Linear and nonlinear inverse problems with practical applications [electronic resource] / Jennifer Mueller, Colorado State University, Fort Collins, Colorado, Samuli Siltanen, University of Helsinki, Helsinki, Finland.

Bibliographic Details
Main Authors: Mueller, Jennifer (Jennifer L.) (Author)
Siltanen, Samuli (Author)
Language:English
Published: Philadelphia : Society for Industrial and Applied Mathematics, [2012]
Series:Computational science and engineering series
Subjects:
Inverse problems (Differential equations)
Online Access:
SIAM eBooks: 2012 (Society for Industrial and Applied Mathematics)
Format: Electronic eBook
Contents:
  • Naíve reconstruction and inverse crimes
  • Ill-posedness in inverse problems
  • Truncated singular value decomposition
  • Tikhonov regularization
  • Total variation regularization
  • Besov space regularization using wavelets
  • Discretization-invariance
  • Practical X-ray tomography with limited data
  • Projects
  • Nonlinear inverse problems
  • Nonlinear inversion
  • Electrical impedance tomography
  • Simulation of noisy EIT data
  • Complex geometrical optics solutions
  • A regularized D-bar method for direct EIT
  • Other direct solution methods for EIT
  • Projects
  • Banach spaces and Hilbert spaces
  • Mappings and compact operators
  • Fourier transform and Sobolev spaces
  • Iterative solution of linear equations.