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== Operation principle ==
== Operation principle ==


An anamorphic stretch transform (AST)<ref>M. H. Asghari and B. Jalali, "Anamorphic transformation and its application to time-bandwidth compression", Applied Optics, Vol. 52, pp. 6735-6743 (2013). [http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-52-27-6735]</ref><ref>M. H. Asghari and B. Jalali, "Demonstration of analog time-bandwidth compression using anamorphic stretch transform", Frontiers in Optics (FIO 2013), Paper: FW6A.2, Orlando, USA. [http://www.opticsinfobase.org/abstract.cfm?uri=FiO-2013-FW6A.2]</ref> is a mathematical transformation in which analog or digital data is stretched and warped in a specific fashion such that after [[downsampling]], the volume of data is reduced without loss of pertinent information. The recipe for reshaping is prescribed by a mathematical function called ''stretched modulation distribution'' or ''modulation intensity distribution'' (not to be confused with a different function of the same name used in mechanical diagnostics). A stretched modulation distribution is a 3D representation of a type of [[bilinear time–frequency distribution]]<ref> L. Cohen, Time-Frequency Analysis, Prentice-Hall, New York, 1995. ISBN 978-0135945322</ref><ref>S. Qian and D. Chen, Joint Time-Frequency Analysis: Methods and Applications, Chap. 5, Prentice Hall, N.J., 1996.</ref> that describes the dependence of intensity or power on the frequency and time duration of the modulation. It provides insight on how information bandwidth and data volume are modified upon dispersion in the time domain, or upon diffraction in the spatial domain.<ref>J. W. Goodman, "Introduction to Fourier Optics", McGraw-Hill Book Co (1968).</ref> It also provides a blueprint for compressing the data.
An anamorphic stretch transform (AST)<ref>M. H. Asghari and B. Jalali, "Anamorphic transformation and its application to time-bandwidth compression", Applied Optics, Vol. 52, pp. 6735-6743 (2013). [http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-52-27-6735]</ref><ref>M. H. Asghari and B. Jalali, "Demonstration of analog time-bandwidth compression using anamorphic stretch transform", Frontiers in Optics (FIO 2013), Paper: FW6A.2, Orlando, USA. [http://www.opticsinfobase.org/abstract.cfm?uri=FiO-2013-FW6A.2]</ref> is a mathematical transformation in which analog or digital data is stretched and warped in a specific fashion such that after [[downsampling]], the volume of data is reduced without loss of pertinent information. The recipe for reshaping is prescribed by a mathematical function called ''stretched modulation distribution'' or ''modulation intensity distribution'' (not to be confused with a different function of the same name used in mechanical diagnostics). A stretched modulation distribution is a 3D representation of a type of [[bilinear time–frequency distribution]]<ref> L. Cohen, Time-Frequency Analysis, Prentice-Hall, New York, 1995. ISBN 978-0135945322</ref><ref>B. Boashash, ed., “Time-Frequency Signal Analysis and Processing – A Comprehensive Reference”, Elsevier Science, Oxford, 2003.</ref><ref>S. Qian and D. Chen, Joint Time-Frequency Analysis: Methods and Applications, Chap. 5, Prentice Hall, N.J., 1996.</ref> that describes the dependence of intensity or power on the frequency and time duration of the modulation. It provides insight on how information bandwidth and data volume are modified upon dispersion in the time domain, or upon diffraction in the spatial domain.<ref>J. W. Goodman, "Introduction to Fourier Optics", McGraw-Hill Book Co (1968).</ref> It also provides a blueprint for compressing the data.


The mathematical transformation emulates propagation of the signal through a physical medium with specific dispersion and diffraction properties,<ref>T. Jannson, "Real-time Fourier transformation in dispersive optical fibers", Opt. Lett. 8, 232–234 (1983).</ref><ref>D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves", Nature 450, 1054–1057 (2007).</ref><ref>B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias and J. M. Dudley, "Real-time full bandwidth measurement of spectral noise in supercontinuum generation", Scientific Reports 2, Article number: 882 (2012).</ref> but with an engineered nonlinear kernel.
The mathematical transformation emulates propagation of the signal through a physical medium with specific dispersion and diffraction properties,<ref>T. Jannson, "Real-time Fourier transformation in dispersive optical fibers", Opt. Lett. 8, 232–234 (1983).</ref><ref>D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves", Nature 450, 1054–1057 (2007).</ref><ref>B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias and J. M. Dudley, "Real-time full bandwidth measurement of spectral noise in supercontinuum generation", Scientific Reports 2, Article number: 882 (2012).</ref> but with an engineered nonlinear kernel.

Revision as of 10:49, 10 November 2014

An anamorphic stretch transform (AST) is a mathematical transform used for data compression. It can be applied to analog signals such as communication data or to digital data such as images.[1][2] For data compression, AST warps the data in a manner resembling anamorphosis[3] and surrealist artworks.[4][5]

Operation principle

An anamorphic stretch transform (AST)[6][7] is a mathematical transformation in which analog or digital data is stretched and warped in a specific fashion such that after downsampling, the volume of data is reduced without loss of pertinent information. The recipe for reshaping is prescribed by a mathematical function called stretched modulation distribution or modulation intensity distribution (not to be confused with a different function of the same name used in mechanical diagnostics). A stretched modulation distribution is a 3D representation of a type of bilinear time–frequency distribution[8][9][10] that describes the dependence of intensity or power on the frequency and time duration of the modulation. It provides insight on how information bandwidth and data volume are modified upon dispersion in the time domain, or upon diffraction in the spatial domain.[11] It also provides a blueprint for compressing the data.

The mathematical transformation emulates propagation of the signal through a physical medium with specific dispersion and diffraction properties,[12][13][14] but with an engineered nonlinear kernel.

Applications

Image compression

The world today is awash in digital information captured by sensors or generated in computer simulations. Coping with the fire hose of digital information in this era requires to develop more efficient methods to compress the volume of data without dropping the vital information. Lossless image compression methods based on reversible algorithms do not provide large compression factors. Lossy image compression methods such as JPEG,[15] JPEG 2000[16] and WebP,[17] provide higher compression factors at the price of losing information. AST is a physics-based mathematical operator that reduces the image brightness bandwidth without proportional increase in its size, thus providing space-bandwidth product compression. It does so by self-adaptive stretching of the image without feature detection or prior knowledge of the image. AST can be operated as a standalone image compression technique or combined with a secondary compression method such as standard JPEG, JPEG 2000 or WebP to improve their performance.[18]

Time domain signals

The AST technology makes it possible to not only capture and digitize signals that are faster than the speed of the sensor and the digitizer, but also to minimize the volume of the data generated in the process. The transformation causes the signal to be reshaped is such a way that sharp features are stretched more than coarse features. Upon subsequent sampling, this self-adaptive stretch (SAS) causes more digital samples to be allocated to sharp features where they are needed the most, and fewer to coarse features where they would be redundant.

AST has been experimentally proven to enhance ultrafast signal measurements[19][20] and analog to digital conversion[21][22][23] in terms of operation bandwidth and compression of the volume of the generated data. AST is a promising solution for the big data problem in rare cancer cell detection systems[24] by compressing the amount of data generated without losing the vital information.

References

  1. ^ http://newsroom.ucla.edu/portal/ucla/ucla-research-team-invents-new-249693.aspx
  2. ^ http://www.photonics.com/Article.aspx?AID=55602
  3. ^ J. L. Hunt, B. G. Nickel, and C. Gigault, "Anamorphic images", American Journal of Physics 68, 232–237 (2000).
  4. ^ Editors of Phaidon Press (2001). "The 20th-Century art book." (Reprinted. ed.). London: Phaidon Press. ISBN 0714835420.
  5. ^ http://www.scienceagogo.com/news/20131120231425.shtml
  6. ^ M. H. Asghari and B. Jalali, "Anamorphic transformation and its application to time-bandwidth compression", Applied Optics, Vol. 52, pp. 6735-6743 (2013). [1]
  7. ^ M. H. Asghari and B. Jalali, "Demonstration of analog time-bandwidth compression using anamorphic stretch transform", Frontiers in Optics (FIO 2013), Paper: FW6A.2, Orlando, USA. [2]
  8. ^ L. Cohen, Time-Frequency Analysis, Prentice-Hall, New York, 1995. ISBN 978-0135945322
  9. ^ B. Boashash, ed., “Time-Frequency Signal Analysis and Processing – A Comprehensive Reference”, Elsevier Science, Oxford, 2003.
  10. ^ S. Qian and D. Chen, Joint Time-Frequency Analysis: Methods and Applications, Chap. 5, Prentice Hall, N.J., 1996.
  11. ^ J. W. Goodman, "Introduction to Fourier Optics", McGraw-Hill Book Co (1968).
  12. ^ T. Jannson, "Real-time Fourier transformation in dispersive optical fibers", Opt. Lett. 8, 232–234 (1983).
  13. ^ D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves", Nature 450, 1054–1057 (2007).
  14. ^ B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias and J. M. Dudley, "Real-time full bandwidth measurement of spectral noise in supercontinuum generation", Scientific Reports 2, Article number: 882 (2012).
  15. ^ W. B. Pennebaker and J. L. Mitchell, "JPEG still image data compression standard", 3rd ed., Springer, 1993.
  16. ^ A. Skodras, C. Christopoulos, and T. Ebrahimi, "The JPEG 2000 still image compression standard", IEEE Signal Process. Mag., vol. 18, pp. 36–58, 2001.
  17. ^ https://developers.google.com/speed/webp/
  18. ^ M. H. Asghari and B. Jalali, "Image compression using the feature-selective stretch transform", 13th IEEE International Symposium on Signal Processing and Information Technology (ISSPIT 2013), Athens, Greece.
  19. ^ F. Li, Y. Park, and J. Azana, “Linear characterization of optical pulses with durations ranging from the picosecond to the nanosecond regime using ultrafast photonic differentiation”, J. Lightwave Technol. 27, 4623–4633 (2009).
  20. ^ C. Wang and J. P. Yao, "Complete Characterization of an Optical Pulse Based on Temporal Interferometry Using an Unbalanced Temporal Pulse Shaping System", J. Lightwave Technol. 29, 789–800 (2011).
  21. ^ G. C. Valley, "Photonic analog-to-digital converters", Optics Express 15, 1955–1982 (2007).
  22. ^ J. Stigwall and S. Galt, "Signal reconstruction by phase retrieval and optical backpropagation in phase-diverse photonic time-stretch systems", Journal of Lightwave Technology 25, 3017–3027 (2007).
  23. ^ W. Ng, T. D. Rockwood, G. A. Sefler, and G. C. Valley, "Demonstration of a large stretch-ratio (M=41) photonic analog-to-digital converter with 8 ENOB for an input signal bandwidth of 10 GHz", IEEE Photonics Technology Letters 24, 1185–1187 (2012).
  24. ^ K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, "High-throughput single-microparticle imaging flow analyzer", Proc. Nat. Acad. Sci., vol. 109, pp. 11630–11635, 2012.
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