Courses in Summer Term 2019

Mathematical Image Processing

  • Preliminary Discussion: in SR 5 (INF 205) at 11:15 on April 17th 2019
  • Target Audience: Bachelor/Master in Mathematics, Master Scientific Computing and related fields
  • Time: every Wednesday 11:15-12:45
  • Place: Seminar room SR 5 in the Mathematikon (INF 205)
  • Lecturer: Stefania Petra
  • Language: English

    Content

    Theory: Fundamentals of functional analysis, calculus of variations and convex analysis; continuous and discrete image models.

    Algorithms: Proximal-point and splitting methods

    Applications: Convex models in image processing (denoising, deblurring, decompression, MRI, tomography etc.)

    The content of the lecture is targeted at students of mathematics and scientific computing with a long-term interest in mathematical imaging, to prepare them for more advanced topics closer to research. The lecture notes are available and are self-contained and basic mathematical tools from functional and convex analysis will be provided. In an effort to help students draw relationships between the theoretical concepts and practical applications, the course is accompanied by an optional programming project.

    Literature

    • K. Bredies, D. Lorenz, Mathematische Bildverarbeitung: Einführung in Grundlagen und moderne Theorie, Vieweg+Teubner, 2011
    • R.T. Rockafellar, R.J.-B. Wets, Variational Analysis, Springer, 2004
    • H.H. Bauschke, P.L. Combettes, Convex Analysis and Monotone Operator Teory in Hilbert Spaces, Springer, 2011
    • H. Attouch, G. Buttazzo, G. Michaille, Variational Analysis in Sobolev and BV Spaces, SIAM, 2006
    • F. Natterer, F. Wübbeling. Mathematical Methods in Image Reconstruction, SIAM 2001

Lecture Notes: Mathematical Image Processing       

Seminar: Compressed Sensing      


Past Courses

Lecture (ST 18)           Hauptseminar: Probabilistische Graphische Modelle
Lecture (ST 17)           Convex Optimization
Lecture (WT 16/17)    Compressed Sensing
Lecture (SS 15)           Applied Convex Analysis