Image & Signal Analysis

Blurry view of a street
Noisy blurred (folded) image - we want to learn whether we can restore the original image or at least read the license plate.
Funktionsprinzip des Computertomographen
Computertomographie: Das zu untersuchende Objekt f wird mit Röntgenstrahlen aus verschiedenen Richtungen durchleuchtet und die verbleibende Intensität der Strahlung auf der Rückseite gemessen, wobei dies aus verschiedenen Richtungen wiederholt wird. Aus den gesammelten Daten Rf muss anschießend der Absorbtionskoeffizient f des Objektes bestimmt werden.

The lecture deals with methods of signal and image analysis and reconstruction.  These include, for example, frequency analysis, edge detection or the analysis of noise content. Various tools will be introduced, such as the fast Fourier transform or wavelet transform. We will also discuss the Radon transform and its application in computed tomography.

Topics:

  • Fast Fourier Transformation
  • Filtering signals and images
  • Wavelet transformation
  • Denoising of signals and images
  • Quality measures for images

Some topics are covered in greater depth in the seminar “Mathematical Image Processing”.

Moodle: Link to course page

 

Literatur:

  • K. Bredies und D. Lorenz, Mathematical Image Processing
  • A. Iske, Approximation, Springer 2018
  • F. Natterer, The Mathematics of Computerized Tomography, Classics in Applied Mathematics 32, SIAM, 2001