Research Interests
Theoretical

Methodical

Applications

Publications
You can find a full list of my scientific publications here (last update: March 2017) or at my google scholar profile.
Five Key Publications
 S.R Arridge, P. Beard, M.M. Betcke, B.T. Cox, N. Huynh, F. Lucka, O. Ogunlade, and E.Zhang. Accelerated highresolution photoacoustic tomography via compressed sensing. Physics in Medicine and Biology 61(24):8908, 2016.
 S.R. Arridge, M.M. Betcke, B.T. Cox, F. Lucka, and B.E. Treeby. On the adjoint operator in photoacoustic tomography. Inverse Problems 32(11):115012, 2016.
 M. Burger and F. Lucka. Maximum a posteriori estimates in linear inverse problems with logconcave priors are proper Bayes estimators. Inverse Problems 30(11):114004, 2014.
 F. Lucka. Fast Markov chain Monte Carlo sampling for sparse Bayesian inference in highdimensional inverse problems using L1type priors. Inverse Problems 28(12):125012, 2012.
 F. Lucka, S. Pursiainen, M. Burger, and C.H. Wolters. Hierarchical Bayesian inference for the EEG inverse problem using realistic FE head models: Depth localization and source separation for focal primary currents. NeuroImage 61(4):13641382, 2012.
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 postprint version with slightly less typos on this webpage. Here is a short abstract:
Biomedical imaging techniques became a key technology to assess the structure or function of living organisms in a noninvasive 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 illposed, which means that a robust and reliable reconstruction is not possible unless additional apriori information on the quantity of interest is incorporated into the solution method. Bayesian inversion is a mathematical methodology to formulate and employ apriori 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 apriori information within the Bayesian framework.
Reviews
Reviewer for the following journals / conferences:
 Biomedical Physics & Engineering Express
 Computer Methods and Programs in Biomedicine
 Computational Statistics and Data
 IEEE Transactions on Medical Imaging
 IEEE Transactions on Image Processing
 Inverse Problems
 Inverse Problems and Imaging
 Inverse Problems in Science and Engineering
 Journal of Inverse and Illposed Problems
 Journal of Mathematical Imaging and Vision
 Jounal of Optics
 Journal of the Optical Society of America A
 Mathematical Problems in Engineering
 NeuroImage
 Neurological Research
 Optics Express
 SIAM Journal on Imaging Sciences
 SPARS
Referee for:
 German National Academic Foundation (Studienstiftung des deutschen Volkes)
 University of Innsbruck, Austria
Organization of Symposia and Workshops
 Minisymposium on "New tricks for old problems: Novel computational methods for inverse problems", at the Applied Inverse Problems conference in Hangzhou, May 29  Jun 02, 2017.
 Minisymposium on "Imaging in the fast lane: in pursuit of dynamical information", at the SIAM conference on Imaging Science in Albuquerque, May 2326, 2016.
 Minisymposium on "Bayesian Computation" , at the Applied Inverse Problems conference in Helsinki, May 2529, 2015.
Talks and Posters
(for very similar talks/posters, I only uploaded the latest version to this website to save space...)
 "Enhancing Dynamic, SubSampled 3D Photoacoustic Tomography by Simultaneous Motion Estimation", IMA Conference on Inverse Problems from Theory to Application, Cambridge, Sep 19  21, 2017.
 "Challenges of Sparse Bayesian Inversion and Uncertainty Quantication", Bayesian and Nonlinear Inverse Problems, Lorenz Center, Leiden, Aug 28  Sep 1, 2017.
 "An Experimental Study of Blood Oxygen Saturation Imaging via Quantitative Photoacoustic Tomography", Applied Inverse Problems (AIP), Hangzhou, May 29  Jun 2, 2017.
 "Enhancing Dynamic, SubSampled 3D Photoacoustic Tomography by Simultaneous Motion Estimation", Applied Inverse Problems (AIP), Hangzhou, May 29  Jun 2, 2017.
 "Total Variation Regularization and Related Topics", three lectures given in the course "GV08 Optimization and Inverse Problems in Imaging" by Simon Arridge, Mar. 2017.
 "Enhancing Compressed Sensing Photoacoustic Tomography by Simultaneous Motion Estimation.", Workshop: Shape, Images and Optimization , Münster, Mar 2, 2017.
 "The IllPosedness Always Rings Twice  Risk Estimators for Choosing Regularization Parameters in Inverse Problems", Interdisciplinary data science workshop , Cambridge, Feb 9, 2017.
 "Compressed Sensing for High Resolution 3D Photoacoustic Tomography", INdAM Workshop on Biomedical Imaging , Rome, Feb 9, 2017.
 "Sparse Dynamic High Resolution Photoacoustic Tomography", Centre for Inverse Problems Seminar, UCL, London, Jan 27, 2017.
 "SubSampled Dynamic Photoacoustic Tomography with Sparsity Constraints", IFIP WG 7.4 Workshop on Inverse Problems and Imaging, Mülheim a.d. Ruhr, Dec 19, 2016.
 "An Experiment in Quantitative Photoacoustic Tomography", QPAT Workshop @ UCL, London, Nov 10, 2016.
 "Variational Image Reconstruction for Dynamic High Resolution Photoacoustic Tomography", Developments in Healthcare Imaging  Connecting with Industry, Cambridge, Oct 19, 2016.
 "Accelerated HighResolution Photoacoustic Tomography via Compressed Sensing", SIAM Imaging Science conference, Albuquerque, May 24, 2016.
 "Can Compressed Sensing Accelerate HighResolution Photoacoustic Tomography?", Numerical Analysis and Scientific Computing" seminar at Emory, Atlanta, May 19, 2016.
 "Can Compressed Sensing Accelerate HighResolution Photoacoustic Tomography?", "Applied Math Colloquium", WWU, Apr. 20, 2016.
 "HighDimensional Bayesian Inversion with Priors Far from Gaussians.", SIAM Uncertainty Quantification conference, Lausanne, Apr. 6, 2016.
 "Recent Advances in Bayesian Inference for Biomedical Imaging.", "Workshop on Inverse Problems", Edinburgh: Mar. 17, 2016.
 "4D PAT based on Sparse Variational Methods.", "New trends in Hybrid Ultrasonic Imaging" conference, Orléans, Mar. 9, 2016.
 "Sparse Bayesian Inversion in Biomedical Imaging.", "Signal Image Processing" seminar, Telecom ParisTech Paris, Mar. 3, 2016.
 "Variational Image Reconstruction for Dynamic High Resolution Photoacoustic Tomography" , SPIE Photonics West, San Francisco, Feb. 1318, 2016.
 "Variational Image Reconstruction in 4D Photoacoustic Tomography" , Compressive Sensing and Sparsity: Theory and Applications in Tomography, Manchester, Nov. 1213, 2015.
 "Variational Methods for Dynamic HighResolution Photoacoustic Tomography", Variational Methods for Dynamic Inverse Problems and Imaging, Münster, Sep. 2830, 2015.
 "Hierarchical Bayesian Inference for Combined EEG/MEG Source Analysis" , BaCI, Utrecht, Sep. 15, 2015.
 "Towards Dynamic High Resolution Photoacoustic Tomography", ICIAM, Beijing, Aug. 1014, 2015.
 "Samplebased Sparse Bayesian Inversion in Biomedical Imaging" , ICIAM, Beijing, Aug. 1014, 2015.
 "Towards 4D Photoacoustic Tomography" , SPARS, Cambridge, Jul. 69, 2015.
 "Challenges of 4D Photoacoustic Tomography" , Challenges in Dynamic Imaging Data Workshop, Cambridge, Jun. 911, 2015.
 "Recent Advances in Bayesian Inference for Inverse Problems" , Applied Inverse Problems, Helsinki, May 2529, 2015.
 "Towards Dynamic High Resolution Photoacoustic Tomography" , A talk given in the seminar of our Center for Medical Image Computing, Apr. 15, 2015.
 "Total Variation Regularization and Related Topics", three lectures given in the course "GV08 Optimization and Inverse Problems in Imaging" by Simon Arridge, Mar. 2015.
 "Samplebased Bayesian Inference in Inverse Problems" , Applied Maths Seminar, Warwick, Feb. 13, 2015.
 "Challenges of Dynamic High Resolution Photoacoustic Tomography" , Institute for Applied Mathematics, Münster, Feb. 2, 2015.
 "Samplebased Bayesian Inversion" , Inverse Days, Tampere, Dec. 911, 2014.
 "Sparse Recovery Conditions and Realistic Forward Modeling in EEG/MEG Source Reconstruction" , UCLDuke Workshop on Sensing and Analysis of HighDimensional Data  SAHD, London, Sep. 45, 2014.
 "Sparse Recovery Conditions and Realistic Forward Modeling in EEG/MEG Source Reconstruction" , Conference ""Inverse Problems  from Theory to Applications"  IPTA, Bristol, Aug. 2628, 2014.
 "Sparse Recovery Conditions and Realistic Forward Modeling in EEG/MEG Source Reconstruction" , Workshop "Innovative Verarbeitung bioelektrischer und biomagnetischer Signale"  bbs2014 , Berlin, Apr. 1011, 2014.
 "Sparse Recovery Conditions and Realistic Forward Modeling in EEG/MEG Source Reconstruction" , Matheon Workshop on Compressed Sensing and its Applications , Berlin, Dec. 0913, 2013.
 "Hierarchical FullyBayesian Inference for Combined EEG/MEG Source Analysis of Evoked Responses: From Simulations to Real Data" , Neurovisionen 9, Cologne, Nov. 29, 2013.
 "Computational and Theoretical Aspects of L1type Priors in Bayesian Inverse Problems" , International Workshop on Inverse Problems and Regularization Theory, Fudan University, Shanghai, Sep. 2629, 2013.
 "Recent Results on L1type Priors in Bayesian Inverse Problems", Shanghai International Workshop on Recent Advances in Inverse Problems and Imaging Science, Shanghai Jiao Tong University, Sep. 2122, 2013.
 "Hierarchical FullyBayesian Inference for Combined EEG/MEG Source Analysis of Evoked Responses: From Simulations to Real Data" , International Conference on Basic and Clinical Multimodal Imaging (BaCI) , Geneva, Sep. 0508, 2013.
 "Computational and Theoretical Aspects of SparsityConstraints in Bayesian Inversion" , Applied Inverse Problems Conference , Daejeon, Jul. 0105, 2013.
 "Hierarchical Bayesian Modeling for EEG/MEG: From Simulated to Experimental Data" , Applied Inverse Problems Conference , Daejeon, Jul. 0105, 2013.
 "Hierarchical Bayesian Modeling and Another Type of Sparsity" , Applied Math Colloquium, UCLA, May 29, 2013.
 "The Bayesian Approach to Inverse Problems and Imaging" , two introductory talks given at Stanley Osher's level set collective seminar, UCLA: Talk I (April 30, 2013) , Talk II (May 5, 2013) .
 "Sparsity Constraints in Bayesian Inversion" , 18th "Inverse Days" Conference , Jyväskylä, Dec. 1719, 2012.
 "The Bayesian Approach to Inverse Problems" , three introductory talks given at the DAMTP, Centre for Mathematical Sciences, University of Cambridge, Nov. 13.15., 2012. Overview , Talk I , Talk II , Talk III .
 "Hierarchical FullyBayesian Inference for EEG/MEG combination: Examination of Depth Localization and Source Separation using Realistic FE Head Models" , Neurovisionen 8, Aachen, Oct. 26, 2012.
 "Hierarchical FullyBayesian Inference for EEG and MEG" , a talk given at during the visit of Matti Hämäläinen, WWU Münster, Oct. 12, 2012.
 "Hierarchical FullyBayesian Inference for EEG/MEG combination: Examination of Depth Localization and Source Separation using Realistic FE Head Models" , 18th International Conference on Biomagnetism (Biomag 2012), Paris, Aug. 2630, 2012.
 "MCMC Sampling for Bayesian Inference using L1type Priors" , a talk given at a seminar of our workgroup, WWU Münster, June 25, 2012.
 "A lecture on the inverse problem of EEG/MEG" , WWU Münster, May 14, 2012.
 "Hierarchical Bayesian Models for Focal EEG/MEG Inversion" , Workshop "Innovative Verarbeitung bioelektrischer und biomagnetischer Signale"  bbs2012, Berlin, Apr. 19, 2012.
 "Bioelectromagnetism in Neuroscience" , a talk given togehter with Johannes Vorwerk at the Skiseminar of the Institute for Computational and Applied Mathematics 2012 , Feb. 29, 2012.
 "Hierarchical Bayesian Estimation for the EEG Inverse Problem using Realistic FE Head Models: Depth Localization and Source Separation for Focal Primary Currents" , Autumn School "The Multimodal Brain", Tübingen, Oct. 56, 2011.
 "Hierarchical Bayesian Models for EEG Inversion: Depth Localization and Source Separation for Focal Sources in Realistic FE Head Models" , Annual meeting of the DGBMT, Freiburg, Sep. 28, 2011.
 "Hierarchical Bayesian Approaches to the Inverse Problem of EEG/MEG Current Density Reconstruction" , Annual meeting of the DMV, Köln, Sep. 20, 2011.
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 it on this webpage. Here is the abstract:
This thesis deals with the inverse problem of EEG/MEG source reconstruction: The estimation of the activityrelated 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 illconditioned 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).Code
 L1GibbsSampler.zip : Code and examples for the L1 single component Gibbs Sampler descripted in "Fast Markov chain Monte Carlo sampling for sparse Bayesian inference in highdimensional inverse problems using L1type priors", Inverse Problems, 2012.