## Description

__Figure 1:__ Isomap embedding of digits images. The $32\times 32$ images are naturally distributed according to the number they represent.

__Figure 2:__ Blur from wide-field microscope (left) can be expressed in a low-dimensional space composed of elementary blur operators (right).

##### Description of the project

Non-linear embedding such as Isomap, Graph Laplacian or Principal Component Analysis (PCA) are rely on the computation of Euclidean distance between the high-dimensional datapoint. However, several practical dataset are naturally defined on non-Euclidean domain.

This is the case in cryogenic Electron Microscopy (cryo-EM). The observed images can be defined as point on the manifold of 3-dimensional rotations SO(3).

In this project, we will investigate original approaches to handle dataset that are not defined on non-Euclidean domain.

This project requires strong interest for mathematical analysis.

## Organisation

##### Organisation

Any of the above project can be adapted into either a **Bachelor** or a **Master** thesis.

You will be supervised by at least two different person. Please reach out with one of the following for a first inquiry:

- Valentin Debarnot, valentin.debarnot[@]unibas.ch.
- Ivan Dokmanić, ivan.dokmanic[@]unibas.ch