Abstract

In the transformation based compression algorithms of digital hologram for three-dimensional object, the balance between compression ratio and normalized root mean square (NRMS) error is always the core of algorithm development. The Wavelet transform method is efficient to achieve high compression ratio but NRMS error is also high. In order to solve this issue, we propose a hologram compression method using Wavelet-Bandelets transform. Our simulation and experimental results show that the Wavelet-Bandelets method has a higher compression ratio than Wavelet methods and all the other methods investigated in this paper, while it still maintains low NRMS error.

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References

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  1. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
    [CrossRef] [PubMed]
  2. M. L. Piao, N. Kim, and J. H. Park, “Phase contrast projection display using photopolymer,” J. Opt. Soc. Korea 12(4), 319–325 (2008).
    [CrossRef]
  3. T. J. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, “Compression of digital holograms for three-dimensional object reconstruction and recognition,” Appl. Opt. 41(20), 4124–4132 (2002).
    [CrossRef] [PubMed]
  4. G. A. Mills and I. Yamaguchi, “Effects of quantization in phase-shifting digital holography,” Appl. Opt. 44(7), 1216–1225 (2005).
    [CrossRef] [PubMed]
  5. A. Shortt, T. J. Naughton, and B. Javidi, “Compression of digital holograms of three-dimensional objects using wavelets,” Opt. Express 14(7), 2625–2630 (2006).
    [CrossRef] [PubMed]
  6. A. E. Shortt, T. J. Naughton, and B. Javidi, “Histogram approaches for lossy compression of digital holograms of three-dimensional objects,” IEEE Trans. Image Process. 16(6), 1548–1556 (2007).
    [CrossRef] [PubMed]
  7. H. Yoshikawa and J. Tamai, “Holographic image compression by motion picture coding,” Proc. SPIE 2652, 2–9 (1996).
    [CrossRef]
  8. Y. H. Seo, H. J. Choi, J. S. Yoo, G. S. Lee, C. H. Kim, S. H. Lee, S. H. Lee, and D. W. Kim, “Digital hologram compression technique by eliminating spatial correlations based on MCTF,” Opt. Commun. 283(21), 4261–4270 (2010).
    [CrossRef]
  9. E. Darakis and T. J. Naughton, “Compression of digital hologram sequences using MPEG-4,” Proc. SPIE 7358, 735811 (2009).
    [CrossRef]
  10. Y. H. Seo, H. J. Choi, and D. W. Kim, “3D scanning-based compression technique for digital hologram video,” Signal Process. 22(2), 144–156 (2007).
  11. E. Le Pennec and S. Mallat, “Sparse geometric image representation with Bandelets,” IEEE Trans. Image Process. 14(4), 423–438 (2005).
    [CrossRef] [PubMed]
  12. E. Le Pennec and S. Mallat, “Non linear image approximation with Bandelets,” Tech. Rep. CMAP / École Polytechnique (2003).
  13. E. Le Pennec and S. Mallat, “Bandelets image approximation and compression,” Multiscale Model. Simul. 4(3), 992–1039 (2005).
    [CrossRef]
  14. C. Bernard and E. Le Pennec, “Adaptation of regular grid filtering to irregular grids,” Tech. Rep. CMAP / École Polytechnique (2003).
  15. T. Bose, Digital Signal and Image Processing (Wiley, 2003), Chap. 11, pp. 623–669.
  16. T. W. Ng and K. T. Ang, “Fourier-transform method of data compression and temporal fringe pattern analysis,” Appl. Opt. 44(33), 7043–7049 (2005).
    [CrossRef] [PubMed]

2010

Y. H. Seo, H. J. Choi, J. S. Yoo, G. S. Lee, C. H. Kim, S. H. Lee, S. H. Lee, and D. W. Kim, “Digital hologram compression technique by eliminating spatial correlations based on MCTF,” Opt. Commun. 283(21), 4261–4270 (2010).
[CrossRef]

2009

E. Darakis and T. J. Naughton, “Compression of digital hologram sequences using MPEG-4,” Proc. SPIE 7358, 735811 (2009).
[CrossRef]

2008

2007

Y. H. Seo, H. J. Choi, and D. W. Kim, “3D scanning-based compression technique for digital hologram video,” Signal Process. 22(2), 144–156 (2007).

A. E. Shortt, T. J. Naughton, and B. Javidi, “Histogram approaches for lossy compression of digital holograms of three-dimensional objects,” IEEE Trans. Image Process. 16(6), 1548–1556 (2007).
[CrossRef] [PubMed]

2006

2005

E. Le Pennec and S. Mallat, “Sparse geometric image representation with Bandelets,” IEEE Trans. Image Process. 14(4), 423–438 (2005).
[CrossRef] [PubMed]

E. Le Pennec and S. Mallat, “Bandelets image approximation and compression,” Multiscale Model. Simul. 4(3), 992–1039 (2005).
[CrossRef]

T. W. Ng and K. T. Ang, “Fourier-transform method of data compression and temporal fringe pattern analysis,” Appl. Opt. 44(33), 7043–7049 (2005).
[CrossRef] [PubMed]

G. A. Mills and I. Yamaguchi, “Effects of quantization in phase-shifting digital holography,” Appl. Opt. 44(7), 1216–1225 (2005).
[CrossRef] [PubMed]

2002

1997

1996

H. Yoshikawa and J. Tamai, “Holographic image compression by motion picture coding,” Proc. SPIE 2652, 2–9 (1996).
[CrossRef]

Ang, K. T.

Choi, H. J.

Y. H. Seo, H. J. Choi, J. S. Yoo, G. S. Lee, C. H. Kim, S. H. Lee, S. H. Lee, and D. W. Kim, “Digital hologram compression technique by eliminating spatial correlations based on MCTF,” Opt. Commun. 283(21), 4261–4270 (2010).
[CrossRef]

Y. H. Seo, H. J. Choi, and D. W. Kim, “3D scanning-based compression technique for digital hologram video,” Signal Process. 22(2), 144–156 (2007).

Darakis, E.

E. Darakis and T. J. Naughton, “Compression of digital hologram sequences using MPEG-4,” Proc. SPIE 7358, 735811 (2009).
[CrossRef]

Frauel, Y.

Javidi, B.

Kim, C. H.

Y. H. Seo, H. J. Choi, J. S. Yoo, G. S. Lee, C. H. Kim, S. H. Lee, S. H. Lee, and D. W. Kim, “Digital hologram compression technique by eliminating spatial correlations based on MCTF,” Opt. Commun. 283(21), 4261–4270 (2010).
[CrossRef]

Kim, D. W.

Y. H. Seo, H. J. Choi, J. S. Yoo, G. S. Lee, C. H. Kim, S. H. Lee, S. H. Lee, and D. W. Kim, “Digital hologram compression technique by eliminating spatial correlations based on MCTF,” Opt. Commun. 283(21), 4261–4270 (2010).
[CrossRef]

Y. H. Seo, H. J. Choi, and D. W. Kim, “3D scanning-based compression technique for digital hologram video,” Signal Process. 22(2), 144–156 (2007).

Kim, N.

Le Pennec, E.

E. Le Pennec and S. Mallat, “Sparse geometric image representation with Bandelets,” IEEE Trans. Image Process. 14(4), 423–438 (2005).
[CrossRef] [PubMed]

E. Le Pennec and S. Mallat, “Bandelets image approximation and compression,” Multiscale Model. Simul. 4(3), 992–1039 (2005).
[CrossRef]

Lee, G. S.

Y. H. Seo, H. J. Choi, J. S. Yoo, G. S. Lee, C. H. Kim, S. H. Lee, S. H. Lee, and D. W. Kim, “Digital hologram compression technique by eliminating spatial correlations based on MCTF,” Opt. Commun. 283(21), 4261–4270 (2010).
[CrossRef]

Lee, S. H.

Y. H. Seo, H. J. Choi, J. S. Yoo, G. S. Lee, C. H. Kim, S. H. Lee, S. H. Lee, and D. W. Kim, “Digital hologram compression technique by eliminating spatial correlations based on MCTF,” Opt. Commun. 283(21), 4261–4270 (2010).
[CrossRef]

Y. H. Seo, H. J. Choi, J. S. Yoo, G. S. Lee, C. H. Kim, S. H. Lee, S. H. Lee, and D. W. Kim, “Digital hologram compression technique by eliminating spatial correlations based on MCTF,” Opt. Commun. 283(21), 4261–4270 (2010).
[CrossRef]

Mallat, S.

E. Le Pennec and S. Mallat, “Bandelets image approximation and compression,” Multiscale Model. Simul. 4(3), 992–1039 (2005).
[CrossRef]

E. Le Pennec and S. Mallat, “Sparse geometric image representation with Bandelets,” IEEE Trans. Image Process. 14(4), 423–438 (2005).
[CrossRef] [PubMed]

Mills, G. A.

Naughton, T. J.

E. Darakis and T. J. Naughton, “Compression of digital hologram sequences using MPEG-4,” Proc. SPIE 7358, 735811 (2009).
[CrossRef]

A. E. Shortt, T. J. Naughton, and B. Javidi, “Histogram approaches for lossy compression of digital holograms of three-dimensional objects,” IEEE Trans. Image Process. 16(6), 1548–1556 (2007).
[CrossRef] [PubMed]

A. Shortt, T. J. Naughton, and B. Javidi, “Compression of digital holograms of three-dimensional objects using wavelets,” Opt. Express 14(7), 2625–2630 (2006).
[CrossRef] [PubMed]

T. J. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, “Compression of digital holograms for three-dimensional object reconstruction and recognition,” Appl. Opt. 41(20), 4124–4132 (2002).
[CrossRef] [PubMed]

Ng, T. W.

Park, J. H.

Piao, M. L.

Seo, Y. H.

Y. H. Seo, H. J. Choi, J. S. Yoo, G. S. Lee, C. H. Kim, S. H. Lee, S. H. Lee, and D. W. Kim, “Digital hologram compression technique by eliminating spatial correlations based on MCTF,” Opt. Commun. 283(21), 4261–4270 (2010).
[CrossRef]

Y. H. Seo, H. J. Choi, and D. W. Kim, “3D scanning-based compression technique for digital hologram video,” Signal Process. 22(2), 144–156 (2007).

Shortt, A.

Shortt, A. E.

A. E. Shortt, T. J. Naughton, and B. Javidi, “Histogram approaches for lossy compression of digital holograms of three-dimensional objects,” IEEE Trans. Image Process. 16(6), 1548–1556 (2007).
[CrossRef] [PubMed]

Tajahuerce, E.

Tamai, J.

H. Yoshikawa and J. Tamai, “Holographic image compression by motion picture coding,” Proc. SPIE 2652, 2–9 (1996).
[CrossRef]

Yamaguchi, I.

Yoo, J. S.

Y. H. Seo, H. J. Choi, J. S. Yoo, G. S. Lee, C. H. Kim, S. H. Lee, S. H. Lee, and D. W. Kim, “Digital hologram compression technique by eliminating spatial correlations based on MCTF,” Opt. Commun. 283(21), 4261–4270 (2010).
[CrossRef]

Yoshikawa, H.

H. Yoshikawa and J. Tamai, “Holographic image compression by motion picture coding,” Proc. SPIE 2652, 2–9 (1996).
[CrossRef]

Zhang, T.

Appl. Opt.

IEEE Trans. Image Process.

E. Le Pennec and S. Mallat, “Sparse geometric image representation with Bandelets,” IEEE Trans. Image Process. 14(4), 423–438 (2005).
[CrossRef] [PubMed]

A. E. Shortt, T. J. Naughton, and B. Javidi, “Histogram approaches for lossy compression of digital holograms of three-dimensional objects,” IEEE Trans. Image Process. 16(6), 1548–1556 (2007).
[CrossRef] [PubMed]

J. Opt. Soc. Korea

Multiscale Model. Simul.

E. Le Pennec and S. Mallat, “Bandelets image approximation and compression,” Multiscale Model. Simul. 4(3), 992–1039 (2005).
[CrossRef]

Opt. Commun.

Y. H. Seo, H. J. Choi, J. S. Yoo, G. S. Lee, C. H. Kim, S. H. Lee, S. H. Lee, and D. W. Kim, “Digital hologram compression technique by eliminating spatial correlations based on MCTF,” Opt. Commun. 283(21), 4261–4270 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

E. Darakis and T. J. Naughton, “Compression of digital hologram sequences using MPEG-4,” Proc. SPIE 7358, 735811 (2009).
[CrossRef]

H. Yoshikawa and J. Tamai, “Holographic image compression by motion picture coding,” Proc. SPIE 2652, 2–9 (1996).
[CrossRef]

Signal Process.

Y. H. Seo, H. J. Choi, and D. W. Kim, “3D scanning-based compression technique for digital hologram video,” Signal Process. 22(2), 144–156 (2007).

Other

C. Bernard and E. Le Pennec, “Adaptation of regular grid filtering to irregular grids,” Tech. Rep. CMAP / École Polytechnique (2003).

T. Bose, Digital Signal and Image Processing (Wiley, 2003), Chap. 11, pp. 623–669.

E. Le Pennec and S. Mallat, “Non linear image approximation with Bandelets,” Tech. Rep. CMAP / École Polytechnique (2003).

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Figures (12)

Fig. 3
Fig. 3

Diagram of hologram compression uses the transform method.

Fig. 1
Fig. 1

Diagram of using Bandelet transform for the proposed method.

Fig. 4
Fig. 4

Configuration for hologram recording by using the phase-shifting

Fig. 5
Fig. 5

The algorithm of the proposed method.

Fig. 6
Fig. 6

. (a) Geometric flows of 2-D Wavelet transform of hologram, (b) determination of geometric flow in each small block, (c) an example of pixel value approximation when C = 5.

Fig. 2
Fig. 2

Diagram of compression image use Bandelets transform.

Fig. 7
Fig. 7

NRMS error versus compression ratio plot of DCT transform, Wavelet transform, and the proposed Bandelets-Wavelet transform.

Fig. 8
Fig. 8

NRMS error versus compression ratio plot when we change mother function of wavelet transform.

Fig. 9
Fig. 9

Compression ratio versus T plot; (a), (b) with cubic object located at 490 mm from CCD, and (c), (d) with screw object at 810 mm.

Fig. 11
Fig. 11

(a) NRMS errors versus quantization of levels with cubic object located at 490mm from CCD.(b) Compression ratio versus quantization of levels with cubic object located at 490mm from CCD.

Fig. 10
Fig. 10

(a) NRMS errors versus size of block with cubic object located at 490mm from CCD. (b) Compression ratio versus size of block with cubic object located at 490mm from CCD (see main text).

Fig. 12
Fig. 12

Reconstruction of the object; (a), (b), (c) the screw object with (a) size of block 32 × 32, (b) size of block 4 × 4 and (c) size of block 8 × 8; (d), (e), (f) the cubic object with (d) T = 40, (e) T = 30 and (f) T = 10; (g), (h), (k) the cubic object with (g) quantization of level 4bit, (h) quantization of level 3 bit and (k) quantization of level 2bit.

Equations (5)

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W ( a , b ) = f ( t ) 1 | a | ψ * ( t b a ) d t
ψ a , b ( t ) = 1 | a | ψ * ( t b a ) ,
W ( a , b ) = f ( t ) ψ a , b ( t ) d t .
N R M S e r r o r = [ n = 0 N x 1 m = 0 N y 1 { | U ( n , m ) | | U ' ( n , m ) | } 2 n = 0 N x 1 m = 0 N y 1 | U ( n , m ) | 2 ] 1 / 2
R = o r i g i n a l h o l o g r a m s i z e c o m p r e s s e d h o l o g r a m s i z e

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