Non-Separable 3D Integer Wavelet Transform for Lossless Data Compression

Teerapong Orachon; Suvit Poomrittigul; Taichi Yoshida; Masahiro Iwahashi; Somchart Chokchaitam

doi:doi:10.11648/j.cssp.20140306.11

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Non-Separable 3D Integer Wavelet Transform for Lossless Data Compression

Teerapong Orachon, Suvit Poomrittigul, Taichi Yoshida, Masahiro Iwahashi, Somchart Chokchaitam

Published in Science Journal of Circuits, Systems and Signal Processing (Volume 3, Issue 6)

Received: 22 December 2014 Accepted: 8 January 2015 Published: 20 January 2015

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Abstract

This paper proposes a three-dimensional (3D) integer wavelet transform with reduced amount of rounding noise. Non-separable multi-dimensional lifting structures are introduced to decrease the total number of lifting steps. Since the lifting step contains a rounding operation, variance of the rounding noise generated due to the rounding operation inside the transform is reduced. This paper also investigates performance of the transform from various aspects such as 1) variance of the noise in frequency domain and those in pixel domain, 2) the rate distortion curve in lossy coding mode and the entropy rate in lossless coding mode, 3) computational time of the transforms, and 4) feature comparison with other methods. The proposed wavelet transform has a merit that its output signal, apart from the rounding noise, is exactly the same as the conventional separable structure which is a cascade of 1D structure. Due to this compatibility, it becomes possible to utilize legacy of previously designed 1D wavelet transforms with preferable properties such as the regularity. Furthermore, total amount of the rounding noise which is generated due to integer expression of signal values inside the transform is significantly reduced. This is because the total number of rounding operations is decreased by introducing the non-separable multi-dimensional lifting structure which includes multi-dimensional memory accessing. It contributes to increase coding performance of a system based on the 3D wavelet transform. As a result of experiments, it was observed that the proposed method increases performance of data compression of various 3D input signals.

Published in	Science Journal of Circuits, Systems and Signal Processing (Volume 3, Issue 6)
DOI	10.11648/j.cssp.20140306.11
Page(s)	35-46
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Wavelet, Transform, Lifting, 3D, Rounding, Coding

References

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APA Style

Teerapong Orachon, Suvit Poomrittigul, Taichi Yoshida, Masahiro Iwahashi, Somchart Chokchaitam. (2015). Non-Separable 3D Integer Wavelet Transform for Lossless Data Compression. Science Journal of Circuits, Systems and Signal Processing, 3(6), 35-46. https://doi.org/10.11648/j.cssp.20140306.11

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ACS Style

Teerapong Orachon; Suvit Poomrittigul; Taichi Yoshida; Masahiro Iwahashi; Somchart Chokchaitam. Non-Separable 3D Integer Wavelet Transform for Lossless Data Compression. Sci. J. Circuits Syst. Signal Process. 2015, 3(6), 35-46. doi: 10.11648/j.cssp.20140306.11

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AMA Style

Teerapong Orachon, Suvit Poomrittigul, Taichi Yoshida, Masahiro Iwahashi, Somchart Chokchaitam. Non-Separable 3D Integer Wavelet Transform for Lossless Data Compression. Sci J Circuits Syst Signal Process. 2015;3(6):35-46. doi: 10.11648/j.cssp.20140306.11

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@article{10.11648/j.cssp.20140306.11,
  author = {Teerapong Orachon and Suvit Poomrittigul and Taichi Yoshida and Masahiro Iwahashi and Somchart Chokchaitam},
  title = {Non-Separable 3D Integer Wavelet Transform for Lossless Data Compression},
  journal = {Science Journal of Circuits, Systems and Signal Processing},
  volume = {3},
  number = {6},
  pages = {35-46},
  doi = {10.11648/j.cssp.20140306.11},
  url = {https://doi.org/10.11648/j.cssp.20140306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cssp.20140306.11},
  abstract = {This paper proposes a three-dimensional (3D) integer wavelet transform with reduced amount of rounding noise. Non-separable multi-dimensional lifting structures are introduced to decrease the total number of lifting steps. Since the lifting step contains a rounding operation, variance of the rounding noise generated due to the rounding operation inside the transform is reduced. This paper also investigates performance of the transform from various aspects such as 1) variance of the noise in frequency domain and those in pixel domain, 2) the rate distortion curve in lossy coding mode and the entropy rate in lossless coding mode, 3) computational time of the transforms, and 4) feature comparison with other methods. The proposed wavelet transform has a merit that its output signal, apart from the rounding noise, is exactly the same as the conventional separable structure which is a cascade of 1D structure. Due to this compatibility, it becomes possible to utilize legacy of previously designed 1D wavelet transforms with preferable properties such as the regularity. Furthermore, total amount of the rounding noise which is generated due to integer expression of signal values inside the transform is significantly reduced. This is because the total number of rounding operations is decreased by introducing the non-separable multi-dimensional lifting structure which includes multi-dimensional memory accessing. It contributes to increase coding performance of a system based on the 3D wavelet transform. As a result of experiments, it was observed that the proposed method increases performance of data compression of various 3D input signals.},
 year = {2015}
}

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TY  - JOUR
T1  - Non-Separable 3D Integer Wavelet Transform for Lossless Data Compression
AU  - Teerapong Orachon
AU  - Suvit Poomrittigul
AU  - Taichi Yoshida
AU  - Masahiro Iwahashi
AU  - Somchart Chokchaitam
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DO  - 10.11648/j.cssp.20140306.11
T2  - Science Journal of Circuits, Systems and Signal Processing
JF  - Science Journal of Circuits, Systems and Signal Processing
JO  - Science Journal of Circuits, Systems and Signal Processing
SP  - 35
EP  - 46
PB  - Science Publishing Group
SN  - 2326-9073
UR  - https://doi.org/10.11648/j.cssp.20140306.11
AB  - This paper proposes a three-dimensional (3D) integer wavelet transform with reduced amount of rounding noise. Non-separable multi-dimensional lifting structures are introduced to decrease the total number of lifting steps. Since the lifting step contains a rounding operation, variance of the rounding noise generated due to the rounding operation inside the transform is reduced. This paper also investigates performance of the transform from various aspects such as 1) variance of the noise in frequency domain and those in pixel domain, 2) the rate distortion curve in lossy coding mode and the entropy rate in lossless coding mode, 3) computational time of the transforms, and 4) feature comparison with other methods. The proposed wavelet transform has a merit that its output signal, apart from the rounding noise, is exactly the same as the conventional separable structure which is a cascade of 1D structure. Due to this compatibility, it becomes possible to utilize legacy of previously designed 1D wavelet transforms with preferable properties such as the regularity. Furthermore, total amount of the rounding noise which is generated due to integer expression of signal values inside the transform is significantly reduced. This is because the total number of rounding operations is decreased by introducing the non-separable multi-dimensional lifting structure which includes multi-dimensional memory accessing. It contributes to increase coding performance of a system based on the 3D wavelet transform. As a result of experiments, it was observed that the proposed method increases performance of data compression of various 3D input signals.
VL  - 3
IS  - 6
ER  -

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Author Information

Teerapong Orachon

Department of Electrical Engineering, Nagaoka University of Technology, Nagaoka, Japan
Suvit Poomrittigul

Department of Computer Technology, Pathumwan Institute of Technology, Bangkok, Thailand
Taichi Yoshida

Department of Electrical Engineering, Nagaoka University of Technology, Nagaoka, Japan
Masahiro Iwahashi

Department of Electrical Engineering, Nagaoka University of Technology, Nagaoka, Japan
Somchart Chokchaitam

Department of Electrical Engineering, Thammasat University, Bangkok, Thailand

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APA Style

Teerapong Orachon, Suvit Poomrittigul, Taichi Yoshida, Masahiro Iwahashi, Somchart Chokchaitam. (2015). Non-Separable 3D Integer Wavelet Transform for Lossless Data Compression. Science Journal of Circuits, Systems and Signal Processing, 3(6), 35-46. https://doi.org/10.11648/j.cssp.20140306.11

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ACS Style

Teerapong Orachon; Suvit Poomrittigul; Taichi Yoshida; Masahiro Iwahashi; Somchart Chokchaitam. Non-Separable 3D Integer Wavelet Transform for Lossless Data Compression. Sci. J. Circuits Syst. Signal Process. 2015, 3(6), 35-46. doi: 10.11648/j.cssp.20140306.11

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AMA Style

Teerapong Orachon, Suvit Poomrittigul, Taichi Yoshida, Masahiro Iwahashi, Somchart Chokchaitam. Non-Separable 3D Integer Wavelet Transform for Lossless Data Compression. Sci J Circuits Syst Signal Process. 2015;3(6):35-46. doi: 10.11648/j.cssp.20140306.11

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@article{10.11648/j.cssp.20140306.11,
  author = {Teerapong Orachon and Suvit Poomrittigul and Taichi Yoshida and Masahiro Iwahashi and Somchart Chokchaitam},
  title = {Non-Separable 3D Integer Wavelet Transform for Lossless Data Compression},
  journal = {Science Journal of Circuits, Systems and Signal Processing},
  volume = {3},
  number = {6},
  pages = {35-46},
  doi = {10.11648/j.cssp.20140306.11},
  url = {https://doi.org/10.11648/j.cssp.20140306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cssp.20140306.11},
  abstract = {This paper proposes a three-dimensional (3D) integer wavelet transform with reduced amount of rounding noise. Non-separable multi-dimensional lifting structures are introduced to decrease the total number of lifting steps. Since the lifting step contains a rounding operation, variance of the rounding noise generated due to the rounding operation inside the transform is reduced. This paper also investigates performance of the transform from various aspects such as 1) variance of the noise in frequency domain and those in pixel domain, 2) the rate distortion curve in lossy coding mode and the entropy rate in lossless coding mode, 3) computational time of the transforms, and 4) feature comparison with other methods. The proposed wavelet transform has a merit that its output signal, apart from the rounding noise, is exactly the same as the conventional separable structure which is a cascade of 1D structure. Due to this compatibility, it becomes possible to utilize legacy of previously designed 1D wavelet transforms with preferable properties such as the regularity. Furthermore, total amount of the rounding noise which is generated due to integer expression of signal values inside the transform is significantly reduced. This is because the total number of rounding operations is decreased by introducing the non-separable multi-dimensional lifting structure which includes multi-dimensional memory accessing. It contributes to increase coding performance of a system based on the 3D wavelet transform. As a result of experiments, it was observed that the proposed method increases performance of data compression of various 3D input signals.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Non-Separable 3D Integer Wavelet Transform for Lossless Data Compression
AU  - Teerapong Orachon
AU  - Suvit Poomrittigul
AU  - Taichi Yoshida
AU  - Masahiro Iwahashi
AU  - Somchart Chokchaitam
Y1  - 2015/01/20
PY  - 2015
N1  - https://doi.org/10.11648/j.cssp.20140306.11
DO  - 10.11648/j.cssp.20140306.11
T2  - Science Journal of Circuits, Systems and Signal Processing
JF  - Science Journal of Circuits, Systems and Signal Processing
JO  - Science Journal of Circuits, Systems and Signal Processing
SP  - 35
EP  - 46
PB  - Science Publishing Group
SN  - 2326-9073
UR  - https://doi.org/10.11648/j.cssp.20140306.11
AB  - This paper proposes a three-dimensional (3D) integer wavelet transform with reduced amount of rounding noise. Non-separable multi-dimensional lifting structures are introduced to decrease the total number of lifting steps. Since the lifting step contains a rounding operation, variance of the rounding noise generated due to the rounding operation inside the transform is reduced. This paper also investigates performance of the transform from various aspects such as 1) variance of the noise in frequency domain and those in pixel domain, 2) the rate distortion curve in lossy coding mode and the entropy rate in lossless coding mode, 3) computational time of the transforms, and 4) feature comparison with other methods. The proposed wavelet transform has a merit that its output signal, apart from the rounding noise, is exactly the same as the conventional separable structure which is a cascade of 1D structure. Due to this compatibility, it becomes possible to utilize legacy of previously designed 1D wavelet transforms with preferable properties such as the regularity. Furthermore, total amount of the rounding noise which is generated due to integer expression of signal values inside the transform is significantly reduced. This is because the total number of rounding operations is decreased by introducing the non-separable multi-dimensional lifting structure which includes multi-dimensional memory accessing. It contributes to increase coding performance of a system based on the 3D wavelet transform. As a result of experiments, it was observed that the proposed method increases performance of data compression of various 3D input signals.
VL  - 3
IS  - 6
ER  -

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