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Convex Analysis for Image Processing

Winter Term 2013/2014

Convex Analysis for Image Processing

Lecturer: Laurent Hoeltgen,
Office hours: Wednesday, 14:00-16:00
Examiner: Prof. Dr. Joachim Weickert
Lectures (3h) with exercises (1h)
(6 credit points)

Time and Location:
Tuesday 16-18 in Building E1 3, HS 001
Friday 12-14 in Building E1 3, HS 001

First lecture: Tuesday, October 21, 2014

AnnouncementsDescriptionPrerequisitesLecture notesAssignmentsExamsLiterature

  • The registration for the lecture is now possible. For further details, see below.
  • Important details concerning the registration for the exam can be found below.
  • There will be no lecture on Tuesday, January 13th 2015 and Friday, January 16th 2015.
  • The lecture on November 3rd and November 7th will take place in Room HS003 instead of HS001.
  • The lecture on November 11th will take place in Room HS003 instead of HS001.
  • The second exam has been rescheduled to March 26, 10-12 in seminar room 016 in Building E1 3.

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.

The script can be downloaded here. It will be updated continuously during the semester.


Homework will be assigned bi-weekly. To qualify for the exam you need 50% of the points from these assignments. Submissions in groups of at most 2 people are possible and strongly encouraged.

Due dateAssignmentAdditional Material
2014-10-31Assignment 1-
2014-11-14Assignment 2-
2014-11-28Assignment 3-
2014-12-12Assignment 4-
2015-01-09Assignment 5Plots
2014-01-16Assignment 6Material for the programming assignment
2014-12-05Optional Programming Assignment 1
2015-01-30Optional Programming Assignment 2
2015-01-30Optional Programming Assignment 3

The registration for the exam in the HISPOS system is mandatory. If you have difficulties registering, do not hesitate to contact studium@cs.uni-saarland.de.

The first exam will be on the 13th February 2015 from 12:00 to 14:00 in HS001 Bldg. E1 3. There will also be a second exam on the 26th March 2015 from 10:00 to 12:00 in SR016 Bldg. E1 3. These will be closed books exams lasting 2 hours.

In order to register for the Lecture, write an e-mail to Laurent Hoeltgen. The subject line must begin with the tag [CAIP14]. Further, please provide the following information: first name, last name, date of birth, student ID number (e.g. Matrikel), course of study (e.g. Bachelor, Master, ...), subject of your studies (e.g. computer science, mathematics, ...). These information are necessary to give you credit points for a successful participation in the lecture at the end of the semester. Please ensure that the provided information is correct. Note that the e-mail address from which you send this information will be used to provide you with urgent information concerning the lecture. Therefore, use an address, that you check regularly. Finally, this registration is for internal purposes at our chair only and completely independent of any System like LSF/Hispos. They require a separate registration.

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.)

Last change: Laurent Hoeltgen 04.12.2014

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