The topic suggestions are grouped by the specialisations where they best fit in. The list is not exhaustive and you don't have to choose a topic from the list, you can agree something different with your supervisor. You can find completed theses on the University of Helsinki E-thesis service.

If you are interested in doing your Master's thesis on one of the suggested topics, please contact the supervisor responsible for the topic. The lists are continuously updated and topics takes are replaced with new suggestions.

You can also find some thesis topics listed in Overleaf.

1. A badly focused photograph can be sharpened digitally. In mathematical terms, this is an inverse problem called deconvolution. The topic of the master’s thesis is to apply analytical and learning methods to blurred photographs and compare their performance. Analytical deconvolution methods include Tikhonov regularisation with preconditioning and total variation regularisation. Machine learning should be done using convolutional neural networks (CNNs). Prerequisites: course "Inverse problems 1: convolution and deconvolution” (MAST31401) and some experience in machine learning programming. 

2. Sometimes image classifiers based on convolutional neural networks (CNNs) can be fooled by structured noise. The thesis topic is to examine whether such a vulnerability can be overcome by total variation regularisation as a preprocessing step. Prerequisites: course "Inverse problems 1: convolution and deconvolution” (MAST31401) and some experience in machine learning programming. 

3. Image noise removal, or denoising, is one of the standard challenges in image processing. The mathematics of inverse problems offers suitable methods, for example Total Variation (TV) regularisation. However, TV regularisation involves a parameter controlling the strength of the denoising. Watch this video.

   Optimal choice of the parameter is a deep question in inverse problems research. There are several methods in the literature. Int this MSc thesis project you get to implement a web-based test for human subjects. That way we can find what parameter value people prefer. That is then compared to one of the automatic methods. Prerequisites for the project are courses Applications of matrix computations and Inverse Problems I: convolution and deconvolution. Also, some programming experience is needed.