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Local spectral analysis of images via the wavelet transform based on partial differential equations

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Abstract

We propose method for the local spectral analysis of images via the two-dimensional continuous wavelet transform with the Morlet wavelet based on its representation as a solution of the partial differential equation. It has been shown that a transformed function uniquely determines an initial value for the equation, i.e. a Cauchy problem is stated. Its solving implies that scale parameter a plays a role of “time variable” and two translation parameters b x , b y are spatial independent variables. Numerical examples are given to illustrate the efficiency of the proposed method.

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Authors and Affiliations

  1. Department of Theoretical Physics, Kursk State University, Radishcheva st. 33, 305000, Kursk, Russia

    Eugene B. Postnikov

  2. Department of Mathematics, BITS Pilani-K.K. Birla Goa Campus, Zuarinagar, Goa, India

    Vineet K. Singh

Authors
  1. Eugene B. Postnikov
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  2. Vineet K. Singh
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Correspondence to Eugene B. Postnikov.

Additional information

VKS is grateful for financial support of the BOYSCAST Fellowship 2010–2011 program of the Department of Science and Technology of the Government of India.

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Postnikov, E.B., Singh, V.K. Local spectral analysis of images via the wavelet transform based on partial differential equations. Multidim Syst Sign Process 25, 145–155 (2014). https://doi.org/10.1007/s11045-012-0196-1

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  • DOI: https://doi.org/10.1007/s11045-012-0196-1

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