Journal of Scientific Computing

, Volume 50, Issue 3, pp 665–677

Wavelet-Based De-noising of Positron Emission Tomography Scans

  • Wolfgang Stefan
  • Kewei Chen
  • Hongbin Guo
  • Rosemary A. Renaut
  • Svetlana Roudenko

DOI: 10.1007/s10915-011-9529-8

Cite this article as:
Stefan, W., Chen, K., Guo, H. et al. J Sci Comput (2012) 50: 665. doi:10.1007/s10915-011-9529-8


A method to improve the signal-to-noise-ratio (SNR)of positron emission tomography (PET) scans is presented. A wavelet-based image decomposition technique decomposes an image into two parts, one which primarily contains the desired restored image and the other primarily the remaining unwanted portion of the image. Because the method is based on a texture extraction model that identifies the desired image in the space of bounded variation, these restorations are approximations of piecewise constant images, and are referred to as the cartoon part of the image. Here an approximation using a wavelet decomposition is used which allows solutions to be computed very efficiently. To process 3-D volume data a slice by slice approach in all three directions is adopted. Using a redundant discrete wavelet transform, 3-D restorations can be efficiently computed on standard desktop computers. The method is illustrated for PET images which have been reconstructed from simulated data using the expectation maximization algorithm. When post-processed by the presented wavelet decomposition they show a significant increase in SNR. It is concluded that the new wavelet based method can be used as an alternative to the well established de-noising of PET scans by smoothing with a Gaussian point spread function. In particular, if the volume data are reconstructed using the EM algorithm with a larger number of iterations than the number of iterations that would be used without post-processing, the 3-D images are sharper and show more detail. A MATLAB® based graphical user interface is provided that allows easy exploration of the impact of parameter choices.


Wavelets Denoising Positron emission tomography ROF model Bounded variation 

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Wolfgang Stefan
    • 1
  • Kewei Chen
    • 2
  • Hongbin Guo
    • 3
  • Rosemary A. Renaut
    • 4
  • Svetlana Roudenko
    • 5
  1. 1.The University of Texas, MD AndersenHoustonUSA
  2. 2.Computational Image Analysis ProgramBanner Alzheimer’s Institute & and Banner Good Samaritan Medical CenterPhoenixUSA
  3. 3.Instarecon Inc.ChampaignUSA
  4. 4.School of Mathematical & Statistical SciencesArizona State UniversityPhoenixUSA
  5. 5.Department of MathematicsThe George Washington UniversityWashingtonUSA

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