SUMMARIES
 
 
Nº DATE
DESCRIPTION
1 16/09/2011 Course organization; course description; bibliography; assessment  method.
2   Review of basic concepts from analysis and algebra. Bib: BO6 (Appendix); RB1 (Appendices A, B, C, and D )
3 28/09/2011 Introduction to inverse problems; Examples of direct (forward) problems.
4   Deterministic and statistical point of view;  Well-posedeness in the Hadamard sense; Ill-conditioned inverse problems.
5 12/10/2011 Introduction to inverse problems; Tikhonov regularization; Regularization parameter selection;
5   Generalized Tikhonov regularization; Bayesian   perspective;
7 19/10/2011 Optimization;  Example of  regulatization with robust regularizers.
8   The Majorization minimization framewrok. Examples
9 26/10/2011 Linear operators in function spaces; Compact operators; Singular value decomposition; Geometry of a linear inverse problem; Classification of linear operators;
10    Least  squares solution and pseudo-inverse; Minimization of quadractic functionals. Examples.
8 11/2/2011 Review of probality theory.
9   Statistical inference. Parametric inference. Maximum likelihood  inference:  properties of ML estimators; Cramer-Rao Bound: minimum variance unbiased (MVU) estimator; best linear unbiased estimator (BLUE).
10 11/9/2011 Exponential families.Computing  maximum likelihood estimates. Expectation maximization. Example: mixtures of densities.
11   Bayesian inference: priors; conjugate priors; non-informative priors; improper priors;  nuisance parameters.
 12 23/92011 Bayes estimators. Statistical decision theory: loss function; posterior risk;  maximum probability a posteriori (MAP); posterior mean (PM); additive loss; maximum posterior marginal (MPM); examples.
13   Fourier Transforms of  L1/L2 signals. L2 Hilbert space; Sampling  Functions and sampling theorems; Sampling of 1D and 2D signals; space/frequency lattices; non-rectangular lattices; From continuous signals to finite sequences;  discrete-time Fourier transform (DTFT); discrete Fourier transform (DFT); windowing; fast Fourier Transform.
14 30/11/2011 Approximating a continuous bandlimited signal with a periodic sequences;  spectral decomposition  of the periodic convolution operator; properties.
15   Examples of image blurring:  blurring and noise; linear motion blur; out-of-focus blur; Diffraction-limited  imaging systems; atmospheric turbulence blur; near-field holography.
16 7/11/2011 Space-variant imaging systems. X-ray tomography: Radon  transform; SVD of the Radon  operator; characterization of the inverse problem.
17   Fourier-based methods:  Fourier slice therem; Filtered back projection; implementation issues. CT with TV regularization.
18    
19    
20    
21    
22    
23    
24    
25    
26    
     

Last modification: 7-12-2011