Instructor: Dacian Daescu
Office: Neuberger Hall 313
Phone: (503) 725-3581
E-mail: daescu@pdx.edu
Office Hours: TR 10:30- 11:30
URL: http://web.pdx.edu/~daescu/

Class time and location: TR 17:15-18:30, Neuberger Hall 387

Web resources

• Course notes on inverse problems by Profs. Colin Fox, Geoff K. Nicholls and Sze M. Tan
• Inverse Problems Theory by Albert Tarantola
• Matlab Regularization Tools by Prof. Per Christian Hansen, DTU Compute, Technical University of Denmark.

Additional resources

• Discrete Inverse Problems: Insight and Algorithms by Per Christian Hansen, SIAM 2010.
• Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion by Per Christian Hansen, SIAM 1998.

Lecture Notes

• Week 1
  • Course logistics and motivation (slides)
  • Inverse Problems: introductory concepts and examples
  • Discrete Fourier Transform and an illustrative Matlab example fft_noise.m
  
  
  
• Week 2-3
  • Review of linear algebra. Singular Value Decomposition
  • Least Squares Method & TSVD approximation
  • Example of image blurring and test for Picard condition testpicard.m
  
  
  
• Week 4
  • Tikhonov regularization. Selection of the regularization parameter
  • Tikhonov regularization: general least squares formulation
  • L-curve in the regularization of ill-posed problems
  • L-curve example
  
  
  
• Week 5
  • Generalized Singular Value Decomposition
  • Generalized cross-validation to selection of the regularization parameter
  
  
  
• Week 6
  • Total Variation regularization method
  • Sensitivity to observations and the influence matrix
  
  
  
• Week 7-8
  • Some concepts from probability and statistics and applications (slides)
  • Weighted Least-Squares Estimation, BLUE analysis
  • Iterative Regularization Methods
  
  
  
• Week 9
  • Iterative Regularization: Conjugate Gradient method
  
  
  
• Week 10
  • Nonlinear Inverse Problems: Least-Squares Estimation

FINAL PROJECT, due December 5th, 7:30pm.
Mask matrix mask.m
Masked noisy data file prdata.m and the corresponding image prdata.jpg

Homework assignments