Decomposition methods with applications in neuroscience

The brain is the most important signal processing unit in the human body. It is responsible for receiving, processing and storing information. One of the possibilities to study brain functioning is by placing electrodes on the scalp and recording the synchronous neuronal activity of the brain. Such a recording measures a combination of active processes in the whole brain. Unfortunately, it is also contaminated by artifacts. By extracting the artifacts and removing them, cleaned recordings can be investigated. Furthermore, it is easier to look at speci?c brain activities, like an epileptic seizure, than at a combination. In this thesis, we present di?erent mathematical techniques that can be used to extract individual contributing sources from the measured signals for this purpose. We focused on Canonical Correlation Analysis (CCA Independent Component Analysis (ICA) and Canonical/ Parallel Factor Analysis (CPA). We show that the properties of the sources, extracted with CCA are appropriate to extract muscle artifacts from the brain recordings. We validated this in a study on speech production. We illustrate that ICA algorithms can be used to remove eye artifacts. An important topic in epilepsy research is also accurate localisation of the epileptogenic focus. Based on the brain signals recorded during an epileptic seizure, the localisation of this focus can be derived. However, artifacts often obscure this seizure. In a ?rst step, we removed eye and muscle artifacts to improve the localisation of this focus. In a second step, we developed a method based on CPA that directly extracts the epileptic source. The localisation of this source provides then information on the focus. We also developed some new algorithms. We show how to incorporate spatial constraints into ICA. These constraints are related to how much the sources are present in the di?erent recording electrodes. We show that incorporating such prior knowledge improves the accuracy of the estimation of the sources. A last chapter deals with a new algorithm that combines two decomposition methods: ICA and CPA. We discuss that combining the constraints underlying both decomposition methods is useful in practical applications and show that in several situations the decomposition of the new method outperforms both ordinary ICA and CPA.