Regularization and image restoration using differential equations

  • Authors:

  • Yu-Li You;M. Kaveh

  • Affiliations:

  • University of Minnesota, Department of Electrical Engineering, Minneapolis, MN;University of Minnesota, Department of Electrical Engineering, Minneapolis, MN

  • Venue:
  • ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: image and multidimensional signal processing - Volume V
  • Year:
  • 1993

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Abstract

Linear image restoration is posted as a solution to a set of ordinary differential equations (ODE). Explicit and implicit Euler's methods are used to integrate this set of ODE's. The explicit method introduces a regularization operator to the Van Cittert's method while the implicit method leads to the Tikhonov-Miller restoration. Since both methods are simply numerical integration procedures for the same set of ODE's. the extended Van Cittert's method and the Tikhonov-Miller method are shown to be approximately equivalent in performance if a conversion formula is followed. An analysis of the difference between the restorations by the two methods is included, as well as the ramifications of this conversion formula.