This is a PhD course of 7.5 credits covering the basics of how imaging systems can be described mathematically, image quality assessment and image reconstruction. If you want to take the course, please send an email to Mats Persson at mats.persson@mi.physics.kth.se (current course round: winter 2022/2023).

Schedule

Any changes in the schedule will be announced here. In particular, the schedule for 2023 is tentative.

A2:1069 is the Physics of medical imaging seminar room at Albanova (2nd floor, see map).

Hand-in problem sets

Problem set X

Problem set 1

Problem set 1 has been updated with the following errata and clarifications:
2b "AUC [...] under the assumption of Gaussan statistics" refers to the AUC you get by replacing each probability distribution by a Gaussian distribution with the same mean and variance as the given distributions.
4b it makes more sense to define Delta n = n₂-n₁ than the original n₁-n₂. n should not be subscript on Delta n in the second line.
5b "Express the discrete fourier transform of a continuous function" - here I meant the discrete Fourier transform of the sampled version of a continuous function.

Problem set 2

Problem set 2 has been updated with the following errata and clarifications:
3 this problem shoud give 2 points instead of 1 as it said before. (So the total sum of points of all the problems is 10.)
4b the question should read "Show that the autocorrelation of a(x) is" (i.e. not autocovariance).
5b After multiplying with a filter function, you need to inverse Fourier transform to get the desired noise field.

Problem set 3

Problem set 3 has been updated with the following errata and clarifications:
Problem 1a: There was previously a square missing in the numerator of the expression.

Problem set 4

Problem set 4 has been updated with the following errata and clarifications:
Assume that there are N_* stars in the image. You may need to express the quantities on the axes in terms of N and N*.

Problem set 5 with data files: HW5_deconvolution.mat

Problem set 5 has been updated with the following errata and clarifications:
2 in Eq. 3 H should be applied to H and not to g_meas i.e. the first term should read ||Hg-g_meas||.
2a g(j) should be g_j. Both g_i and g_j are components of the reconstructed image vector g.
2b For implementing the convolution, you can use for example conv2 in matlab or scipy.signal.convolve2d in python. Make sure that the size of the output image is the same as the size of the input image.
2b Changed the recommended algorithm in matlab to fminunc and recommended increasing the maximum number of function evaluations. 3 There was previously an error by a factor 1/2 in the formula that is to be derived, it should be sigma² in front and not sigma²/2. Also, corrected a lowercase delta to uppercase. Clarified that K is the number of time samples.

Problem set 6

Resources

Course memo (last update 2023-01-14)

Course plan

Application form for transfer of credits to enter the credits into Ladok for KTH students.

Instructions for credit transfer for students at Karolinska Institutet.