SUMMARIES
 
 
Nº DATE
DESCRIPTION
1 22/09/2015 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 29/09/2015 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 6/10/2015 Introduction to inverse problems; Tikhonov regularization; Regularization parameter selection;  Generalized Tikhonov regularization; Bayesian   perspective.
6   Optimization;  Example of  regulatization with robust regularizers. The Majorization minimization framework. Examples
7 13/10/2015
 Linear operators in function spaces; Compact operators; Singular value decomposition; Geometry of a linear inverse problem; Classification of linear operators;
8
Least  squares solution and pseudo-inverse; Minimization of quadractic functionals. Examples.
9 20/10/2015 Review of probality theory.
10
Statistical inference. Parametric inference. Maximum likelihood  inference:  properties of ML estimators.
11 27/10/2015 Cramer-Rao Bound: minimum variance unbiased (MVU) estimator; best linear unbiased estimator (BLUE).
12
Exponential families.Computing  maximum likelihood estimates. 
13 3/11/2010
 Expectation maximization. Example: mixtures of densities.
14
Bayesian Inference. The Bayesian Philosophy. Prior, posterior and comnjugate priors. Examples
15 10/11/2015
 Bayes estimators. Statistical decision theory: loss function; posterior risk. 
16
Maximum probability a posteriori (MAP); posterior mean (PM); additive loss; maximum posterior marginal (MPM); examples.
17 17/11/2015 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.
10
Approximating a continuous bandlimited signal with a periodic sequences;  spectral decomposition  of the periodic convolution operator; properties.
11 24/11/2015 Examples of image blurring:  blurring and noise; linear motion blur; out-of-focus blur; Diffraction-limited  imaging systems; atmospheric turbulence blur; near-field holography.
 12
Space-variant imaging systems. X-ray tomography: Radon  transform; SVD of the Radon  operator; characterization of the inverse problem.
Fourier-based methods:  Fourier slice therem; Filtered back projection; implementation issues. CT with TV regularization.
13 8/12/2015 Iterative Methods for Smooth Objective Functions. Stationary Iterative Methods (first/second order). Steepest Descent Method. Landweber/Projected Landweber Methods. Conjugate Gradient Method
14
Non-Quadratic Smooth Objective Functions. 
15 15/12/2015 Shrinkage/Thresholding Iterative Methods. Majorization Minimization revisietd
16
IST- Iterative Shrinkage Thresolding Methods. TwIST-Two step IST. FISTA
17 22/12/2015 Proximal Splitting Optimization Methods. Convex optimization problems. Proximity operators
18    Convex regularizers. Proximal algorithm
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Last modificationn: 06-10-2015