Related papers: On reconstruction of complex-valued once different…
We give a complete characterisation of the reflectionless Schr\"odinger operators on the line with integrable potentials, solve the inverse scattering problem of reconstructing such potentials from the eigenvalues and norming constants, and…
We consider the multi-channel inverse scattering problem in one-dimension in the presence of thresholds and bound states for a potential of finite support. Utilizing the Levin representation, we derive the general Marchenko integral…
We give a general method for rounding linear programs that combines the commonly used iterated rounding and randomized rounding techniques. In particular, we show that whenever iterated rounding can be applied to a problem with some slack,…
We consider the linearized electrical impedance tomography problem in two dimensions on the unit disk. By a linearization around constant coefficients and using a trigonometric basis, we calculate the linearized Dirichlet-to-Neumann…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…
In this paper, we address a particular case of Calder\'on's (or conductivity) inverse problem in dimension two, namely the case of a homogeneous background containing a finite number of cavities (i.e. heterogeneities of infinitely high…
We study the inverse conductivity problem with discontinuous conductivities. We consider, simultaneously, a regularisation and a discretisation for a variational approach to solve the inverse problem. We show that, under suitable choices of…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…
Nonlinearity arising from mutual interactions is one of the two main difficulties to be addressed in inverse scattering. In this paper, we review and describe under a common rationale some approaches which have been introduced in literature…
This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…
We show that the inference problem of constraining the dipole amplitude with inclusive deep inelastic scattering data can be written into a discrete linear inverse problem, in an analogous manner as can be done for computed tomography. To…
In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the…
Learned image reconstruction has become a pillar in computational imaging and inverse problems. Among the most successful approaches are learned iterative networks, which are formulated by unrolling classical iterative optimisation…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…
Building on the well-known total-variation (TV), this paper develops a general regularization technique based on nonlinear isotropic diffusion (NID) for inverse problems with piecewise smooth solutions. The novelty of our approach is to be…
In this work, we consider Dirac-type operators with a constant delay less than two-fifths of the interval and not less than one-third of the interval. For our considered Dirac-type operators, an incomplete inverse spectral problem is…
Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…
We consider the inverse Calder\'on problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, one usually…