Bayesian inverse problems and beyond
Parameter estimation from sparse, noisy data is arguably one of the hardest challenges when solving inverse problems.
Moreover, in many problems inherently characterized by variability, the search for a unique set of parameters is not
only difficult, but also wrong. By viewing all unknowns as random variables, described by their probability density functios,
we acknowledge the possibility that parameters comes from from distribution. In this project we design mathematical and
computational methods for a Bayesian approach to inverse problems and a methodology for dealing with predictions in sample form.
Modeling and simulation of cellular metabolic systems
This project is concerned with designing predictive computational models of the metabolic
processes occurring in human cells in different organs. More specifically, the mathematical model captures the
biochemistry and transports acress cellular membranes, respecting to stoichiometry of the underlying systems.
Statistical source separation in MagnetoEncephaloGraphy (MEG)
The goal of this project is to employ a Baysian framework and recently designed methodology for inverse problems in
imaging to improve the localization of focal activity in
brain from MEG data. Of particular interest is the the separation of extrenal, cortical and deeps sources. The project
is carried out in collaboration with Dr. Johm Mosher from the Epilepsy Center at the Cleveland Clinic.
Structural priors for Electrical Impedance Tomography (EIT)
The lack in specificity of mammograms, whose sensitivity is
remarkable, can be compensated for by EIT, which in turn suffers from poor spatial resolution when it is
not augmented by complementary information. This project studies how to best combine the two complementary
modalitis to improve both the sensitivity and the specificity of breast malignacies detection.