401-4788-16L  Mathematics of (Super-Resolution) Biomedical Imaging

SemesterFrühjahrssemester 2017
DozierendeH. Ammari
Periodizitätjährlich wiederkehrende Veranstaltung
LehrspracheEnglisch



Lehrveranstaltungen

NummerTitelUmfangDozierende
401-4788-16 GMathematics of (Super-Resolution) Biomedical Imaging4 Std.
Mo10:15-12:00HG E 22 »
Do13:15-15:00HG E 22 »
H. Ammari

Katalogdaten

KurzbeschreibungThe aim of this course is to review different methods used to address challenging problems in biomedical imaging. The emphasis will be on scale separation techniques, hybrid imaging, spectroscopic techniques, and nanoparticle imaging. These approaches allow one to overcome the ill-posedness character of imaging reconstruction in biomedical applications and to achieve super-resolution imaging.
LernzielSuper-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.

In this course we shall consider both analytical and computational
matters in biomedical imaging. The issues we consider lead to the investigation of fundamental problems in various branches of mathematics. These include asymptotic analysis, inverse problems, mathematical imaging, optimal control, stochastic modelling, and analysis of physical phenomena. On the other hand, deriving mathematical foundations, and new and efficient computational frameworks and tools in biomedical imaging, requires a deep understanding of the different scales in the physical models, an accurate mathematical modelling of the imaging techniques, and fine analysis of complex physical phenomena.

An emphasis is put on mathematically analyzing acoustic-electric imaging, thermo-elastic imaging, Lorentz force based imaging, elastography, multifrequency electrical impedance tomography, and plasmonic resonant nanoparticles.

Leistungskontrolle

Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Leistungskontrolle als Semesterkurs
ECTS Kreditpunkte8 KP
PrüfendeH. Ammari
FormSessionsprüfung
PrüfungsspracheEnglisch
RepetitionDie Leistungskontrolle wird in jeder Session angeboten. Die Repetition ist ohne erneute Belegung der Lerneinheit möglich.
Prüfungsmodusmündlich 20 Minuten
Diese Angaben können noch zu Semesterbeginn aktualisiert werden; verbindlich sind die Angaben auf dem Prüfungsplan.

Lernmaterialien

 
DokumenteIntroductory Lecture
LiteraturMathematics of Super-Resolution Biomedical Imaging - Lecture Notes
Mathematics of Super-Resolution Biomedical Imaging - Tutorial Notes
Weitere LinksTutorial 01 Codes - SVD Regularizarion
Tutorial 02 Codes - Random Medium Generation
Tutorial 03 Codes - Spherical Means Radon Transform Inversion
Tutorial 04 Codes - Neumann Poincare Operator
Tutorial 05 Codes - Electrical Impedance Tomography
Tutorial 06 Codes - Anomaly Detection Algorithms (MUSIC, Kirchhoff Migration)
Tutorial 07 Codes - Inversion Spherical Radon Transform with Total Variation Regularization
Tutorial 08 Codes - Gradient Descent Magneto Acoustic Tomography
Tutorial 09 Codes - OCT Elastography
Es werden nur die öffentlichen Lernmaterialien aufgeführt.

Gruppen

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Einschränkungen

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Angeboten in

StudiengangBereichTyp
Doktorat Departement MathematikGraduate School / GraduiertenkollegWInformation
Mathematik MasterAuswahl: Numerische MathematikWInformation