My research aims to reconstruct the geometry and material properties of objects from indirect measurements, such as scattered waves or electrical signals.
Inverse scattering problems: mathematical methods developed
– Topological sensitivity techniques to reconstruct bodies from acoustic, elastic, electromagnetic, or thermal wave data, even in attenuating media. lecture notes 2008 ip2008 jmiv10 sy21 ip21
– PDE-constrained optimization methods to identify material parameters and shapes of buried objects. ipse08 aaa13 jcp19
– Bayesian formulations with topological priors, addressed by either ensemble Markov Chain Monte Carlo samplers or PDE-constrained optimization and Laplace approximations. ip20 ip23 amc25 springer25
Main applications envisaged
– Digital Holography: Developed methods for 3D imaging by combining topological derivatives with regularized Gauss-Newton iterations. jcp19 sjis18 sjis16 ip20 ems22
– Electrical Impedance Tomography (EIT): Implemented hybrid topological derivative and gradient-based methods to identify internal structures based on their electrical conductivity. ip12
– Shear Elastography: Devised computational frameworks to quantify uncertainty in the imaging of tissue anomalies, using Bayesian inference to improve diagnostic reliability and topological priors. ip23
– Geophysical imaging: Uncertainty quantification in the imaging of deposits in stratified media by high dimensional Bayesian inference based on Karhunen-Loève expansions. amc25 eccomas24
– Phototermal imaging: Created hybrid optimization techniques with topological methods to identify material parameters and shapes of buried objects. jcp08 jmiv14
Primary methodologies
– Variational formulations of inverse scattering problems constrained by the PDEs governing the waves.
– Analytical expressions for/Numerical approximation of the topological derivatives of shape functionals under initial boundary value problem constraints.
– Design of hybrid topological/gradient and topological/Newton schemes to optimize PDE constrained shape functionals.
– Construction of topological priors for Bayesian formulations.
– Ensemble affine invariant/functional ensemble Markov Chain Monte Carlo samplers
– Karhunen-Loève expansions of random fields
