Compressive sensing is a new field in signal processing and applied mathematics. It allows one to simultaneously sample and compress signals which are known to have a sparse representation in a known basis or dictionary along with the subsequent recovery by linear programming (requiring polynomial (P) time) of the original signals with low or no error [1–3]. Compressive measurements or samples ...

The three-dimensional Schr/Sdinger equation inverse scattering problem with a nonspherically-symmetric potential is related to the filtering problem of computing the linear leastsquares estimate of the three-dimensional random field on the surface of a sphere from noisy observations inside the sphere. The relation consists of associating an estimation problem with the inverse scattering problem...

Some novel numerical approaches to solving direct and inverse obstacle scattering problems are presented. Scattering by finite obstacles and by periodic structures is considered. The emphasis for solving direct scattering problem is on the Modified Rayleigh Conjecture method, recently introduced and tested by the authors. This method is used numerically in scattering by finite obstacles and by ...

The Schur algorithm and its times-domain counterpart, the fast Cholseky recursions, are some efficient signal processing algorithms which are well adapted to the study of inverse scattering problems. These algorithms use a layer stripping approach to reconstruct a lossless scattering medium described by symmetric two-component wave equations which model the interaction of right and left propaga...

Inverse scattering and spectral one-dimensional problems are discussed systematically in a self-contained way. Many novel results due to the author are presented. The classical results are often presented in a new way. Several highlights of the new results include: 1) Analysis of the invertibility of the steps in the Gel’fand-Levitan and Marchenko inversion procedures, 2) Theory of the inverse ...

We will establish far eld identities for the scattering of time-harmonic acoustic waves from sound-soft and sound-hard obstacles and will illustrate two applications of these identities for the inverse obstacle scattering problem. Firstly, we will provide an alternate proof for the Fr echet diierentiability of the far eld pattern with respect to the boundary. Secondly, we will connect the ident...

Abstract. By developing the ∂̄-approach to global ”inverse scattering” at zero energy we give a principal effectivization of the global reconstruction method for the Gel’fandCalderon inverse boundary value problem in three dimensions. This work goes back to results published by the author in 1987, 1988 and proceeds from recent progress in the ∂̄-approach to inverse scattering in 3D published by t...

A static scission configuration in cold ternary fission has been considered in the framework of mean field approach. The inverse scattering method is applied to solve single-particle Schrödinger equation, instead of constrained selfconsistent Hartree–Fock equations. It is shown, that it is possible to simulate one-dimensional three-center system via inverse scattering method in the approximatio...

An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data. The main difference with respect to the standard Inverse Scattering Transform lies in the fact that we have a weighted spectral problem. We therefore have to develop different asy...