Multidimensional Systems and Signal Processing

, Volume 25, Issue 1, pp 145–155 | Cite as

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

  • Eugene B. Postnikov
  • Vineet K. Singh


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.


Wavelet transform 2D Morlet wavelet Local spectrum 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsKursk State UniversityKurskRussia
  2. 2.Department of MathematicsBITS Pilani-K.K. Birla Goa CampusZuarinagarIndia

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