Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-65-11-K-7

Methods of Convex Analysis in Image Processing (4V+2U, 9.0 LP, AUSL)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 9.0 CP 186 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 h
(4V+2U) 9.0 CP 84 h 186 h

Basedata

SWS 4V+2U
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Lecturers
Area of study [MAT-SPAS] Analysis and Stochastics
Livecycle-State [AUSL] Phase-out period

Notice

The course was offered for the last time in SS 2019.

Contents

  • motivation: basic problems of image processing (image restoration: denoising, removal of blur, inpainting; segmentation),
  • convex sets (basic concepts, convex cone, projection and separation theorems),
  • convex functions (basic concepts, continuity of convex functions, convex optimization problems),
  • subgradients (basic concepts, subdifferential calculus, set-valued mappings),
  • duality (Legendre-Fenchel conjugate, Lagrange functions, saddle point problems),
  • numerical optimization methods with application to image processing problems.

Literature

  • A. Auslender, M. Teboulle: Asymptotic Cones and Functions in Optimization and Variational Inequalities,
  • H. H. Bauschke, P. L. Combettes: Convex Analysis and Monotone Operator Theory in Hilbert Spaces,
  • K. Bredies, D. Lorenz: Mathematische Bildverarbeitung,
  • I. Ekeland, R. Temam: Convex Analysis and Variational Problems,
  • F. Facchinei, J.-S. Pang: Finite-Dimensional Variational Inequalities and Complementarity Problems, volume I + II,
  • J.-B. Hiriart-Urruty, C. Lemarechal: Convex Analysis and Minimization Algorithms, volume 1 + 2,
  • J.-B. Hiriart-Urruty, C. Lemarechal: Fundamentals of Convex Analysis,
  • R. T. Rockafellar: Convex Analysis,
  • R. T. Rockafellar, R. J.-B. Wets: Variational Analysis.

Materials

Further literature will be announced in the lecture; Exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

References to Course [MAT-65-11-K-7]

Module Name Context
[MAT-65-11-M-7] Methods of Convex Analysis in Image Processing P: Obligatory 4V+2U, 9.0 LP, AUSL