Abstract

Fast data processing and compression methods based on wavelet transform are fundamental tools in the area of real-time 2D data/image analysis, enabling high definition applications and redundant data reduction. The need for information processing at high data rates motivates the efforts on exploiting the speed and the parallelism of the light for data analysis and compression. Among several schemes for optical wavelet transform implementation, the Haar transform offers simple design and fast computation, plus it can be easily implemented by optical planar interferometry. We present an all optical scheme based on an asymmetric couplers network for achieving fast image processing and compression in the optical domain. The implementation of Haar wavelet transform through a 3D passive structure is supported by theoretical formulation and simulations results. Asymmetrical coupler 3D network design and optimization are reported and Haar wavelet transform, including compression, was achieved, thus demonstrating the feasibility of our approach.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Skodras, C. Christopoulos, and T. Ebrahimi, “The JPEG 2000 still image compression standard,” IEEE Signal Process. Mag. 18, 36–58 (2001).
    [CrossRef]
  2. M. S. Moreolo, V. Sacchieri, G. Cincotti, and G. Junyent, “Trigonometric transforms for high-speed optical networks: all-optical architectures and optical OFDM,” J. Netw. 5, 1248–1253 (2010).
    [CrossRef]
  3. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon 1, 589–636 (2009).
    [CrossRef]
  4. L. W. Cahill and T. T. Le, “Photonic signal processing using MMI elements,” Proc. SPIE 7220, 722003 (2008).
  5. M. S. Moreolo, G. Cincotti, and A. Neri, “Synthesis of optical wavelet filters,” IEEE Photon. Technol. Lett. 16, 1679–1681 (2004).
    [CrossRef]
  6. S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed.(Academic, 1999).
  7. P. N. Topiwala, Wavelet Image and Video Compression, Vol. 450 of Springer International Series in Engineering and Computer Science (Springer, 1998).
  8. O. Rioul and M. Vetterli, “Wavelets and signal processing,” IEEE Signal Proc. Mag. 8, 14–38 (1991).
    [CrossRef]
  9. M. Vetterli, J. Kovacevic, and V. K. Goyal, “Signal processing: Fourier and wavelet representations,” http://www.fourierandwavelets.org/ .
  10. V. Ashok, T. Balakumaran, C. Gowrishankar, I. L. A. Vennila, and A. N. Kumar, “The fast Haar wavelet transform for signal & image processing,” Int. J. Comput. Sci. Inf. Sec. 7, 126–130 (2010).
  11. H.-B. Sun and S. Kawata, “Two-photon photopolymerization and 3D lithographic microfabrication,” in NMR/3D Analysis: Polymerization, of Advances in Polymer Science Series (Springer-Verlag, 2004), Vol. 170, pp. 169–273.
  12. T. Mitsumoto and Y. Naito, “Dependence of the output phase difference on the asymmetry of 3 dB directional couplers,” J. Lightwave Technol. 8, 1571–1576 (1990).
    [CrossRef]
  13. A. Takagi, K. Jinguji, and M. Kawachi, “Design and fabrication of broad-band silica-based optical waveguide couplers with asymmetric structure,” IEEE J. Quantum Electron. 28, 848–855 (1992).
    [CrossRef]
  14. G. Parca, P. Teixeira, and A. Teixeira, “3D interferometric integrated passive scheme for all optical transform,” in 14th International Conference on Transparent Optical Networks (IEEE, 2012).
  15. Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Proc. Lett. 9, 81–84 (2002).
    [CrossRef]

2010 (2)

M. S. Moreolo, V. Sacchieri, G. Cincotti, and G. Junyent, “Trigonometric transforms for high-speed optical networks: all-optical architectures and optical OFDM,” J. Netw. 5, 1248–1253 (2010).
[CrossRef]

V. Ashok, T. Balakumaran, C. Gowrishankar, I. L. A. Vennila, and A. N. Kumar, “The fast Haar wavelet transform for signal & image processing,” Int. J. Comput. Sci. Inf. Sec. 7, 126–130 (2010).

2009 (1)

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon 1, 589–636 (2009).
[CrossRef]

2008 (1)

L. W. Cahill and T. T. Le, “Photonic signal processing using MMI elements,” Proc. SPIE 7220, 722003 (2008).

2004 (1)

M. S. Moreolo, G. Cincotti, and A. Neri, “Synthesis of optical wavelet filters,” IEEE Photon. Technol. Lett. 16, 1679–1681 (2004).
[CrossRef]

2002 (1)

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Proc. Lett. 9, 81–84 (2002).
[CrossRef]

2001 (1)

A. Skodras, C. Christopoulos, and T. Ebrahimi, “The JPEG 2000 still image compression standard,” IEEE Signal Process. Mag. 18, 36–58 (2001).
[CrossRef]

1992 (1)

A. Takagi, K. Jinguji, and M. Kawachi, “Design and fabrication of broad-band silica-based optical waveguide couplers with asymmetric structure,” IEEE J. Quantum Electron. 28, 848–855 (1992).
[CrossRef]

1991 (1)

O. Rioul and M. Vetterli, “Wavelets and signal processing,” IEEE Signal Proc. Mag. 8, 14–38 (1991).
[CrossRef]

1990 (1)

T. Mitsumoto and Y. Naito, “Dependence of the output phase difference on the asymmetry of 3 dB directional couplers,” J. Lightwave Technol. 8, 1571–1576 (1990).
[CrossRef]

Alfalou, A.

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon 1, 589–636 (2009).
[CrossRef]

Ashok, V.

V. Ashok, T. Balakumaran, C. Gowrishankar, I. L. A. Vennila, and A. N. Kumar, “The fast Haar wavelet transform for signal & image processing,” Int. J. Comput. Sci. Inf. Sec. 7, 126–130 (2010).

Balakumaran, T.

V. Ashok, T. Balakumaran, C. Gowrishankar, I. L. A. Vennila, and A. N. Kumar, “The fast Haar wavelet transform for signal & image processing,” Int. J. Comput. Sci. Inf. Sec. 7, 126–130 (2010).

Bovik, A. C.

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Proc. Lett. 9, 81–84 (2002).
[CrossRef]

Brosseau, C.

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon 1, 589–636 (2009).
[CrossRef]

Cahill, L. W.

L. W. Cahill and T. T. Le, “Photonic signal processing using MMI elements,” Proc. SPIE 7220, 722003 (2008).

Christopoulos, C.

A. Skodras, C. Christopoulos, and T. Ebrahimi, “The JPEG 2000 still image compression standard,” IEEE Signal Process. Mag. 18, 36–58 (2001).
[CrossRef]

Cincotti, G.

M. S. Moreolo, V. Sacchieri, G. Cincotti, and G. Junyent, “Trigonometric transforms for high-speed optical networks: all-optical architectures and optical OFDM,” J. Netw. 5, 1248–1253 (2010).
[CrossRef]

M. S. Moreolo, G. Cincotti, and A. Neri, “Synthesis of optical wavelet filters,” IEEE Photon. Technol. Lett. 16, 1679–1681 (2004).
[CrossRef]

Ebrahimi, T.

A. Skodras, C. Christopoulos, and T. Ebrahimi, “The JPEG 2000 still image compression standard,” IEEE Signal Process. Mag. 18, 36–58 (2001).
[CrossRef]

Gowrishankar, C.

V. Ashok, T. Balakumaran, C. Gowrishankar, I. L. A. Vennila, and A. N. Kumar, “The fast Haar wavelet transform for signal & image processing,” Int. J. Comput. Sci. Inf. Sec. 7, 126–130 (2010).

Jinguji, K.

A. Takagi, K. Jinguji, and M. Kawachi, “Design and fabrication of broad-band silica-based optical waveguide couplers with asymmetric structure,” IEEE J. Quantum Electron. 28, 848–855 (1992).
[CrossRef]

Junyent, G.

M. S. Moreolo, V. Sacchieri, G. Cincotti, and G. Junyent, “Trigonometric transforms for high-speed optical networks: all-optical architectures and optical OFDM,” J. Netw. 5, 1248–1253 (2010).
[CrossRef]

Kawachi, M.

A. Takagi, K. Jinguji, and M. Kawachi, “Design and fabrication of broad-band silica-based optical waveguide couplers with asymmetric structure,” IEEE J. Quantum Electron. 28, 848–855 (1992).
[CrossRef]

Kawata, S.

H.-B. Sun and S. Kawata, “Two-photon photopolymerization and 3D lithographic microfabrication,” in NMR/3D Analysis: Polymerization, of Advances in Polymer Science Series (Springer-Verlag, 2004), Vol. 170, pp. 169–273.

Kumar, A. N.

V. Ashok, T. Balakumaran, C. Gowrishankar, I. L. A. Vennila, and A. N. Kumar, “The fast Haar wavelet transform for signal & image processing,” Int. J. Comput. Sci. Inf. Sec. 7, 126–130 (2010).

Le, T. T.

L. W. Cahill and T. T. Le, “Photonic signal processing using MMI elements,” Proc. SPIE 7220, 722003 (2008).

Mallat, S.

S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed.(Academic, 1999).

Mitsumoto, T.

T. Mitsumoto and Y. Naito, “Dependence of the output phase difference on the asymmetry of 3 dB directional couplers,” J. Lightwave Technol. 8, 1571–1576 (1990).
[CrossRef]

Moreolo, M. S.

M. S. Moreolo, V. Sacchieri, G. Cincotti, and G. Junyent, “Trigonometric transforms for high-speed optical networks: all-optical architectures and optical OFDM,” J. Netw. 5, 1248–1253 (2010).
[CrossRef]

M. S. Moreolo, G. Cincotti, and A. Neri, “Synthesis of optical wavelet filters,” IEEE Photon. Technol. Lett. 16, 1679–1681 (2004).
[CrossRef]

Naito, Y.

T. Mitsumoto and Y. Naito, “Dependence of the output phase difference on the asymmetry of 3 dB directional couplers,” J. Lightwave Technol. 8, 1571–1576 (1990).
[CrossRef]

Neri, A.

M. S. Moreolo, G. Cincotti, and A. Neri, “Synthesis of optical wavelet filters,” IEEE Photon. Technol. Lett. 16, 1679–1681 (2004).
[CrossRef]

Parca, G.

G. Parca, P. Teixeira, and A. Teixeira, “3D interferometric integrated passive scheme for all optical transform,” in 14th International Conference on Transparent Optical Networks (IEEE, 2012).

Rioul, O.

O. Rioul and M. Vetterli, “Wavelets and signal processing,” IEEE Signal Proc. Mag. 8, 14–38 (1991).
[CrossRef]

Sacchieri, V.

M. S. Moreolo, V. Sacchieri, G. Cincotti, and G. Junyent, “Trigonometric transforms for high-speed optical networks: all-optical architectures and optical OFDM,” J. Netw. 5, 1248–1253 (2010).
[CrossRef]

Skodras, A.

A. Skodras, C. Christopoulos, and T. Ebrahimi, “The JPEG 2000 still image compression standard,” IEEE Signal Process. Mag. 18, 36–58 (2001).
[CrossRef]

Sun, H.-B.

H.-B. Sun and S. Kawata, “Two-photon photopolymerization and 3D lithographic microfabrication,” in NMR/3D Analysis: Polymerization, of Advances in Polymer Science Series (Springer-Verlag, 2004), Vol. 170, pp. 169–273.

Takagi, A.

A. Takagi, K. Jinguji, and M. Kawachi, “Design and fabrication of broad-band silica-based optical waveguide couplers with asymmetric structure,” IEEE J. Quantum Electron. 28, 848–855 (1992).
[CrossRef]

Teixeira, A.

G. Parca, P. Teixeira, and A. Teixeira, “3D interferometric integrated passive scheme for all optical transform,” in 14th International Conference on Transparent Optical Networks (IEEE, 2012).

Teixeira, P.

G. Parca, P. Teixeira, and A. Teixeira, “3D interferometric integrated passive scheme for all optical transform,” in 14th International Conference on Transparent Optical Networks (IEEE, 2012).

Topiwala, P. N.

P. N. Topiwala, Wavelet Image and Video Compression, Vol. 450 of Springer International Series in Engineering and Computer Science (Springer, 1998).

Vennila, I. L. A.

V. Ashok, T. Balakumaran, C. Gowrishankar, I. L. A. Vennila, and A. N. Kumar, “The fast Haar wavelet transform for signal & image processing,” Int. J. Comput. Sci. Inf. Sec. 7, 126–130 (2010).

Vetterli, M.

O. Rioul and M. Vetterli, “Wavelets and signal processing,” IEEE Signal Proc. Mag. 8, 14–38 (1991).
[CrossRef]

Wang, Z.

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Proc. Lett. 9, 81–84 (2002).
[CrossRef]

Adv. Opt. Photon (1)

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon 1, 589–636 (2009).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Takagi, K. Jinguji, and M. Kawachi, “Design and fabrication of broad-band silica-based optical waveguide couplers with asymmetric structure,” IEEE J. Quantum Electron. 28, 848–855 (1992).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. S. Moreolo, G. Cincotti, and A. Neri, “Synthesis of optical wavelet filters,” IEEE Photon. Technol. Lett. 16, 1679–1681 (2004).
[CrossRef]

IEEE Signal Proc. Lett. (1)

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Proc. Lett. 9, 81–84 (2002).
[CrossRef]

IEEE Signal Proc. Mag. (1)

O. Rioul and M. Vetterli, “Wavelets and signal processing,” IEEE Signal Proc. Mag. 8, 14–38 (1991).
[CrossRef]

IEEE Signal Process. Mag. (1)

A. Skodras, C. Christopoulos, and T. Ebrahimi, “The JPEG 2000 still image compression standard,” IEEE Signal Process. Mag. 18, 36–58 (2001).
[CrossRef]

Int. J. Comput. Sci. Inf. Sec. (1)

V. Ashok, T. Balakumaran, C. Gowrishankar, I. L. A. Vennila, and A. N. Kumar, “The fast Haar wavelet transform for signal & image processing,” Int. J. Comput. Sci. Inf. Sec. 7, 126–130 (2010).

J. Lightwave Technol. (1)

T. Mitsumoto and Y. Naito, “Dependence of the output phase difference on the asymmetry of 3 dB directional couplers,” J. Lightwave Technol. 8, 1571–1576 (1990).
[CrossRef]

J. Netw. (1)

M. S. Moreolo, V. Sacchieri, G. Cincotti, and G. Junyent, “Trigonometric transforms for high-speed optical networks: all-optical architectures and optical OFDM,” J. Netw. 5, 1248–1253 (2010).
[CrossRef]

Proc. SPIE (1)

L. W. Cahill and T. T. Le, “Photonic signal processing using MMI elements,” Proc. SPIE 7220, 722003 (2008).

Other (5)

M. Vetterli, J. Kovacevic, and V. K. Goyal, “Signal processing: Fourier and wavelet representations,” http://www.fourierandwavelets.org/ .

S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed.(Academic, 1999).

P. N. Topiwala, Wavelet Image and Video Compression, Vol. 450 of Springer International Series in Engineering and Computer Science (Springer, 1998).

H.-B. Sun and S. Kawata, “Two-photon photopolymerization and 3D lithographic microfabrication,” in NMR/3D Analysis: Polymerization, of Advances in Polymer Science Series (Springer-Verlag, 2004), Vol. 170, pp. 169–273.

G. Parca, P. Teixeira, and A. Teixeira, “3D interferometric integrated passive scheme for all optical transform,” in 14th International Conference on Transparent Optical Networks (IEEE, 2012).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1.
Fig. 1.

System building blocks for Haar optical wavelet transform (OWT) based all-optical processing and compression. 2D transform process schematic describes low-pass (L) and high-pass (H) filtering until sub-band decomposition.

Fig. 2.
Fig. 2.

3 dB asymmetric optical coupler scheme and scattering matrix.

Fig. 3.
Fig. 3.

3D basic module for 1st-level optical 2D HT.

Fig. 4.
Fig. 4.

Integrated passive scheme for Optical WT-IWT; passive compression is accomplished by spatial selection of LL coefficients, delivered through reported connections.

Fig. 5.
Fig. 5.

Matlab implementation of the proposed 3D scheme performing 1st and 2nd level HT of a 256×256 image (no compression). Sub-band decompositions are reported.

Fig. 6.
Fig. 6.

Matlab implementation of LL selection (compression) applied on 1st and 2nd HT level. Mean square error, peak signal to noise ratio and quality index are reported for each case.

Fig. 7.
Fig. 7.

Matlab implementation of 1 over 4 pixels (left) and 1 over 16 pixels (right) compression. MSE, PSNR, and Q are reported for each case.

Fig. 8.
Fig. 8.

3 dB asymmetric coupler (Magic-T) geometry and design parameters.

Fig. 9.
Fig. 9.

Magic-T design: amplitude and phase optimization. Top, input energy at Section 1 is divided equally through both waveguides, represented in Section 2. Bottom, π phase shift between waveguides at Section 3, corresponding to a generic (before optimization) Coupler Length L. Relative power behavior shows losses for insertion, scattering and diffraction.

Fig. 10.
Fig. 10.

Separation (top) and SCR (bottom) optimization.

Fig. 11.
Fig. 11.

2nd level HT test on planar asymmetric couplers circuit with 4×1 input pixels. Section A, B, and C on cut view; couplers 1, 2, and 3 on top view.

Fig. 12.
Fig. 12.

OptiBPM test on a 8×8 input (top left) with implementation of optical Haar Wavelet Transform (top right), Inverse Transform (bottom left), and Inverse Transform after thresholding on LL components (bottom right). Performance evaluation through MSE, PSNR and Q are reported.

Equations (1)

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

[c10d10c11d11c12d12]=12[110000110000001100001100000011000011][a0a1a2a3a4a5]

Metrics