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Convex Analysis for Image Processing

Winter Term 2010/2011

Convex Analysis for Image Processing

Lecturer: Dr. Simon Setzer,

Office hours: Tuesday, 14:15-15:15

Winter Term 2010/2011

Lectures (3h) with exercises (1h)
(6 credit points)

Time and Location: Monday 16-18 c.t. and Thursday 16-18 c.t., Building E13, Lecture Hall 001

First lecture: Thursday, October 21, 2010

Announcements – Description – Prerequisites – Lecture notes – Assignments – Exams – Literature

Homework 6 is now online.

The exam schedule can be found here.

You can now register here for this course.

Many problems in image processing can be modeled as convex minimization problems. The restored image is thus the minimizer of a suitable convex energy functional. We will cover the foundations of convex analysis (convex sets and functions, subdifferentials, duality, optimality conditions) and their applications to nonsmooth nonlinear optimization.
Except for basic concepts of calculus and linear algebra this course is self-contained, especially, because we will be working in the finite-dimensional setting. There will also be programming assignments which illustrate the relevance of fast optimization algorithms.

Undergraduate knowledge in mathematics (e.g. ''Mathematik für Informatiker I-III''). The lectures will be given in English.

Date	Topic
21.10.	Introduction to image processing
24.10.-28.10	Optimization models in image processing
28.10.-8.11	Proper and lsc functions
8.11.-15.11	Convexity and Lipschitz continuity
18.11.-25.11	Convexity and differentiability
29.11.-6.12	Convexity and differentiability II
9.12.-16.12	Conjugate functions
3.1.-6.1	Duality

Homework will be assigned bi-weekly. To qualify for the exam you need 50% of the points from these assignments.

Due date
8.11.	Assignment 1
22.11.	Assignment 2	sparse_reconstruction.c
13.12.	Assignment 3
6.1.	Assignment 4
27.1.	Assignment 5	L2L1_FBS.c, cameraman_noisy.pgm, BMW_noisy.pgm, L2L1_FBS_solution.c
14.2.	Assignment 6

The first exam will be Tuesday, February 22, 2011 at 9am-12pm in room E1 3, HS001. The second exam will take place Friday, March 25, 2011 (same time, same room).

Please remember that you have to register online for the lecture/exam in the HISPOS system of the Saarland University

The lecture notes which will be provided for this course are self-contained. No textbook is required. Examples of books giving background material and further reading are:

1. Convex analysis
   R. T. Rockafellar, Princeton University Press, 1997
   (Classical text on convex analysis.)
   
   
2. Convex analysis and minimization algorithms I+II
   J.-B. Hiriart-Urruty and C. Lemaréchal, Springer, 1993
   (Provides many nice examples and motivational ideas.)
   
   
3. Convex Optimization
   S. Boyd and L. Vandenberghe, Cambridge University Press, 2004
   (Also available to download at the authors' webpages.)
   
   
4. Perturbation analysis of optimization problems
   Joseph F. Bonnans and A. Shapiro, Springer, 2000
   (Works in the infinite-dimensional setting. Nice introduction to duality.)
   
   
5. Numerical Optimization
   J. Nocedal and S. J. Wright, Springer, 2006
   (Introduction to a wide range of modern optimization techniques. Good motivational examples.)
   
   
6. Image Processing and Analysis
   T. F. Chan and J. Chen, SIAM, 2005
   (Not only restricted to optimization methods in image processing but introduces major models.)
   
   

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