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)


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.


Orthonormal Basis Discrete Fourier Transform Fourier Coefficient Wavelet Packet Tikhonov Regularization 
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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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