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An $\left( n+1\right) -$D coefficient inverse problem for the radiative stationary transport equation is considered for the first time. A globally convergent so-called convexification numerical \ method is developed and its convergence…

High-resolution remote sensing imagery is critical for environmental monitoring, urban mapping, and land cover analysis, but its transmission is often hindered by limited bandwidth and high communication costs. Conventional pipelines…

Describing the solutions of inverse problems arising in signal or image processing is an important issue both for theoretical and numerical purposes. We propose a principle which describes the solutions to convex variational problems…

This paper proposes a neural network approach for solving two classical problems in the two-dimensional inverse wave scattering: far field pattern problem and seismic imaging. The mathematical problem of inverse wave scattering is to…

We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a non-iterative reconstruction method using measurements of the radiating flux at the boundary. The attenuation and scattering…

This review paper explores the state-of-the-art in non-intrusive methods for detecting and characterising buried infrastructure, focusing on Electrical Resistivity Tomography (ERT), Infrared Thermography (IRT), and magnetometry, along with…

Numerical integral operators of convolution type form the basis of most wave-equation-based methods for processing and imaging of seismic data. As several of these methods require the solution of an inverse problem, multiple forward and…

Imaging the inner part of large geological targets is an important issue in geosciences with various applications. Dif- ferent approaches already exist (e.g. gravimetry, electrical tomography) that give access to a wide range of…

Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial…

This paper aims to solve numerically the two-dimensional inverse medium scattering problem with far-field data. This is a challenging task due to the severe ill-posedness and strong nonlinearity of the inverse problem. As already known, it…

Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging because of the non-convex loss functions and the multiple…

Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they…

This is the introductory part of my PhD thesis on inverse problems arising in medical and seismic imaging. The topics include X-ray tomography of scalar and vector fields with partial data, higher order fractional Calder\'on problems,…

Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods leveraging pretrained denoisers, and unrolled architectures…

Inverse analysis has been utilized to understand unknown underground geological properties by matching the observational data with simulators. To overcome the underconstrained nature of inverse problems and achieve good performance, an…

This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…

Bayesian inverse problems use data to update a prior probability distribution on uncertain parameter values to a posterior distribution. Such problems arise in many structural engineering applications, but computational solution of Bayesian…

Deep neural networks have become a foundational tool for addressing imaging inverse problems. They are typically trained for a specific task, with a supervised loss to learn a mapping from the observations to the image to recover. However,…

Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian…

Imaging inverse problems aim to recover high-dimensional signals from undersampled, noisy measurements, a fundamentally ill-posed task with infinite solutions in the null-space of the sensing operator. To resolve this ambiguity, prior…