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

SemesterSpring Semester 2020
LecturersH. Ammari
Periodicityyearly recurring course
Language of instructionEnglish
CommentNOTICE: The exercise class scheduled for 5 March has been cancelled


401-4788-16 GMathematics of (Super-Resolution) Biomedical Imaging
no class on 5 March 2020
4 hrs
Mon09:15-11:00HG E 22 »
Thu13:15-15:00HG E 22 »
H. Ammari

Catalogue data

AbstractThe 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.
ObjectiveSuper-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.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits8 credits
ExaminersH. Ammari
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 20 minutes
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

Recording16 March: Lecture 04, slides 1-12: Scale separation techniques
16 March: Lecture 04, slides 13-21: Scale separation techniques
23 March: Lecture 04, slides 22-34: Scale separation techniques
23 March: Lecture 04, slides 35-42: Scale separation techniques
30 March: Lecture 05, slides 1-20: Photo-acoustic imaging
30 March: Lecture 05, slides 21-27: Photo-acoustic imaging
6 April: Lecture 06, slides 1-19: Quantitative thermo-acoustic imaging
20 April: Lecture 07, slides 1-22: Ultrasonically-induced Lorentz force imaging
27 April: Lecture 08, slides 1-40: Ultrasound-modulated optical tomography
4 May: Lecture 09, slides 1-20: Acousto-electric imaging
11 May: Lecture 10, slides 1-27: Viscoelastic modulus reconstruction and full-field OCT elastography
18 May: Lecture 11, slides 1-32: Effective electrical tissue properties imaging
25 May: Lecture 12, slides 1-21: Plasmonic nanoparticle imaging
DocumentsLecture 00 - Introduction
Lecture 01 - Basic mathematical concepts
Lecture 02 - Tissues properties
Lecture 03 - Layer potential techniques
Lecture 04 - Scale separation techniques
Lecture 05 - Photo-acoustic imaging
Lecture 06 - Quantitative thermo - acoustic imaging
Lecture 07 - Ultrasonically-induced Lorentz force imaging
Lecture 08 - Ultrasound-modulated optical tomography
Lecture 09 - Acousto-electric imaging
Lecture 10 - Viscoelastic modulus reconstruction and full-field OCT elastography
Lecture 11 - Effective electrical tissue properties imaging
Lecture 12 - Plasmonic nanoparticle imaging
LiteratureMathematics of Super-Resolution Biomedical Imaging - Lecture Notes
Mathematics of Super-Resolution Biomedical Imaging - Tutorial Notes
Additional 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
Only public learning materials are listed.


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Offered in

Doctoral Department of MathematicsGraduate SchoolWInformation
Mathematics MasterSelection: Numerical AnalysisWInformation