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Anamorphic stretch transform

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  • Comment: All sources are written by the same people. You need multiple independent sources. Chris1834 (talk) 16:49, 14 January 2014 (UTC)

Anamorphic Stretch Transform (AST), is a mathematical transform used for data compression. It works with analog signals such as communication data or with digital data such as images [1] [2] . For data compression, AST warps the data in a manner resembling Anamorphosis [3] and Surrealism [4] [5] arts.

Operation principle

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 down sampling, 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, also called Modulation Intensity Distribution (not to be confused with a different function of the same name used in mechanical diagnostics). Stretched Modulation Distribution is a 3D plot from a kind of Bilinear time–frequency distribution [8] [9] [10] that describes the dependence of the intensity (power), on the modulation frequency and its time duration. It provides insight on how the information bandwidth and data volume is modified upon dispersion in time domain, or diffraction in spatial domain [11]. It also gives the blueprint for compressing the data.

The mathematical transformation emulates propagation of the signal through a physical medium with specific dispersion/diffraction property Cite error: A <ref> tag is missing the closing </ref> (see the help page). [12] but with engineered nonlinear Kernel.

Applications to 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 [13],JPEG 2000 [14] and WebP [15] , provide higher compression factors with the price of losing information. AST a physics-based mathematical operator that reduces the image brightness bandwidth without proportional increase in its size, i.e. space-bandwidth product compression. It does so by self-adaptive stretching of the image without feature detection or prior knowledge of the image. AST an be operated as a standalone image compression or combined with a secondary compression method such as standard JPEG, JPEG 2000 or WebP to improve their performance [16].

Applications to 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 proved to enhance ultrafast signal measurement [17] [18] and analog to digital conversion [19] [20][21]in terms of operation bandwidth and compression of the volume of the generated data. AST is a promising solution for big data problem in rare cancer cell detection systems [22] by compressing the amount of data generated without losing the vital information.


References

  1. ^ [1]
  2. ^ [2]
  3. ^ J. L. Hunt, B. G. Nickel, and C. Gigault, " Anamorphic images," American Journal of Physics 68, 232-237 (2000).
  4. ^ ...], [contributors Rachel Barnes (2001). The 20th-Century art book. (Reprinted. ed.). London: Phaidon Press. ISBN 0714835420.
  5. ^ [3]
  6. ^ M. H. Asghari, and B. Jalali, "Anamorphic transformation and its application to time-bandwidth compression," Applied Optics, Vol. 52, pp. 6735-6743 (2013). [4]
  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. [5]
  8. ^ L. Cohen, Time-Frequency Analysis, Prentice-Hall, New York, 1995. ISBN 978-0135945322
  9. ^ B. Boashash, editor, “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, 1968 :McGraw-Hill Book Co.
  12. ^ 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).
  13. ^ W. B. Pennebaker and J. L. Mitchell, JPEG still image data compression standard, 3rd ed., Springer, 1993.
  14. ^ A. Skodras, C. Christopoulos, and T. Ebrahimi, "The JPEG 2000 still image compression standard", IEEE Signal Process. Mag., vol. 18, pp. 36 -58, 2001.
  15. ^ [6]
  16. ^ 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.
  17. ^ 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).
  18. ^ 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).
  19. ^ G. C. Valley, "Photonic analog-to-digital converters," Optics Express 15, 1955-1982 (2007).
  20. ^ 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).
  21. ^ 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).
  22. ^ 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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