer for a Weibull source. The support region is defined to be the interval determined by the outermost thresholds of a quantizer and plays an important role in its performance, and hence it motivates this study. The paper reports the following specific results. First, approximation formulas are derived for the outermost thresholds of optimum scalar quantizers for a Weibull distributions. Second, in the case of Rayleigh and exponential distributions the derived approximation formulas are compared for the evaluation of their accuracy with the true values of optimum quantizers. Numerical results show that the formula for the leftmost threshold stays within 1% of the true value for 128 and 256 quantization points or more, for Rayleigh and exponential distribution, respectively, while that for the rightmost threshold does so for 512 and 32 quantization points or more. These formulas exhibit increased accuracy with the number of quantization points. In conclusion, the formulas have high accuracy. The contribution of the paper consists in the derivation of closed accurate formulas for the support of optimum.

• Journal of Korea Multimedia Society
• /
• v.13 no.8
• /
• pp.1154-1162
• /
• 2010

Because it is easy to implement the scalar quantizer, it is used in various video coding systems. Although the scalar quantizer with a large quantization stepsize can reduce the amount of data, it has disadvantage that the reconstructed picture quality is poor. In this paper, we propose an efficient method which improves the coding performance by maintaining original quantization stepsize and increasing the number of quantization reconstruction levels. Simultaneously, for the purpose of solving the problem of transmitting the added symbol informations which is used to indicate the region of quantizer reconstruction level as the number of quantizer reconstruction level is increased, we also suggest the method to reduce the added informations. Therefore, for the intra-coded picture of H.264 video coding system, we generate the huffman codes for the symbol informations of quantization reconstruction regions by 4${\times}$4(horizontal 4 pixels, vertical pixels) block unit. Furthermore, for the inter-coded picture, we also generate the huffman codes for the symbol informations of quantization reconstruction regions by 8${\times}$8 blocks and 4${\times}$4 blocks within a macroblock. Adopting this method of reducing the added information by increasing the number of quantization reconstruction region, It is shown that the coding performance can be improved at the same bitrate.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.24 no.12B
• /
• pp.2391-2400
• /
• 1999

Vector quantizer (VQ) is an efficient data compression technique for low bit rate applications. However, the major disadvantage of VQ is its encoding complexity which increases dramatically as the vector dimension and bit rate increase. Even though one can use a modified VQ to reduce the encoding complexity, it is nearly impossible to implement such a VQ at a high bit rate or for a large vector dimension because of the enormously large memory requirement for the codebook and the very large training sequence (TS) size. To overcome this difficulty, in this paper we propose a novel structurally constrained VQ for the high bit rate and the large vector dimension cases in order to obtain VQ-level performance. Furthermore, this VQ can be extended to the low bit rate applications. The proposed quantization scheme has a form of feed-forward adaptive quantizer with a short adaptation period. Hence, we call this quantization scheme sample-adaptive product quantizer (SAPQ). SAPQ can provide a 2 ~3dB improvement over the Lloyd-Max scalar quantizers.

• Proceedings of the IEEK Conference
• /
• 2004.08c
• /
• pp.832-835
• /
• 2004

In this paper, we proposed a blind watermarking algorithm to use characteristics of a scalar quantizer which is similar with the recommended in the JPEG2000 and JPEG. This algorithm shifts a quantization index according to the value of each watermark bit to prevent losing the watermark information during the compression by quantization. Therefore, the watermark is embedded during the process of quantization, not an additional process for watermarking, and adaptively applied as an assigned quantizer according to application area. In the embedding process, a LFSR(Linear feedback shift register) is used to hide the watermarking positions. Therefore the embedded watermark can be extracted by only the owner who knows the initial value of LFSR without the original image. The experimental results showed that the proposed algorithm satisfies the robustness and imperceptibility corresponding to the major requirement of watermarking.