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Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one and their investigation has experienced several efforts from many researchers in the…
A new version of the convexification method is developed analytically and tested numerically for a 1-D coefficient inverse problem in the frequency domain. Unlike the previous version, this one does not use the so-called "tail function",…
We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on coarse measurements. The approach is motivated by quasi-local numerical effective forward…
This paper concerns the inverse source problem for the time-harmonic wave equation in a one dimensional domain. The goal is to determine the source function from the boundary measurements. The problem is challenging due to complexity of the…
The paper aims a logarithmic stability estimate for the inverse source problem of the one-dimensional Helmholtz equation with attenuation factor in a two layer medium. We establish a stability by using multiple frequencies at the two end…
Mathematical methods of step-by-step and combined shifts are proposed for experimental data processing to reconstruct the measuring system impulse response distorted by shift-invariant blur. Proposed methods base on direct non-blind…
We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The…
We discuss a time-harmonic inverse scattering problem for a nonlinear Helmholtz equation with compactly supported inhomogeneous scattering objects that are described by a nonlinear refractive index in unbounded free space. Assuming the…
We present a recursive algorithm for multi-coefficient inversion in nonlinear Helmholtz equations with polynomial-type nonlinearities, utilizing the linearized Dirichlet-to-Neumann map as measurement data. To achieve effective recursive…
Full waveform inversion (FWI) is a process in which seismic numerical simulations are fit to observed data by changing the wave velocity model of the medium under investigation. The problem is non-linear, and therefore optimization…
This paper is concerned with an inverse boundary value problem for the Helmholtz equation over a bounded domain. The aim is to reconstruct two constant coefficients together with the location and shape of a Dirichlet polygonal obstacle from…
We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…
An inversion method for time-resolved data from ultrafast experiments is introduced, based on forward-optimisation in a trajectory basis. The method is applied to experimental data from x-ray scattering of the photochemical ring-opening…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…
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…
Seismic waves bring information from the physical properties of the earth to the surface. Full waveform inversion (FWI) is a local optimization technique which tries to invert the recorded wave fields to the physical properties. An…
In information fusion, one is often confronted with the following problem: given a preexisting set of measurements about an unknown quantity, what new measurements should one collect in order to accomplish a given fusion task with optimal…
We introduce a new multivariate statistical problem that we refer to as the Ensemble Inverse Problem (EIP). The aim of EIP is to invert for an ensemble that is distributed according to the pushforward of a prior under a forward process. In…
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…
We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited…