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Inversion of the Heat Equation by a Block Based Algorithm Using Spline Wavelet Packets

  • Amir Averbuch
  • Pekka Neittaanmäki
  • Valery Zheludev
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 27)

Abstract

We present a robust algorithm starting from 1D or 2D discrete noised data to approximately invert the heat equation, which is an ill-conditioned problem. Relative contributions of the coherent structure and the noise in different frequency bands of the available data are different. We propose to solve the inversion problem separately in different frequency bands by methods similar to the Tikhonov regularization. This separation is achieved by using spline wavelet packets. The solutions are derived as linear combinations of those wavelet packets.

Keywords

Orthonormal Basis Discrete Fourier Transform Fourier Coefficient Wavelet Packet Tikhonov Regularization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Amir Averbuch
    • 1
    • 2
  • Pekka Neittaanmäki
    • 2
  • Valery Zheludev
    • 1
    • 2
  1. 1.School of Computer ScienceTel Aviv UniversityTel AvivIsrael
  2. 2.Department of Mathematical Information TechnologyUniversity of JyväskyläJyväskyläFinland

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