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TU Delft
Faculty of Electrical Engineering, Mathematics, and Computer Science
Circuits and Systems Group
EE4C03 STATISTICAL DIGITAL SIGNAL PROCESSING
ASSIGNMENT
Fusing noisy and corrupted MRI images
1. Context
Magnetic resonance imaging (MRI) is a technique to scan the human body using magnetic
fields and radio waves. It is a popular imaging technique for medical diagnosis and follow-up of
diseases without any known side effects. In general, the image is built in the spatial frequency
domain by producing one line of the image after the other, which means that it takes some time
to build a full image. Once the image is complete in the spatial Fourier domain, an inverse
Fourier transform is taken to construct the spatial image that is used for medical purposes.
2. Problem
Since the patient is not always still during the imaging process, some lines in the spatial Fourier
domain might be corrupted. If an MRI image of an eye is taken for instance, the spectral lines
where the patient is blinking will be corrupted. Furthermore, the image is also distorted by
noise. That is why in practice multiple consecutive images will be taken to overcome these
deficiencies. The problem now is how to fuse these different images in order to deal with the
corrupted spectral lines and to make the final image robust to noise. At first instance, you
may assume that you know the spatial frequencies where the different images are corrupted,
but also consider the case where these frequencies are not known and they have to be detected
automatically. Clearly, optimal filtering is the tool to use here, but also spectral estimation will
play a role in this project.
3. Assignment
In a group of 2 students, write a compact essay where you briefly present the image fusion
problem, consider the connection to optimal filtering, spectral estimation, and possibly outlier
rejection. Implement several fusing algorithms, and compare the results using MRI data from an
eye. Include your MATLAB code as an appendix. The essay typically has 4—10 pages (except
for the appendix) depending on the number of graphs.
4. Hints
Conduct a brief literature study to orient yourself on this problem. Signal processing aspects of
MRI can be found in [1] and references therein. An MRI dataset will be made available.
5. Consultants
ir. S.P. (Sundeep Prabhakar) Chepuri
Tel: +31-15-27 81797
Email: [email protected]
Room: HB 17.070
Prof. G. (Geert) Leus
Tel: +31-1527 8-4327
Email: [email protected]
Room: HB 17.280
References
[1] M. Lustig, D.L. Donoho, J.M. Santos, and J.M. Pauly, “Compressed sensing mri,” IEEE
Signal Processing Magazine, vol. 25, pp. 72–82, Mar. 2008.
2