EEG measurements are essential for understanding brain activity, but traditional methods struggle to localize deep and weakly measurable signals. Through new mathematical approaches, it is possible to reduce localization errors and achieve better reconstruction of brain activity.
Below, Niranjana Sudheer answers three questions about her doctoral research on weighted regularization methods for the inverse electroencephalography (EEG) problem.
Why is this research important?
Electroencephalography (EEG) is a widely used and non‑invasive method for measuring brain activity by placing electrodes on the scalp. The method is important both for understanding brain function and for diagnosing neurological disorders. A central challenge, however, is the so‑called inverse EEG problem: determining the precise location and orientation of the electrical sources inside the brain based on measurements taken at the scalp. Many different patterns of brain activity can produce the same signals on the scalp, and standard reconstruction methods are known to introduce systematic errors — especially when the sources lie deep within the brain.
What was the goal of the doctoral project?
The aim of the work was to develop improved mathematical methods for solving the inverse EEG problem using regularization. The project combines mathematical modelling, numerical optimization, and insights from computational neuroscience. A key focus was to introduce and analyze weighted regularization methods that can counteract common sources of error, such as depth bias and orientation bias.
What are the most important findings?
The research presents and investigates weighted sparsity‑promoting methods that enhance the ability to localize deep and weak brain activity. The theoretical results show that these methods provide solid recovery guarantees for a broad class of weighting operators. Numerical experiments using realistic head models confirm that the methods achieve low localization errors and in several cases outperform existing approaches. In the long term, this may contribute to more precise diagnostics and a better tool for understanding how the brain functions.
FActs:
Niranjana Sudheer
- Ph.D: NMBU's Faculty of Science and Technology
- Thesis title:
- Norwegian:Vekta regulariseringsmetodar med bruk i det inverse elektroencefalografi (EEG)-problemet
- English: Weighted Regularization Methods with Applications to the Inverse Electroencephalography (EEG) Problem
Niranjana Sudheer will defend her ph.d. thesis at NMBU Friday 17 April 2026. Read more about the event here.