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Mathematical Analysis of Image Information Retained in the Complex Domain Phases Under Additive and Multiplicative Noise

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Advances in Computing and Data Sciences (ICACDS 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1046))

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Abstract

It is often observed that phases in complex transform of images are important ingredients compared to their magnitude for information extraction. Literature indicates that these phases are immune to noise. The aim of this paper is to find the structural (Edge) and statistical information retained by the complex domain phases for the images corrupted with additive white Gaussian noise (AWGN) and multiplicative (speckle) noise. Initially, we measure the edge information preserved by both phase and magnitude only synthesized image using edge mismatch error (EMM), to illustrate the significance of phase in image restoration and reconstruction. A mathematical model for the sensitivity of phase and magnitude is derived to examine the respective rate of deterioration under varying noise strength. Both the mathematical finding and experimental results indicate that the phase of any complex transform is degraded slowly compared to its magnitude. Comparative analysis of effect of noise on these phases is also investigated and reported.

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Notes

  1. 1.

    In our earlier work a comparative analysis on different phases reveal the importance of phase based reconstruction over magnitude based reconstruction [9].

  2. 2.

    The phase only reconstructed image was synthesized from the phase of respective transform (such as FT, CWT and CT) with unity magnitude. Similarly, the magnitude only reconstructed image was synthesized by preserving magnitude information with unity phase.

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Authors and Affiliations

  1. Koneru Lakshmaiah Education Foundation, Vijayawada, 522502, AP, India

    Susant Kumar Panigrahi

  2. National Institute of Technology, Rourkela, 769008, Odisha, India

    Supratim Gupta

Authors
  1. Susant Kumar Panigrahi
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  2. Supratim Gupta
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Corresponding author

Correspondence to Susant Kumar Panigrahi .

Editor information

Editors and Affiliations

  1. University of KwaZulu-Natal, Durban, South Africa

    Mayank Singh

  2. Computer Science and Engineering, Jaypee Institute of Information Technology, Waknaghat, Himachal Pradesh, India

    P.K. Gupta

  3. Department of Computer Science and Engineering, Jaypee University of Engineering and Technology, Guna, Madhya Pradesh, India

    Vipin Tyagi

  4. ÚTIA AV ČR, Institute of Information Theory and Automation, Prague 8, Praha, Czech Republic

    Jan Flusser

  5. School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, ON, Canada

    Tuncer Ören

  6. CSE Department, Inderprastha Engineering College, Ghaziabad, Uttar Pradesh, India

    Rekha Kashyap

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Panigrahi, S.K., Gupta, S. (2019). Mathematical Analysis of Image Information Retained in the Complex Domain Phases Under Additive and Multiplicative Noise. In: Singh, M., Gupta, P., Tyagi, V., Flusser, J., Ören, T., Kashyap, R. (eds) Advances in Computing and Data Sciences. ICACDS 2019. Communications in Computer and Information Science, vol 1046. Springer, Singapore. https://doi.org/10.1007/978-981-13-9942-8_59

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  • DOI: https://doi.org/10.1007/978-981-13-9942-8_59

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-9941-1

  • Online ISBN: 978-981-13-9942-8

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