Department of Mathematics

Mathematics of Super-Resolution Biomedical Imaging

Please note that this page is old.
Check in the VVZ for a current information.
Professor Prof. Dr. Habib Ammari
Time Mo 10-12, Th 13-15
Francisco Romero Room HG E 22

Aims of the Course

Super-resolution imaging is a collective name for a number of emerging techniques that achieve resolution below the conventional resolution limit, defined as the minimum distance that two point-source objects have to be in order to distinguish the two sources from each other. In this course we describe recent advances in scale separation techniques, spectroscopic approaches, multi-wave imaging, and nanoparticle imaging. The objective is fivefold: (i) To provide asymptotic expansions for both internal and boundary perturbations that are due to the presence of small anomalies; (ii) To apply those asymptotic formulas for the purpose of identifying the material parameters and certain geometric features of the anomalies; (iii) To design efficient inversion algorithms in multi-wave modalities; (iv) to develop inversion techniques using multi-frequency measurements; (v) to develop a mathematical and numerical framework for nanoparticle imaging.

Applications of the anomaly detection and multi-wave approaches in medical imaging are described in some detail. In particular, the use of asymptotic analysis to improve a multitude of emerging imaging techniques is highlighted. These imaging modalities include both single-wave and multi-wave approaches. They can be divided into three groups: (i) Those using boundary or scattering measurements such as electrical impedance tomography, ultrasound, and infrared tomographies; (ii) Those using internal measurements such as magnetic resonance elastography; (iii) Those using boundary measurements obtained from internal perturbations of the medium such as photoacoustic tomography, impediography, and magnetoacoustic imaging.

This course is offered every year in the Spring semester.

Course Material

Introductory Lesson

Lecture Notes

Tutorial Notes

Matlab Codes

SVD regularization code

Random medium generation codes

Spherical means Radon transform inversion

Neumann Poincaré Operator

Electrical Impedance Tomography

Anomaly detection algorithms: MUSIC for Conductivity and MUSIC, Backpropagation and Kirchhoff migration for Helmholtz

Inversion of the spherical radon transform with total variation regularization

Gradient descent for magneto acoustic imaging

OCT Elastography


Wichtiger Hinweis:
Diese Website wird in älteren Versionen von Netscape ohne graphische Elemente dargestellt. Die Funktionalität der Website ist aber trotzdem gewährleistet. Wenn Sie diese Website regelmässig benutzen, empfehlen wir Ihnen, auf Ihrem Computer einen aktuellen Browser zu installieren. Weitere Informationen finden Sie auf
folgender Seite.

Important Note:
The content in this site is accessible to any browser or Internet device, however, some graphics will display correctly only in the newer versions of Netscape. To get the most out of our site we suggest you upgrade to a newer browser.
More information

© 2016 Mathematics Department | Imprint | Disclaimer | 30 June 2016