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The Extended 1-D (One-Dimensional) Discrete Phase Retrieval Problem

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Computer Aided Systems Theory – EUROCAST 2015 (EUROCAST 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9520))

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Abstract

In this work we discuss some difficulties that can be encountered when one uses iterative methods for finding a solution of a one-dimensional discrete phase retrieval problem. Iterative methods are widely used but, unfortunately, they often stagnate. We shall show that by using an extended form of the one-dimensional discrete phase retrieval problem, we can find a solution to the problem.

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References

  1. Dumitrescu, B.: Positive Trigonometric Polynomials and Signal Processing Applications. Springer, Dordrecht, The Netherlands (2007)

    MATH  Google Scholar 

  2. Hayes, M.H., Lim, J.S., Oppenheim, A.V.: Signal reconstruction from phase or magnitude. IEEE Trans. Acoust. Speech Signal Process. ASSP 28(6), 672–680 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hurt, N.E.: Phase Retrieval and Zero Crossings. Kluwer Academic Publishers, Dordrecht/Boston/London (1989)

    Book  MATH  Google Scholar 

  4. Izraelevitz, D., Lim, J.S.: A new direct algorithm for image reconstruction from Fourier transform magnitude. IEEE Trans. Acoust. Speech Signal Process. ASSP 35(4), 511–518 (1987)

    Article  MATH  Google Scholar 

  5. Oppenheim, A.V., Lim, J.S.: The importance of phase in signals. Proc. IEEE 69(5), 529–541 (1981)

    Article  Google Scholar 

  6. Oppenheim, A.V., Schafer, R.W., Buck, J.R.: Discrete-Time Signal Processing. Prentice-Hall, Upper Saddle River (1999)

    Google Scholar 

  7. Quatieri, T.F., Oppenheim, A.V.: Iterative techniques for minimum phase signal reconstruction from phase or magnitudes. IEEE Trans. Acoust. Speech Signal Process. ASSP 29(6), 1187–1193 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  8. Rusu, C., Astola, J.: Iterative one-dimensional phase. In: Proceedings of SMMSP 2006, Florence, pp. 95–100, 2–3 September 2006

    Google Scholar 

  9. Rusu, C., Astola, J.: About magnitude input data in 1-D discrete phase retrieval problem. In: Proceedings of EUSIPCO 2007, Poznan, 3–7 September 2007

    Google Scholar 

  10. Rusu, C., Astola, J.: About positive trigonometric polynomials and 1-D discrete phase retrieval problem. In: Proceedings of EUSIPCO 2012, Bucharest, 27–31 August 2012

    Google Scholar 

  11. Yagle, A.E., Bell, A.E.: One- and two-dimensional minimum and nonminimum phase retrieval by solving linear systems of equations. IEEE Trans. Sig. Process. 47(11), 2978–2989 (1999)

    Article  MATH  Google Scholar 

  12. Yegnanarayana, B., Saikia, D.K., Krishnan, T.R.: Significance of group delay functions in signal reconstruction from spectral magnitude and phase. IEEE Trans. Acoust. Speech Signal Process. ASSP 32, 610–623 (1984)

    Article  Google Scholar 

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Acknowledgments

The work of first author has been supported by Grant PAV3M PN-II-PT-PCCA-2013-4-1762.

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Authors and Affiliations

  1. Faculty of Electronics, Telecommunications and Information Technology, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Corneliu Rusu

  2. Tampere International Center for Signal Processing, Tampere University of Technology, Tampere, Finland

    Jaakko Astola

Authors
  1. Corneliu Rusu
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  2. Jaakko Astola
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Corresponding author

Correspondence to Corneliu Rusu .

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Editors and Affiliations

  1. de Gran Canaria, Universidad de las Palmas de Gran Canari, Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. Johannes Kepler University Linz, Linz, Austria

    Franz Pichler

  3. de Gran Canaria, Universidad de las Palmas de Gran Canari, Las Palmas de Gran Canaria, Spain

    Alexis Quesada-Arencibia

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Rusu, C., Astola, J. (2015). The Extended 1-D (One-Dimensional) Discrete Phase Retrieval Problem. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2015. EUROCAST 2015. Lecture Notes in Computer Science(), vol 9520. Springer, Cham. https://doi.org/10.1007/978-3-319-27340-2_79

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  • DOI: https://doi.org/10.1007/978-3-319-27340-2_79

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27339-6

  • Online ISBN: 978-3-319-27340-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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