Related papers: Remarks on the factorization and monotonicity meth…
We study an inverse source scattering problem for the Schr\"odinger equation with a quadratic nonlinearity. In general, uniqueness of inverse source problems can not be guaranteed at a fixed energy. Therefore, additional information is…
When a signal is recorded in an enclosed room, it typically gets affected by reverberation. This degradation represents a problem when dealing with audio signals, particularly in the field of speech signal processing, such as automatic…
The initial value problem for the general coupled Hirota system with nonzero boundary conditions at infinity is solved by reporting a rigorous theory of the inverse scattering transform. With the help of a suitable uniformization variable,…
Here we obtain explicit formulae for bounds on the complex electrical polarizability at a given frequency of an inclusion with known volume that follow directly from the quasistatic bounds of Bergman and Milton on the effective complex…
A factorization formula for wave functions, which is basic in the inverse spectral transform approach to initial-boundary value problems, is proved in greater generality than before. Applications follow. Related compatibility questions for…
We deal with the inverse problem of reconstructing acoustic material properties or/and external sources for the time-domain acoustic wave model. The traditional measurements consist of repeated active (or passive) interrogations, as the…
We present a Newton-like method to solve inverse problems and to quantify parameter uncertainties. We apply the method to parameter reconstruction in optical scatterometry, where we take into account a priori information and measurement…
Non-trivial analysis problems require posets with infinite ascending and descending chains. In order to compute reasonably precise post-fixpoints of the resulting systems of equations, Cousot and Cousot have suggested accelerated fixpoint…
This paper investigates the problem of time-harmonic acoustic scattering in an inhomogeneous medium with a complex topological structure. Specifically, the medium is anisotropic and contains several disjoint sound-soft obstacles. This model…
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…
This paper investigates the inverse scattering problems using sampling methods with near field measurements. The near field measurements appear in two classical inverse scattering problems: the inverse scattering for obstacles and the…
This paper is concerned with reconstruction issue of inverse obstacle problems governed by partial differential equations and consists of two parts. (i) The first part considers the foundation of the probe and enclosure methods for an…
Scattering of time-harmonic plane wave by two parallel semi-infinite rows, but with staggered edges, is considered on square lattice. The condition imposed on the semi-infinite rows is a discrete analogue of Neumann boundary condition. A…
Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally defined on unbounded domains are constructed. This is done by coupling recently developed high order local absorbing boundary conditions (ABCs)…
Analytical methods are fundamental in studying acoustics problems. One of the important tools is the Wiener-Hopf method, which can be used to solve many canonical problems with sharp transitions in boundary conditions on a plane/plate.…
In this work we shall review the (phased) inverse scattering problem and then pursue the phaseless reconstruction from far-field data with the help of the concept of scattering coefficients. We perform sensitivity, resolution and stability…
We systematically study antithetic initial noise in diffusion models, discovering that pairing each noise sample with its negation consistently produces strong negative correlation. This universal phenomenon holds across datasets, model…
We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation $\Delta u…
We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy…
We consider the inverse problem of determining a general semilinear term appearing in nonlinear parabolic equations. For this purpose, we derive a new criterion that allows to prove global recovery of some general class of semilinear terms…