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We propose an optimization approach to design cost-effective electrical power transmission networks. That is, we aim to select both the network structure and the line conductances (line sizes) so as to optimize the trade-off between network…
Photo-acoustic tomography is a newly developed hybrid imaging modality that combines a high-resolution modality with a high-contrast modality. We analyze the reconstruction of diffusion and absorption parameters in an elliptic equation and…
Installation of capacitors in distribution networks is one of the most used procedure to compensate reactive power generated by loads and, consequently, to reduce technical losses. So, the problem consists in identifying the optimal…
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…
Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…
A multi-scale approach to the inverse reconstruction of a pattern's microstructure is reported. Instead of a correlation function, a pair of entropic descriptors (EDs) is proposed for stochastic optimization method. The first of them…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…
This paper studies the extremum seeking control (ESC) problem for a class of constrained nonlinear systems. Specifically, we focus on a family of constraints allowing to reformulate the original nonlinear system in the so-called…
This paper is devoted to the analysis of a second order method for recovering the \emph{a priori} unknown shape of an inclusion $\omega$ inside a body $\Omega$ from boundary measurement. This inverse problem - known as electrical impedance…
The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization…
A new gradient-based adaptive sampling method is proposed for design of experiments applications which balances space filling, local refinement, and error minimization objectives while reducing reliance on delicate tuning parameters. High…
The importance of ultrasound is well established in the imaging of human tissue. In order to enhance image quality by exploiting nonlinear effects, recently techniques such as harmonic imaging and nonlinearity parameter tomography have been…
We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here, irreducible uncertainties refers to uncertainties in the…
This work deals with the problem of distributed data acquisition under non-linear communication constraints. More specifically, we consider a model setup where $M$ distributed nodes take individual measurements of an unknown structured…
In inclusion detection in electrical impedance tomography, the support of perturbations (inclusion) from a known background conductivity is typically reconstructed from idealized continuum data modelled by a Neumann-to-Dirichlet map. Only…
We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of…
In Electrical Impedance Tomography (EIT), the internal conductivity of a body is recovered via current and voltage measurements taken at its surface. The reconstruction task is a highly ill-posed nonlinear inverse problem, which is very…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
The problem of optimization of propagation-based phase-contrast imaging setups is considered in the case of projection X-ray imaging and three-dimensional tomography with phase retrieval. For two-dimensional imaging, a simple model for a…
High resolution ultrasound image reconstruction from a reduced number of measurements is of great interest in ultrasound imaging, since it could enhance both the frame rate and image resolution. Compressive deconvolution, combining…