Regularization Methods for Nonlinear Ill-Posed Problems with Applications to Phase Reconstruction

  • Barbara Blaschke-Kaltenbacher
  • Heinz W. Engl


This conference has shown again that many inverse problems arise in medical imaging and nondestructive testing. Mathematically, such problems involve e.g. parameter identification from boundary measurements (see e.g. [36]), inverse scattering (see e.g. [12], [13], [14]), or phase reconstruction (see e.g. [40]). The mathematical formulation of inverse problems usually gives rise to ill-posed problems in Hadamard’s sense, where especially the lack of stability causes numerical difficulties. We take this as a motivation to survey some results about convergence and convergence rates for regularization methods for nonlinear illposed problems, which have to be used to deal with the instability issue. Again motivated by some talks at this conference, we illustrate our results by some phase reconstruction problems.


Inverse Problem Convergence Rate Regularization Method Tikhonov Regularization Boundary Measurement 
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Copyright information

© Springer-Verlag Wien 1997

Authors and Affiliations

  • Barbara Blaschke-Kaltenbacher
    • 1
  • Heinz W. Engl
    • 1
  1. 1.Institut für MathematikJohannes Kepler UniversitätLinzAustria

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