Felix Lucka

welcome to my academic web site

Research Interests

Theoretical

  • Inverse problems
  • Deep learning
  • Variational regularization
  • Compressed sensing
  • Bayesian inference
  • Mathematical modeling

Methodical

  • Computational optimization
  • Deep neural networks
  • Markov chain Monte Carlo
  • Numerics for PDEs

Main Applications

  • X-ray Computed Tomography (CT)
  • Photoacoustic Tomography (PAT)
  • Ultrasound Imaging (US)
  • Electroencephalography (EEG) and Magnetoencephalography (MEG)

Publications

You can find a full and up-to-date list of my scientific publications on my google scholar profile.

Five Key Publications

Dissertation

I submitted my PhD thesis with the title Bayesian Inversion in Biomedical Imaging in December, 2014, and defended it on the 23rd of January, 2015. You can find a post-print version with slightly less typos here. Here is a short abstract:

Biomedical imaging techniques became a key technology to assess the structure or function of living organisms in a non-invasive way. Besides innovations in the instrumentation, the development of new and improved methods for processing and analysis of the measured data has become a vital field of research. Building on traditional signal processing, this area nowadays also comprises mathematical modeling, numerical simulation and inverse problems. The latter describes the reconstruction of quantities of interest from measured data and a given generative model. Unfortunately, most inverse problems are ill-posed, which means that a robust and reliable reconstruction is not possible unless additional a-priori information on the quantity of interest is incorporated into the solution method. Bayesian inversion is a mathematical methodology to formulate and employ a-priori information in computational schemes to solve the inverse problem. This thesis develops a recent overview on Bayesian inversion and exemplifies the presented concepts and algorithms in various numerical studies including challenging biomedical imaging applications with experimental data. A particular focus is on using sparsity as a-priori information within the Bayesian framework.

Reviews

Reviewer for the following journals / conferences (check out my publons profile):

Referee for:

Organization of Symposia and Workshops

Talks and Posters

(for very similar talks/posters, I only uploaded the latest version to this website to save space; just email me if you're interested in something not available here)

Diploma Thesis (Master's Thesis)

I submitted my diploma thesis with the title Hierarchical Bayesian Approaches to the Inverse Problem of EEG/MEG Current Density Reconstruction in March, 2011. You can find it here. This is the abstract:

This thesis deals with the inverse problem of EEG/MEG source reconstruction: The estimation of the activity-related ion currents by measuring the induced electromagnetic fields outside the skull is a challenging mathematical inverse problem, as the number of free parameters within the corresponding forward model is much larger than the number of measurements. Additionally, the problem is ill-conditioned due to the smoothing propagation characteristics of the fields through the human tissue. The thesis is devoted to the introduction of a special class of statistical models, called hierarchical Bayesian models to overcome both obstacles. For this sake, it consists of four main parts: The mathematical modeling and challenges of bioelectromagnetism, a theoretical introduction of the model, the algorithmical aspects of the implementation and their practical use and properties within simulation studies. Technically, a focus of interest is on a certain class of inference algorithms that are based on alternated conditional walks through the parameter space. The forward computation will be done with a realistic high resolution finite element (FE) model of a human head.

If you're interested in these topics, it might also be worthwhile to check out PhD thesis (see above).

Software