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

| Peer-Reviewed

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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), 2015. Published by Science Publishing Group

Keywords

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

References

[1]	Chao He, Dong, J., Zheng, Y. F., Zhigang Gao: Optimal 3-D coefficient tree structure for 3-D wavelet video coding, IEEE Trans. Circuits and Systems for Video Technology, vol.13, Issue 10, pp.961-972 (2003)
[2]	Aggoun, A.: Compression of 3D integral images using 3D wavelet transform, IEEE Journal of Display Technology, vol.7, Issue 11, pp.586-592 (2011)
[3]	B. Penna, T. Tillo, E. Magli, G. Olmo: Progressive 3-D coding of hyperspectral images based on JPEG 2000, IEEE Geoscience, Remote Sensing Letters, vol.3, issue 1, pp.125-129 (2006)
[4]	Z. Xiong, X. Wu, S. Cheng, J. Hua:Lossy-to-lossless compression of medical volumetric data using three-dimensional integer wavelet transforms, IEEE Trans Medical Imaging, 22 (3), pp.459-70 (2003)
[5]	ISO / IEC FCD 15444-1, Joint Photographic Experts Group: JPEG 2000 image coding system, (March 2000)
[6]	Skodras, A., Christopoulos, C., Ebrahimi, T.: The JPEG 2000 still image compression standard. IEEE Signal ProcessingMagazine, 18, pp.36-58 (2001)
[7]	A. Descampe, F. Devaux, G. Rouvroy, J. D. Legat, J. J. Quisquater and B. Macq: A flexible hardware JPEG 2000 decoder for digital cinema, IEEE Trans. Circuits and Systems for Video Technology, vol. 16, issue 11, pp.1397-1410 (Nov. 2006)
[8]	Kaneko, K., Ohta, N.: 4K applications beyond digital cinema. In: Proc. Int. Conf. Virtual Syst. Multimedia, pp. 133-136 (2010)
[9]	C. Chrysafis, A. Ortega: Line-based, reduced memory, wavelet image compression, IEEE Trans. Image Processing, vol.9, no.3, pp.378-389 (March 2000)
[10]	G. Shi, W. Liu, Li Zhang and Fu Li: An efficient folded architecture for lifting-based discrete wavelet transform, IEEE Trans. Circuits, Systems II express briefs, vol.56, no.4, pp.290-294 (April 2009)
[11]	Bing-Fei Wu, Chung-Fu Lin: A high-performance and memory-efficient pipeline architecture for the 5/3 and 9/7 discrete wavelet transform of JPEG 2000 codec, IEEE Trans. Circuits and Systems for Video Technology, vol.15, no.12, pp.1615-1628 (Dec. 2005)
[12]	Siqi Li: The regularity of wavelet transform with the high order vanishing moments, Proc. IEEE International Conf. Measurement, Information and Control (ICMIC), vol.2, pp.1358-1361 (2013)
[13]	Vetterli, M., Herley, C.: Wavelets and filter banks: theory and design," IEEE Trans. Signal Processing, vol.40, Issue 9, pp.2207-2232 (1992)
[14]	Zhang, Y., Bull, D.R., Reinhard, E.: Perceptually lossless high dynamic range image compression with JPEG 2000, Proc. IEEE International Conference on Image Processing, pp.1057-1060 (2012)
[15]	Shih, Y.S., Zhang, W.C., Sheng, H., et.al.: Bio-inspired JPEG XR CODEC design for lossless HDR biomedical image, Proc. International Computer Symposium, pp. 148-153 (2010)
[16]	N. Zhang, X. Wu: Lossless compression of color mosaic images, IEEE Trans. on Image Processing, vol.15, no.6, pp.1379-1388 (June 2006)
[17]	PengweiHao,Qingyun Shi: Reversible Integer KLT for progressive-to-lossless compression of multiple component images, IEEE International Conf. on Image Processing (ICIP), vol. 1, pp. 633-636 (Sept. 2003)
[18]	M. Iwahashi, M. Ogawa, H. Kiya: Avoidance of singular point in integer orthonormal transform for lossless coding, IEEE Trans. on Signal Processing, vol.60, no.5, pp.2648-2653 (May 2012)
[19]	S.Poomrittigul, M. Ogawa, M.Iwahashi, H.Kiya: Reversible color transform for Bayer color filter array images, APSIPA Transactions on Signal and Information Processing, vol.2, pp.1-10 (Sept. 2013)
[20]	H. S. Malvar, G. J. Sullivan, S. Srinivasan: Lifting-based reversible color transformations for image compression, SPIE vol. 7073 (2008)
[21]	V. Britanak, P. Yip and K. R. Rao: Discrete cosine and sine transform, general properties, fast algorithm and integer approximations, Academic Press (2007)
[22]	A. Benazza-Benyahia, J. C. Pesquet and M. Hamdi: Vector-lifting schemes for lossless coding and progressive archival of multispectral images, IEEE Trans. on Geoscience & Remote Sensing, vol.40, issue 9, pp.2011-2024 (Sep. 2002)
[23]	S. Chokchaitam, M. Iwahashi: Lossless lossy image compression based on non-separable two-dimensional L-SSKF, IEEE International Symposium, Circuits and Systems (ISCAS), pp.421-424 (May 2002)
[24]	D. S. Taubman: Adaptive, non-separable lifting transforms for image compression, IEEE International Conference on Image Processing (ICIP), vol.3, pp.772-776 (1999)
[25]	S. Fukuma, M. Iwahashi and N. Kambayashi: Adaptive multi-channel prediction for lossless scalable coding, IEEE International Symposium on Circuits and Systems (ISCAS), no.IV, pp. 467-470 (May 1999)
[26]	M. Kaaniche, J. C. Pesquet, A. B. Benyahia, B. P. Popescu: Two-dimensional non separable adaptive lifting scheme for still and stereo image coding, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp.1298-1301 (March 2010)
[27]	M. Kaaniche, B. P. Popescu, A. B. Benyahia, J.C. Pesquet: Adaptive lifting scheme with sparse criteria for image coding, EURASIP Journal on Advances in Signal Processing: Special Issue on New Image and Video Representations Based on Sparsity, vol. 2012, pp.1-22 (Jan.2012)
[28]	T. Yoshida, T. Suzuki, S. Kyochi, M. Ikehara: Two dimensional non-separable adaptive directional lifting structure of discrete wavelet transform, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.1529-1532 (May 2011)
[29]	T. Yoshida, T. Suzuki, S. Kyochi, M. Ikehara: Two dimensional non-separable adaptive directional lifting structure of discrete wavelet transform, IEICE Trans. Fundamentals, vol.E94-A, no.10, pp.1920-1927 (Oct. 2011)
[30]	M. Iwahashi, H. Kiya: Non separable 2D factorization of separable 2D DWT for lossless image coding, IEEE International Conference Image Processing (ICIP), pp.17-20 (Nov. 2009)
[31]	M. Iwahashi, H. Kiya: A New lifting structure of non separable 2D DWT with compatibility to JPEG 2000, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), IVMSP, P9.7, pp.1306-1309 (March 2010)
[32]	T. Strutz, I. Rennert, Two-dimensional integer wavelet transform with reduced influence of rounding operations, EURASIP Journal on Advances in Signal Processing, vol.2012, 2012:75, ISSN:1687-6180 (April 2012)
[33]	M. Iwahashi, H. Kiya: Discrete wavelet transforms: Non separable two dimensional discrete wavelet transform for image signals, ISBN 980-953-307-580-3, InTech (2013)
[34]	M. Iwahashi, T. Orachon, H. Kiya: Three dimensional discrete wavelet transform with deduced number of lifting steps, IEEE International Conference on Image Processing (ICIP), no.WA.L4, pp.1651-1654 (Sept. 2013)

Cite This Article

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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  -

Copy | Download

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

Download PDF

Sections

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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  -

Copy | Download