Abstract

A three-dimensional (3-D) image-compression algorithm based on integer wavelet transforms and zerotree coding is presented. The embedded coding of zerotrees of wavelet coefficients (EZW) algorithm is extended to three dimensions, and context-based adaptive arithmetic coding is used to improve its performance. The resultant algorithm, 3-D CB-EZW, efficiently encodes 3-D image data by the exploitation of the dependencies in all dimensions, while enabling lossy and lossless decompression from the same bit stream. Compared with the best available two-dimensional lossless compression techniques, the 3-D CB-EZW algorithm produced averages of 22%, 25%, and 20% decreases in compressed file sizes for computed tomography, magnetic resonance, and Airborne Visible Infrared Imaging Spectrometer images, respectively. The progressive performance of the algorithm is also compared with other lossy progressive-coding algorithms.

© 2000 Optical Society of America

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1999 (1)

A. Bilgin, P. J. Sementilli, M. W. Marcellin, “Progressive image coding using trellis coded quantization,” IEEE Trans. Image Process. 8, 1638–1643 (1999).
[CrossRef]

1998 (2)

I. Daubechies, W. Sweldens, “Factoring wavelet and subband transforms into lifting steps,” J. Fourier Anal. Applica. 4, 245–267 (1998).

R. Calderbank, I. Daubechies, W. Sweldens, B.-L. Yeo, “Wavelet transforms that map integers to integers,” J. Appl. Computa. Harmonics Anal. 5, 332–369 (1998).
[CrossRef]

1997 (4)

S. Dewitte, J. Cornelis, “Lossless integer wavelet transform,” IEEE Signal Process. Lett. 4, 158–160 (1997).
[CrossRef]

Z. Xiong, K. Ramchandran, M. T. Orchard, “Space-frequency quantization for wavelet image coding,” IEEE Trans. Image Process. 6, 1473–1486 (1997).

R. L. Joshi, H. Jafarkani, J. H. Kasner, T. R. Fischer, N. Farvardin, M. W. Marcellin, R. H. Bamberger, “Comparison of different methods of classification in subband coding of images,” IEEE Trans. Image Process. 6, 1473–1486 (1997).
[CrossRef] [PubMed]

A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
[CrossRef] [PubMed]

1996 (3)

A. Said, W. A. Pearlman, “A new fast and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circuits Sys. Video Technol. 6, 243–250 (1996).
[CrossRef]

A. Said, W. Pearlman, “An image multiresolution representation for lossless and lossy compression,” IEEE Trans. Image Process. 5, 1303–1310 (1996).
[CrossRef] [PubMed]

J. Wang, H. K. Huang, “Medical image compression by using three-dimensional wavelet transformation,” IEEE Trans. Med. Imag. 15, 547–554 (1996).
[CrossRef]

1995 (4)

J. A. Saghri, A. G. Tescher, J. T. Reagan, “Practical transform coding of multispectral imagery,” IEEE Signal Process. Mag. 12, 32–43 (1995).
[CrossRef]

S. Wong, L. Zaremba, D. Gooden, H. K. Huang, “Radiologic image compression—a review,” Proc. IEEE 83, 194–219 (1995).
[CrossRef]

V. D. Vaughn, T. S. Wilkinson, “System considerations for multispectral image compression designs,” IEEE Signal Process. Mag. 12, 19–31 (1995).
[CrossRef]

T. P. O’Rourke, R. L. Stevenson, “Human visual system based wavelet decomposition for image compression,” J. Vis. Commun. Image Represent. 6, 109–121 (1995).
[CrossRef]

1993 (1)

J. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. Signal Process. 41, 3445–3462 (1993).
[CrossRef]

1992 (1)

J. W. Woods, T. Naveen, “A filter based bit allocation scheme for subband compression of HDTV,” IEEE Trans. Image Process. 1, 436–440 (1992).
[CrossRef] [PubMed]

1987 (1)

I. H. Witten, R. M. Neal, J. Cleary, “Arithmetic coding for data compression,” Commun. ACM 30, 520–540 (1987).
[CrossRef]

1984 (1)

J. Rissanen, “Universal coding, information, prediction, and estimation,” IEEE Trans. Inf. Theory 30, 629–636 (1984).
[CrossRef]

Adelson, E. H.

E. H. Adelson, E. Simoncelli, R. Hingorani, “Orthogonal pyramid transforms for image coding,” in Visual Communications and Image Processing II, T. R. Hsing, ed., Proc. SPIE845, 50–58 (1987).
[CrossRef]

Aiazzi, B.

B. Aiazzi, P. S. Alba, S. Baronti, L. Alparone, “Three-dimensional lossless compression based on a separable generalized recursive interpolation,” in Proceedings of the 1996 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 85–88.

Alba, P. S.

B. Aiazzi, P. S. Alba, S. Baronti, L. Alparone, “Three-dimensional lossless compression based on a separable generalized recursive interpolation,” in Proceedings of the 1996 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 85–88.

Allen, J. D.

A. Zandi, J. D. Allen, E. L. Schwartz, M. Boliek, “CREW: compression with reversible embedded wavelets,” in Proceedings of the 1995 IEEE Data Compression Conference (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 212–221.

Alparone, L.

B. Aiazzi, P. S. Alba, S. Baronti, L. Alparone, “Three-dimensional lossless compression based on a separable generalized recursive interpolation,” in Proceedings of the 1996 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 85–88.

Bamberger, R. H.

R. L. Joshi, H. Jafarkani, J. H. Kasner, T. R. Fischer, N. Farvardin, M. W. Marcellin, R. H. Bamberger, “Comparison of different methods of classification in subband coding of images,” IEEE Trans. Image Process. 6, 1473–1486 (1997).
[CrossRef] [PubMed]

Baronti, S.

B. Aiazzi, P. S. Alba, S. Baronti, L. Alparone, “Three-dimensional lossless compression based on a separable generalized recursive interpolation,” in Proceedings of the 1996 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 85–88.

Barreto, C. S.

C. S. Barreto, G. V. Mendonca, “Enhanced zerotree wavelet transform image coding exploiting similarities inside subbands,” in Proceedings of the 1996 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 549–551.

Baskurt, A.

A. Baskurt, H. Benoit-Cattin, C. Odet, “On a 3-D medical image coding method using a separable 3-D wavelet transform,” in Medical Imaging 1995: Image Display, Y. Kim, ed., Proc. SPIE2431, 184–194 (1995).

Benoit-Cattin, H.

A. Baskurt, H. Benoit-Cattin, C. Odet, “On a 3-D medical image coding method using a separable 3-D wavelet transform,” in Medical Imaging 1995: Image Display, Y. Kim, ed., Proc. SPIE2431, 184–194 (1995).

Bilgin, A.

A. Bilgin, P. J. Sementilli, M. W. Marcellin, “Progressive image coding using trellis coded quantization,” IEEE Trans. Image Process. 8, 1638–1643 (1999).
[CrossRef]

Boliek, M.

E. L. Schwartz, A. Zandi, M. Boliek, “Implementation of compression with reversible embedded wavelets,” in Applications of Digital Image Processing XVIII, A. G. Tescher, ed., Proc. SPIE2564, 32–43 (1995).
[CrossRef]

A. Zandi, J. D. Allen, E. L. Schwartz, M. Boliek, “CREW: compression with reversible embedded wavelets,” in Proceedings of the 1995 IEEE Data Compression Conference (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 212–221.

Calderbank, R.

R. Calderbank, I. Daubechies, W. Sweldens, B.-L. Yeo, “Wavelet transforms that map integers to integers,” J. Appl. Computa. Harmonics Anal. 5, 332–369 (1998).
[CrossRef]

Chang, P.-Y.

J. Li, P.-Y. Chang, C.-C. J. Kuo, “On the improvements of embedded zerotree wavelet (EZW) coding,” in Visual Communications and Image Processing ’95, L. T. Wu, ed., Proc. SPIE2501, 1490–1501 (1995).
[CrossRef]

Chen, C. W.

J. Luo, X. Wang, C. W. Chen, K. J. Parker, “Volumetric medical image compression with three-dimensional wavelet transform and octave zerotree coding,” in Visual Communications and Image Processing ’96, R. Ansari, J. J. Smith, eds., Proc. SPIE2727, 579–590 (1996).
[CrossRef]

Chen, J.-H.

X. Wu, J.-H. Chen, “Context modeling and entropy coding of wavelet coefficients for image compression,” in Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 3097–3100.

Chen, Y.

Y. Chen, W. A. Pearlman, “Three-dimensional subband coding of video using the zero-tree method,” in Visual Communications and Image Processing ’96, R. Ansari, M. J. Smith, eds., Proc. SPIE2727, 1302–1309 (1996).
[CrossRef]

Chu, C. H.

M. A. Pratt, C. H. Chu, S. Wong, “Volume compression of MRI data using zerotrees of wavelet coefficients,” in Wavelet Applications in Signal and Image Processing IV, M. A. Unser, A. Aldroubi, A. F. Laine, eds., Proc. SPIE2825, 752–763 (1996).
[CrossRef]

Cleary, J.

I. H. Witten, R. M. Neal, J. Cleary, “Arithmetic coding for data compression,” Commun. ACM 30, 520–540 (1987).
[CrossRef]

Cornelis, J.

S. Dewitte, J. Cornelis, “Lossless integer wavelet transform,” IEEE Signal Process. Lett. 4, 158–160 (1997).
[CrossRef]

Cover, T.

T. Cover, J. Thomas, Elements of Information Theory (Wiley, New York, 1991).
[CrossRef]

Daubechies, I.

R. Calderbank, I. Daubechies, W. Sweldens, B.-L. Yeo, “Wavelet transforms that map integers to integers,” J. Appl. Computa. Harmonics Anal. 5, 332–369 (1998).
[CrossRef]

I. Daubechies, W. Sweldens, “Factoring wavelet and subband transforms into lifting steps,” J. Fourier Anal. Applica. 4, 245–267 (1998).

Dewitte, S.

S. Dewitte, J. Cornelis, “Lossless integer wavelet transform,” IEEE Signal Process. Lett. 4, 158–160 (1997).
[CrossRef]

Farvardin, N.

R. L. Joshi, H. Jafarkani, J. H. Kasner, T. R. Fischer, N. Farvardin, M. W. Marcellin, R. H. Bamberger, “Comparison of different methods of classification in subband coding of images,” IEEE Trans. Image Process. 6, 1473–1486 (1997).
[CrossRef] [PubMed]

Fischer, T. R.

R. L. Joshi, H. Jafarkani, J. H. Kasner, T. R. Fischer, N. Farvardin, M. W. Marcellin, R. H. Bamberger, “Comparison of different methods of classification in subband coding of images,” IEEE Trans. Image Process. 6, 1473–1486 (1997).
[CrossRef] [PubMed]

Franques, V. T.

V. T. Franques, V. K. Jain, “Enhanced wavelet-based zerotree coding of images,” in Proceedings of the 1996 IEEE Data Compression Conference (Institute of Electrical and Electronics Engineers, New York, 1996), p. 436.

Gooden, D.

S. Wong, L. Zaremba, D. Gooden, H. K. Huang, “Radiologic image compression—a review,” Proc. IEEE 83, 194–219 (1995).
[CrossRef]

Hingorani, R.

E. H. Adelson, E. Simoncelli, R. Hingorani, “Orthogonal pyramid transforms for image coding,” in Visual Communications and Image Processing II, T. R. Hsing, ed., Proc. SPIE845, 50–58 (1987).
[CrossRef]

Huang, H. K.

J. Wang, H. K. Huang, “Medical image compression by using three-dimensional wavelet transformation,” IEEE Trans. Med. Imag. 15, 547–554 (1996).
[CrossRef]

S. Wong, L. Zaremba, D. Gooden, H. K. Huang, “Radiologic image compression—a review,” Proc. IEEE 83, 194–219 (1995).
[CrossRef]

Jafarkani, H.

R. L. Joshi, H. Jafarkani, J. H. Kasner, T. R. Fischer, N. Farvardin, M. W. Marcellin, R. H. Bamberger, “Comparison of different methods of classification in subband coding of images,” IEEE Trans. Image Process. 6, 1473–1486 (1997).
[CrossRef] [PubMed]

Jain, V. K.

V. T. Franques, V. K. Jain, “Enhanced wavelet-based zerotree coding of images,” in Proceedings of the 1996 IEEE Data Compression Conference (Institute of Electrical and Electronics Engineers, New York, 1996), p. 436.

Joshi, R. L.

R. L. Joshi, H. Jafarkani, J. H. Kasner, T. R. Fischer, N. Farvardin, M. W. Marcellin, R. H. Bamberger, “Comparison of different methods of classification in subband coding of images,” IEEE Trans. Image Process. 6, 1473–1486 (1997).
[CrossRef] [PubMed]

Kasner, J. H.

R. L. Joshi, H. Jafarkani, J. H. Kasner, T. R. Fischer, N. Farvardin, M. W. Marcellin, R. H. Bamberger, “Comparison of different methods of classification in subband coding of images,” IEEE Trans. Image Process. 6, 1473–1486 (1997).
[CrossRef] [PubMed]

Kovacevic, J.

M. Vetterli, J. Kovacevic, Wavelets and Subband Coding (Prentice-Hall, Englewood Cliffs, N.J., 1995).

Kuo, C.-C. J.

J. Li, P.-Y. Chang, C.-C. J. Kuo, “On the improvements of embedded zerotree wavelet (EZW) coding,” in Visual Communications and Image Processing ’95, L. T. Wu, ed., Proc. SPIE2501, 1490–1501 (1995).
[CrossRef]

Lau, K. L.

K. L. Lau, W. K. Vong, W. Y. Ng, “Lossless compression of 3-D images by variable predictive coding,” in Proceedings of the Second Singapore International Conference on Image Processing (World Scientific, Singapore, 1992), pp. 161–165.

Li, J.

J. Li, P.-Y. Chang, C.-C. J. Kuo, “On the improvements of embedded zerotree wavelet (EZW) coding,” in Visual Communications and Image Processing ’95, L. T. Wu, ed., Proc. SPIE2501, 1490–1501 (1995).
[CrossRef]

Luo, J.

J. Luo, X. Wang, C. W. Chen, K. J. Parker, “Volumetric medical image compression with three-dimensional wavelet transform and octave zerotree coding,” in Visual Communications and Image Processing ’96, R. Ansari, J. J. Smith, eds., Proc. SPIE2727, 579–590 (1996).
[CrossRef]

Marcellin, M. W.

A. Bilgin, P. J. Sementilli, M. W. Marcellin, “Progressive image coding using trellis coded quantization,” IEEE Trans. Image Process. 8, 1638–1643 (1999).
[CrossRef]

R. L. Joshi, H. Jafarkani, J. H. Kasner, T. R. Fischer, N. Farvardin, M. W. Marcellin, R. H. Bamberger, “Comparison of different methods of classification in subband coding of images,” IEEE Trans. Image Process. 6, 1473–1486 (1997).
[CrossRef] [PubMed]

Memon, N.

X. Wu, N. Memon, “CALIC—a context based adaptive lossless image codec,” in Proceedings of the 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1890–1893.

Mendonca, G. V.

C. S. Barreto, G. V. Mendonca, “Enhanced zerotree wavelet transform image coding exploiting similarities inside subbands,” in Proceedings of the 1996 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 549–551.

Naveen, T.

J. W. Woods, T. Naveen, “A filter based bit allocation scheme for subband compression of HDTV,” IEEE Trans. Image Process. 1, 436–440 (1992).
[CrossRef] [PubMed]

Neal, R. M.

I. H. Witten, R. M. Neal, J. Cleary, “Arithmetic coding for data compression,” Commun. ACM 30, 520–540 (1987).
[CrossRef]

Ng, W. Y.

K. L. Lau, W. K. Vong, W. Y. Ng, “Lossless compression of 3-D images by variable predictive coding,” in Proceedings of the Second Singapore International Conference on Image Processing (World Scientific, Singapore, 1992), pp. 161–165.

Nguyen, T.

G. Strang, T. Nguyen, Wavelets and Filter Banks (Wellesley-Cambridge Press, Wellesley, Mass., 1996).

O’Rourke, T. P.

T. P. O’Rourke, R. L. Stevenson, “Human visual system based wavelet decomposition for image compression,” J. Vis. Commun. Image Represent. 6, 109–121 (1995).
[CrossRef]

Odet, C.

A. Baskurt, H. Benoit-Cattin, C. Odet, “On a 3-D medical image coding method using a separable 3-D wavelet transform,” in Medical Imaging 1995: Image Display, Y. Kim, ed., Proc. SPIE2431, 184–194 (1995).

Orchard, M. T.

Z. Xiong, K. Ramchandran, M. T. Orchard, “Space-frequency quantization for wavelet image coding,” IEEE Trans. Image Process. 6, 1473–1486 (1997).

Parker, K. J.

J. Luo, X. Wang, C. W. Chen, K. J. Parker, “Volumetric medical image compression with three-dimensional wavelet transform and octave zerotree coding,” in Visual Communications and Image Processing ’96, R. Ansari, J. J. Smith, eds., Proc. SPIE2727, 579–590 (1996).
[CrossRef]

Pearlman, W.

A. Said, W. Pearlman, “An image multiresolution representation for lossless and lossy compression,” IEEE Trans. Image Process. 5, 1303–1310 (1996).
[CrossRef] [PubMed]

Pearlman, W. A.

A. Said, W. A. Pearlman, “A new fast and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circuits Sys. Video Technol. 6, 243–250 (1996).
[CrossRef]

Y. Chen, W. A. Pearlman, “Three-dimensional subband coding of video using the zero-tree method,” in Visual Communications and Image Processing ’96, R. Ansari, M. J. Smith, eds., Proc. SPIE2727, 1302–1309 (1996).
[CrossRef]

Pratt, M. A.

M. A. Pratt, C. H. Chu, S. Wong, “Volume compression of MRI data using zerotrees of wavelet coefficients,” in Wavelet Applications in Signal and Image Processing IV, M. A. Unser, A. Aldroubi, A. F. Laine, eds., Proc. SPIE2825, 752–763 (1996).
[CrossRef]

Ramchandran, K.

Z. Xiong, K. Ramchandran, M. T. Orchard, “Space-frequency quantization for wavelet image coding,” IEEE Trans. Image Process. 6, 1473–1486 (1997).

Reagan, J. T.

J. A. Saghri, A. G. Tescher, J. T. Reagan, “Practical transform coding of multispectral imagery,” IEEE Signal Process. Mag. 12, 32–43 (1995).
[CrossRef]

Rissanen, J.

J. Rissanen, “Universal coding, information, prediction, and estimation,” IEEE Trans. Inf. Theory 30, 629–636 (1984).
[CrossRef]

Saghri, J. A.

J. A. Saghri, A. G. Tescher, J. T. Reagan, “Practical transform coding of multispectral imagery,” IEEE Signal Process. Mag. 12, 32–43 (1995).
[CrossRef]

Said, A.

A. Said, W. Pearlman, “An image multiresolution representation for lossless and lossy compression,” IEEE Trans. Image Process. 5, 1303–1310 (1996).
[CrossRef] [PubMed]

A. Said, W. A. Pearlman, “A new fast and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circuits Sys. Video Technol. 6, 243–250 (1996).
[CrossRef]

Sapiro, G.

M. J. Weinberger, G. Seroussi, G. Sapiro, “LOCO-I: a low complexity, context-based lossless image compression algorithm,” in Proceedings of the 1996 IEEE Data Compression Conference (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 140–149.

Schwartz, E. L.

A. Zandi, J. D. Allen, E. L. Schwartz, M. Boliek, “CREW: compression with reversible embedded wavelets,” in Proceedings of the 1995 IEEE Data Compression Conference (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 212–221.

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M. J. Weinberger, G. Seroussi, G. Sapiro, “LOCO-I: a low complexity, context-based lossless image compression algorithm,” in Proceedings of the 1996 IEEE Data Compression Conference (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 140–149.

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R. Calderbank, I. Daubechies, W. Sweldens, B.-L. Yeo, “Wavelet transforms that map integers to integers,” J. Appl. Computa. Harmonics Anal. 5, 332–369 (1998).
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I. Daubechies, W. Sweldens, “Factoring wavelet and subband transforms into lifting steps,” J. Fourier Anal. Applica. 4, 245–267 (1998).

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M. Vetterli, J. Kovacevic, Wavelets and Subband Coding (Prentice-Hall, Englewood Cliffs, N.J., 1995).

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K. L. Lau, W. K. Vong, W. Y. Ng, “Lossless compression of 3-D images by variable predictive coding,” in Proceedings of the Second Singapore International Conference on Image Processing (World Scientific, Singapore, 1992), pp. 161–165.

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J. Wang, H. K. Huang, “Medical image compression by using three-dimensional wavelet transformation,” IEEE Trans. Med. Imag. 15, 547–554 (1996).
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J. Luo, X. Wang, C. W. Chen, K. J. Parker, “Volumetric medical image compression with three-dimensional wavelet transform and octave zerotree coding,” in Visual Communications and Image Processing ’96, R. Ansari, J. J. Smith, eds., Proc. SPIE2727, 579–590 (1996).
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[CrossRef] [PubMed]

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M. J. Weinberger, G. Seroussi, G. Sapiro, “LOCO-I: a low complexity, context-based lossless image compression algorithm,” in Proceedings of the 1996 IEEE Data Compression Conference (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 140–149.

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X. Wu, N. Memon, “CALIC—a context based adaptive lossless image codec,” in Proceedings of the 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1890–1893.

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Z. Xiong, K. Ramchandran, M. T. Orchard, “Space-frequency quantization for wavelet image coding,” IEEE Trans. Image Process. 6, 1473–1486 (1997).

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[CrossRef] [PubMed]

Yeo, B.-L.

R. Calderbank, I. Daubechies, W. Sweldens, B.-L. Yeo, “Wavelet transforms that map integers to integers,” J. Appl. Computa. Harmonics Anal. 5, 332–369 (1998).
[CrossRef]

Zandi, A.

E. L. Schwartz, A. Zandi, M. Boliek, “Implementation of compression with reversible embedded wavelets,” in Applications of Digital Image Processing XVIII, A. G. Tescher, ed., Proc. SPIE2564, 32–43 (1995).
[CrossRef]

A. Zandi, J. D. Allen, E. L. Schwartz, M. Boliek, “CREW: compression with reversible embedded wavelets,” in Proceedings of the 1995 IEEE Data Compression Conference (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 212–221.

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S. Wong, L. Zaremba, D. Gooden, H. K. Huang, “Radiologic image compression—a review,” Proc. IEEE 83, 194–219 (1995).
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Commun. ACM (1)

I. H. Witten, R. M. Neal, J. Cleary, “Arithmetic coding for data compression,” Commun. ACM 30, 520–540 (1987).
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S. Dewitte, J. Cornelis, “Lossless integer wavelet transform,” IEEE Signal Process. Lett. 4, 158–160 (1997).
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IEEE Signal Process. Mag. (2)

V. D. Vaughn, T. S. Wilkinson, “System considerations for multispectral image compression designs,” IEEE Signal Process. Mag. 12, 19–31 (1995).
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J. A. Saghri, A. G. Tescher, J. T. Reagan, “Practical transform coding of multispectral imagery,” IEEE Signal Process. Mag. 12, 32–43 (1995).
[CrossRef]

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A. Said, W. A. Pearlman, “A new fast and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circuits Sys. Video Technol. 6, 243–250 (1996).
[CrossRef]

IEEE Trans. Image Process (1)

A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
[CrossRef] [PubMed]

IEEE Trans. Image Process. (5)

J. W. Woods, T. Naveen, “A filter based bit allocation scheme for subband compression of HDTV,” IEEE Trans. Image Process. 1, 436–440 (1992).
[CrossRef] [PubMed]

Z. Xiong, K. Ramchandran, M. T. Orchard, “Space-frequency quantization for wavelet image coding,” IEEE Trans. Image Process. 6, 1473–1486 (1997).

R. L. Joshi, H. Jafarkani, J. H. Kasner, T. R. Fischer, N. Farvardin, M. W. Marcellin, R. H. Bamberger, “Comparison of different methods of classification in subband coding of images,” IEEE Trans. Image Process. 6, 1473–1486 (1997).
[CrossRef] [PubMed]

A. Bilgin, P. J. Sementilli, M. W. Marcellin, “Progressive image coding using trellis coded quantization,” IEEE Trans. Image Process. 8, 1638–1643 (1999).
[CrossRef]

A. Said, W. Pearlman, “An image multiresolution representation for lossless and lossy compression,” IEEE Trans. Image Process. 5, 1303–1310 (1996).
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IEEE Trans. Med. Imag. (1)

J. Wang, H. K. Huang, “Medical image compression by using three-dimensional wavelet transformation,” IEEE Trans. Med. Imag. 15, 547–554 (1996).
[CrossRef]

IEEE Trans. Signal Process. (1)

J. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. Signal Process. 41, 3445–3462 (1993).
[CrossRef]

J. Appl. Computa. Harmonics Anal. (1)

R. Calderbank, I. Daubechies, W. Sweldens, B.-L. Yeo, “Wavelet transforms that map integers to integers,” J. Appl. Computa. Harmonics Anal. 5, 332–369 (1998).
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J. Fourier Anal. Applica. (1)

I. Daubechies, W. Sweldens, “Factoring wavelet and subband transforms into lifting steps,” J. Fourier Anal. Applica. 4, 245–267 (1998).

J. Vis. Commun. Image Represent (1)

T. P. O’Rourke, R. L. Stevenson, “Human visual system based wavelet decomposition for image compression,” J. Vis. Commun. Image Represent. 6, 109–121 (1995).
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S. Wong, L. Zaremba, D. Gooden, H. K. Huang, “Radiologic image compression—a review,” Proc. IEEE 83, 194–219 (1995).
[CrossRef]

Other (20)

M. Vetterli, J. Kovacevic, Wavelets and Subband Coding (Prentice-Hall, Englewood Cliffs, N.J., 1995).

G. Strang, T. Nguyen, Wavelets and Filter Banks (Wellesley-Cambridge Press, Wellesley, Mass., 1996).

E. L. Schwartz, A. Zandi, M. Boliek, “Implementation of compression with reversible embedded wavelets,” in Applications of Digital Image Processing XVIII, A. G. Tescher, ed., Proc. SPIE2564, 32–43 (1995).
[CrossRef]

J. Luo, X. Wang, C. W. Chen, K. J. Parker, “Volumetric medical image compression with three-dimensional wavelet transform and octave zerotree coding,” in Visual Communications and Image Processing ’96, R. Ansari, J. J. Smith, eds., Proc. SPIE2727, 579–590 (1996).
[CrossRef]

B. Aiazzi, P. S. Alba, S. Baronti, L. Alparone, “Three-dimensional lossless compression based on a separable generalized recursive interpolation,” in Proceedings of the 1996 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 85–88.

M. A. Pratt, C. H. Chu, S. Wong, “Volume compression of MRI data using zerotrees of wavelet coefficients,” in Wavelet Applications in Signal and Image Processing IV, M. A. Unser, A. Aldroubi, A. F. Laine, eds., Proc. SPIE2825, 752–763 (1996).
[CrossRef]

A. Baskurt, H. Benoit-Cattin, C. Odet, “On a 3-D medical image coding method using a separable 3-D wavelet transform,” in Medical Imaging 1995: Image Display, Y. Kim, ed., Proc. SPIE2431, 184–194 (1995).

K. L. Lau, W. K. Vong, W. Y. Ng, “Lossless compression of 3-D images by variable predictive coding,” in Proceedings of the Second Singapore International Conference on Image Processing (World Scientific, Singapore, 1992), pp. 161–165.

A. Zandi, J. D. Allen, E. L. Schwartz, M. Boliek, “CREW: compression with reversible embedded wavelets,” in Proceedings of the 1995 IEEE Data Compression Conference (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 212–221.

M. J. Weinberger, G. Seroussi, G. Sapiro, “LOCO-I: a low complexity, context-based lossless image compression algorithm,” in Proceedings of the 1996 IEEE Data Compression Conference (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 140–149.

X. Wu, N. Memon, “CALIC—a context based adaptive lossless image codec,” in Proceedings of the 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1890–1893.

ftp://carlos.wustl.edu .

http://makalu.jpl.nasa.gov .

Y. Chen, W. A. Pearlman, “Three-dimensional subband coding of video using the zero-tree method,” in Visual Communications and Image Processing ’96, R. Ansari, M. J. Smith, eds., Proc. SPIE2727, 1302–1309 (1996).
[CrossRef]

E. H. Adelson, E. Simoncelli, R. Hingorani, “Orthogonal pyramid transforms for image coding,” in Visual Communications and Image Processing II, T. R. Hsing, ed., Proc. SPIE845, 50–58 (1987).
[CrossRef]

J. Li, P.-Y. Chang, C.-C. J. Kuo, “On the improvements of embedded zerotree wavelet (EZW) coding,” in Visual Communications and Image Processing ’95, L. T. Wu, ed., Proc. SPIE2501, 1490–1501 (1995).
[CrossRef]

V. T. Franques, V. K. Jain, “Enhanced wavelet-based zerotree coding of images,” in Proceedings of the 1996 IEEE Data Compression Conference (Institute of Electrical and Electronics Engineers, New York, 1996), p. 436.

C. S. Barreto, G. V. Mendonca, “Enhanced zerotree wavelet transform image coding exploiting similarities inside subbands,” in Proceedings of the 1996 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 549–551.

X. Wu, J.-H. Chen, “Context modeling and entropy coding of wavelet coefficients for image compression,” in Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 3097–3100.

T. Cover, J. Thomas, Elements of Information Theory (Wiley, New York, 1991).
[CrossRef]

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Figures (24)

Fig. 1
Fig. 1

Wavelet analysis and synthesis.

Fig. 2
Fig. 2

Dyadic wavelet analysis.

Fig. 3
Fig. 3

Three-dimensional wavelet analysis.

Fig. 4
Fig. 4

Diagram of the forward wavelet transform by use of lifting.

Fig. 5
Fig. 5

Diagram of the inverse wavelet transform by use of lifting.

Fig. 6
Fig. 6

Two-dimensional dyadic wavelet decomposition.

Fig. 7
Fig. 7

Diagram of the 3-D tree structure.

Fig. 8
Fig. 8

Diagram of the 3-D context model.

Fig. 9
Fig. 9

Progressive performance of the 3-D CB-EZW algorithm on the CT_skull data set at an average rate of 0.1 bit/pixel. Results obtained by use of the 2-D SPIHT algorithm are included for reference.

Fig. 10
Fig. 10

Progressive performance of the 3-D CB-EZW algorithm on the CT_skull data set at an average rate of 0.5 bit/pixel. Results obtained by use of the 2-D SPIHT algorithm are included for reference.

Fig. 11
Fig. 11

Original slice 79 of the CT_skull image volume.

Fig. 12
Fig. 12

Reconstructed slice 79 of the CT_skull image volume obtained by use of the 3-D CB-EZW method with a 16-slice coding unit at 0.1 bit/pixel.

Fig. 13
Fig. 13

Reconstructed slice 79 of the CT_skull image volume obtained by use of the 3-D CB-EZW method with a 128-slice coding unit at 0.1 bit/pixel.

Fig. 14
Fig. 14

Reconstructed slice 79 of the CT_skull image volume obtained by use of the 2-D SPIHT method at 0.1 bit/pixel.

Fig. 15
Fig. 15

Reconstructed slice 79 of the CT_skull image volume obtained by use of the 3-D CB-EZW method with a 16-slice coding unit at 0.5 bit/pixel.

Fig. 16
Fig. 16

Reconstructed slice 79 of the CT_skull image volume obtained by use of the 3-D CB-EZW method with a 128-slice coding unit at 0.5 bit/pixel.

Fig. 17
Fig. 17

Reconstructed slice 79 of the CT_skull image volume obtained by use of the 2-D SPIHT method at 0.5 bit/pixel.

Fig. 18
Fig. 18

Original slice 83 of the CT_skull image volume.

Fig. 19
Fig. 19

Reconstructed slice 83 of the CT_skull image volume obtained by use of the 3-D CB-EZW method with a 16-slice coding unit at 0.1 bit/pixel.

Fig. 20
Fig. 20

Reconstructed slice 83 of the CT_skull image volume obtained by use of the 3-D CB-EZW method with a 128-slice coding unit at 0.1 bit/pixel.

Fig. 21
Fig. 21

Reconstructed slice 83 of the CT_skull image volume obtained by use of the 2-D SPIHT method at 0.1 bit/pixel.

Fig. 22
Fig. 22

Reconstructed slice 83 of the CT_skull image volume obtained by use of the 3-D CB-EZW method with a 16-slice coding unit at 0.5 bit/pixel.

Fig. 23
Fig. 23

Reconstructed slice 83 of the CT_skull image volume obtained by use of the 3-D CB-EZW method with a 128-slice coding unit at 0.5 bit/pixel.

Fig. 24
Fig. 24

Reconstructed slice 83 of the CT_skull image volume obtained by use of the 2-D SPIHT method at 0.5 bit/pixel.

Tables (9)

Tables Icon

Table 1 Description of the CT Data

Tables Icon

Table 2 Description of the MR Data

Tables Icon

Table 3 Comparison of Different Integer Wavelet Transforms on the CT Dataa

Tables Icon

Table 4 Comparison of Different Integer Wavelet Transforms on the MR Dataa

Tables Icon

Table 5 Comparison of Different Integer Wavelet Transforms on the AVIRIS Dataa

Tables Icon

Table 6 Comparison of Different Coding-Unit Sizes and Decomposition Levels on the First 128 Slices of the CT_skull Data

Tables Icon

Table 7 Comparison of Different Image-Compression Methods on the CT Dataa

Tables Icon

Table 8 Comparison of Different Image-Compression Methods on the MR Dataa

Tables Icon

Table 9 Comparison of Different Image-Compression Methods on the AVIRIS Dataa

Equations (43)

Equations on this page are rendered with MathJax. Learn more.

HzH˜z+GzG˜z=2z-l,
HzH˜-z+GzG˜-z=0,
s0n=x2n,
d0n=x2n+1.
din=di-1n-k piksi-1n-k,
sin=si-1n-k uikdin-k,
sn=sMnK,
dn=KdMn.
sMn=Ksn,
dMn=dnK.
si-1n=sin+k uikdin-k,
di-1n=din+k piksi-1n-k.
x2n=s0n,
x2n+1=d0n.
din=di-1n-k piksi-1n-k+12,
sin=si-1n-k uikdin-k+12,
si-1n=sin+k uikdin-k+12,
di-1n=din+k piksi-1n-k+12.
dn=x2n+1-12x2n+x2n+2+12,
sn=x2n+14dn-1+dn+12.
dn=x2n+1-916x2n+x2n+2-116x2n-2+x2n+4+12,
sn=x2n+14dn-1+dn+12.
dn=x2n+1-12x2n+x2n+2+12,
sn=x2n+1964dn-1+dn-364dn-2+dn+1+12.
dn=x2n+1-75128x2n+x2n+2-25256x2n-2+x2n+4+3256x2n-4+x2n+6+12,
sn=x2n+14dn-1+dn-12.
d1n=x2n+1-12x2n+x2n+2+12,
sn=x2n+14d1n-1+d1n+12,
dn=d1n-116-sn-1+sn+sn+1-sn+2+12.
dn=x2n+1-x2n,
sn=x2n+12 dn.
d1n=x2n+1-x2n,
sn=x2n+d1n2,
dn=d1n-14d1n-1-d1n+1+12.
d1n=x2n+1-x2n,
sn=x2n+d1n2,
dn=d1n+28sn-1-sn+38sn-sn+1+28 d1n+1+12.
C=TI.
Iˆ=T-1Cˆ.
MSE=1V I-Iˆ2=1V C-Cˆ2=1Vmn |Cm, n-Cˆm, n|2,
2x, 2y, 2z,2x+1, 2y, 2z,2x, 2y+1, 2z,2x, 2y, 2z+1,2x+1, 2y+1, 2z,2x+1, 2y, 2z+1,2x, 2y+1, 2z+1,2x+1, 2y+1, 2z+1
x+Lx, y, z,x, y+Ly, z,x, y, z+Lz,x+Lx, y+Ly, z,x+Lx, y, z+Lz,x, y+Ly, z+Lz,x+Lx, y+Ly, z+Lz
PSNR=10 log102552MSE,

Metrics