- Fourier analysis
- Sampling theory
- 3D-reconstruction
- Radon transform
- Central section theorem
- Image restoration
- Transfer theory
- Correlation
- Convolution
- Multivariate statistics
HL2007 Mathematical Methods of 3D Microscopy 7.5 credits
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Course syllabus as PDF
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Course syllabus HL2007 (Autumn 2007–)Content and learning outcomes
Course contents
Intended learning outcomes
The main purpose is to introduce basic mathematical methods used in tomography, electron and light microscopy of other forms of biomedical imaging.
After completion of the course the student should:
- Understand Fourier analysis in 2 and 3 dimensions
- Understand the concepts and use of convolution and correlation in 2 and 3 dimensions
- Understand and be able to apply the convolution and the correlation theorem
- Be able to build the Fourier transform of a composite function from the Fourier transforms of its component functions
- Understand and be able to derive the central section theorem
- Understand the concept of pointspread functions and transfer functions and their correction
- Understand sampling theory and the methods of alignment in 2 and 3 dimensions
- Understand multivariate statistical methods as applied to images
Literature and preparations
Specific prerequisites
Bachelor’s degree in Engineering physics, Electrical Engineering, Computer Science or equivalent. Basic knowledge of anatomy.
Literature
Bracewell, Ronald N., Fourier Analysis and Imaging, Academic/Plenum Publishers 2004, ISBN-10: 0306481871
Koeck, Philip J. B., Introduction to Biophysical Electron Microscopy (compendium)
Examination and completion
Grading scale
Examination
- TEN1 - Examination, 6.0 credits, grading scale: A, B, C, D, E, FX, F
- LAB1 - Laboratory Work, 1.5 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
If the course is discontinued, students may request to be examined during the following two academic years.
Other requirements for final grade
Passed written exam (TEN1; 6 cr.) grading A-F.
Passed lab works (LAB1; 1.5 cr.) grading P/F.
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Offered by
Main field of study
Education cycle
Supplementary information
Notice that the final schedule is not yet decided and the dates can be changed.