Related papers: The inverse obstacle problem for nonlinear inclusi…
This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main…
Multi-wave inverse problems are indirect imaging methods using the interaction of two different imaging modalities. One brings spatial accuracy, and the other contrast sensitivity. The inversion method typically involve two steps. The first…
Inverse scattering focuses on recovering unknown scatterers from wave measurements. A fundamental challenge is determining whether an inverse obstacle problem can be resolved from a single far-field measurement, a task particularly…
Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…
We extend the monotonicity method for direct exact reconstruction of inclusions in the partial data Calder\'on problem, to the case of general anisotropic conductivities in any spatial dimension $d\geq 2$. From a local Neumann-to-Dirichlet…
The image reconstruction problem of the tomographic imaging technique magnetic particle imaging (MPI) requires the solution of a linear inverse problem. One prerequisite for this task is that the imaging operator that describes the mapping…
We extend the study of inverse boundary value problems to the setting of fully nonlinear PDEs by considering an inverse source problem for the Monge-Amp\`ere equation \[ \det D^2 u = F. \] We prove that, on a convex Euclidean domain in the…
We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of $\mathds{1}_{\{p\leq0\}}$ to the image plane, where $\mathds{1}$ denotes the indicator function…
We construct a monotone continuous $Q^1$ finite element method on the uniform mesh for the anisotropic diffusion problem with a diagonally dominant diffusion coefficient matrix. The monotonicity implies the discrete maximum principle.…
The inverse scattering problem for biharmonic waves, governing flexural vibrations of elastic plates, presents fundamental analytical challenges distinct from acoustic inverse problems due to the fourth-order differential operator and…
We consider the time-harmonic Maxwell system in a domain with a generalized impedance edge-corner, namely the presence of two generalized impedance planes that intersect at an edge. The impedance parameter can be $0, \infty$ or a finite…
Physics has played a fundamental role in medicine sciences, specially in imaging diagnostic. Currently, image reconstruction techniques are already taught in Physics courses and there is a growing interest in new potential applications. The…
The problem studied in this paper is ultrasound image reconstruction from frequency-domain measurements of the scattered field from an object with contrast in attenuation and sound speed. The case where the object has uniform but unknown…
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…
We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
A new approach to nonlinear modelling is presented which, by incorporating the global behaviour of the model, lifts shortcomings of both least squares and total least squares parameter estimates. Although ubiquitous in practice, a least…
In this paper, we address the question of information preservation in ill-posed, non-linear inverse problems, assuming that the measured data is close to a low-dimensional model set. We provide necessary and sufficient conditions for the…
The article is devoted to the development of numerical methods for solving variational inequalities with relatively strongly monotone operators. We consider two classes of variational inequalities related to some analogs of the Lipschitz…
We investigate the monotonicity method for fractional semilinear elliptic equations with power type nonlinearities. We prove that if-and-only-if monotonicity relations between coefficients and the derivative of the Dirichlet-to-Neumann map…