Related papers: Iterative reconstruction methods for wave equation…
Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…
In this article, we discuss sixth-order and seventh-order iterative methods for nonlinear equations. Derivative-based and derivative-free, both categories are presented for said iterative methods. Especially sixth-order derivative-based and…
Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
The initial-value problem for cylindrical gravitational waves is studied through the development of the inverse scattering method scheme. The inverse scattering transform in this case can be viewed as a transformation of the Cauchy data to…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
We establish a direct link between the time-reversal technique and the so-called adjoint method for imaging. Using this relationship, we derive new solution strategies for an inverse problem which arises in telecommunication. These…
We calculate certain estimates for the solution of the characteristic problem of the wave equation reduced to first order, in terms of the free data prescribed on two transverse surfaces, one of which is characteristic. Estimates of such…
There are two main approaches to solve inverse coefficient determination problems for wave equations: the Boundary Control method and an approach based on geometric optics. These notes focus on the Boundary Control method, but we will have…
The purpose of this report is a study of the algebraic approach possibilities to reconstruct images. This approach is reduced to solution of the large system of linear algebraic equations. We also point out some possible further…
An ill-posed Cauchy problem for the wave equation is considered: the solution is to be determined by the Cauchy data on some part of the time-space boundary. By means of Fourier method we obtain a regularization algorithm for this problem,…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
In this paper we develop numerical algorithm for solving inverse problem for the wave equation using Boundary Control method. The results of numerical experiments are represented.
We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the…
Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…
We establish inversion formulas of the so called filtered back-projection type to recover a function supported in the ball in even dimensions from its spherical means over spheres centered on the boundary of the ball. We also find several…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
We extend the key idea behind the generalized Petviashvili method of Ref. \cite{gP} by proposing a novel technique based on a similar idea. This technique systematically eliminates from the iteratively obtained solution a mode that is…
Two iterative techniques are described for decomposing a long-slit spectrum into the individual spectra of the point sources along the slit and the spectrum of the underlying background. One technique imposes the strong constraint that the…