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HL2007 Mathematical Methods of 3D Microscopy 7.5 credits

Administer About course

Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus HL2007 (Autumn 2007–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

  • Fourier analysis
  • Sampling theory
  • 3D-reconstruction
  • Radon transform
  • Central section theorem
  • Image restoration
  • Transfer theory
  • Correlation
  • Convolution
  • Multivariate statistics

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.

Recommended prerequisites

No information inserted

Equipment

No information inserted

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

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

A, B, C, D, E, FX, F

Examination

  • LAB1 - Laboratory Work, 1.5 credits, grading scale: P, F
  • TEN1 - Examination, 6.0 credits, grading scale: A, B, C, D, E, FX, 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.

Other requirements for final grade

Passed written exam (TEN1; 6 cr.) grading A-F.
Passed lab works (LAB1; 1.5 cr.) grading P/F.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Profile picture Philip Köck

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

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

CBH/Biomedical Engineering and Health Systems

Main field of study

Physics

Education cycle

Second cycle

Add-on studies

No information inserted

Contact

Philip Koeck, koeck@kth.se

Supplementary information

Notice that the final schedule is not yet decided and the dates can be changed.