Leonid Pestov

• Immanuel Kant Baltic Federal University

The paper is devoted to numerical research of the medical ultrasound tomography problem. This problem consists in finding small inclusions in the breast tissue by boundary measurements of the acoustic waves generated by sources located on the boundary. For medical diagnostic, it is important to recover the image of the acoustical medium and to dete...

The inverse problem of medical ultrasound tomography consists in finding small inclusions in the breast tissue by boundary measurements of acoustic waves generated by sources located on the boundary. In this work, we describe some results of simulations of this problem in 2D. The simulations include the solution of direct and inverse problems. We c...

One of the most effective methods for detecting weak scattering objects (diffractors) associated with cracked-cavernous hydrocarbon reservoirs is the CSP (Common Scattering Point) method [1]. This method is the most effective for weakly inhomogeneous media. The CSP method can be supplemented by a preliminary continuation of the wave field to a cert...

Reflection or scattering of acoustical wave on an obstacle at any moment may be considered as interaction of two interconnected vectors: the particle velocity vector of the incident wave and the generated vector of the reflected or scattered wave. In this paper an accurate statistical analysis of the amplitudes and phases of the interconnected vect...

Reflection or scattering of acoustical wave on an obstacle at any moment may be considered as interaction of two interconnected vectors: the particle velocity vector of the incident wave and the generated vector of the reflected or scattered wave. In this paper an accurate statistical analysis of the amplitudes and phases of the interconnected vect...

This work is devoted to acoustical imaging in semi-geodesic coordinates (or ray coordinates) for 2D Marmousi model. Unlike well-known migration methods (Reverse Time Migration, Kirchhoff migration, etc.), we do not assume the knowledge of the velocity model. Inverse data are waves at the line z = 0, generated by the boundary sources located at the...

This work is devoted to the medical ultrasound imaging problem. We present some results of numerical modeling, using Reverse Time Migration procedure. In the numerical experiment we use acoustical model that simulates cross-section of breast containing fat, glandular tissue and weak inclusions with a radius from 0:8mm. It is impossible to determine...

We consider the inverse multidimensional problem for the wave equation with unknown variable speed and absorption. A linear procedure based on the boundary control method for determining both coefficients is proposed.

We consider the inverse multidimensional problem for wave equation with unknown variable speed and absorption. A linear procedure based on the BC method for absorption reconstruction is proposed. The speed stays unknown.

We consider an inverse problem for the wave equation: find the speed of sound given a reaction operator on a part of the boundary. An approach for solving the problem is proposed based on the boundary control method developed by M. I. Belishev. In this case the method applies by a choice of retarded sources of a special form. The reconstruction of...

The inverse problem for the wave equation with instant lagging source on a segment of the boundary y=0 is considered. The problem is posed of determining the sound velocity depending smoothly on both spatial coordinates in response to the medium on the same segment. In a regularizing statement, uniqueness of the problem is proven under the eikonal...

The statement and some questions of the solution to the inverse problem of diffusion tomography are considered. Some numerical results of the solution and the regularization technique are briefly discussed. The main characteristics of this approach is taking account of the circular symmetry in the statement. The algorithm proposed for the solution...