Leonid Pestov

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 determine the values of velocity, attenuation and density. In the paper, we describe a numerical experiment of visualization of several inclusions using the energy version of the reverse time migration (RTM). Certainly, the RTM image does not separate velocity and attenuation inclusions. However, kinematic and amplitude analysis gives a possibility to estimate values of the velocity and attenuation. As a result, we split the RTM image into two ones. Note that in this paper we consider the scalar value of sound velocity.

The work is devoted to the problem of determining small sound speed fluctuations in glandular tissue for specific breast model [1], [2]. Our approach, proposed in [3],[4], is based on visualization of inclusions and unknown inner boundary between fat and glandular tissues and determination of sound speeds in inclusions using kinematic argument. In this work we examine stability of our algorithm with respect to a noise in the original breast sound speed model. We use Gaussian noise with different intensity.

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 certain depth for strongly inhomogeneous medium. In this paper we use Reverse Time Datuming (RTD) procedure for this purpose [2, 3, 4]. The new CSP-RTD method is based on both CSP and RTD methods for determining deep-seated diffractors in complex acoustic medium. The results of numerical studies of CSP-RTD method for a complex acoustic model is presented. The comparison of CSP-RTD method and RTM method is also presented.

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 same line. Our approach is based on the Boundary Control method and a relation between some Imaging condition of the forward problem and velocity image.

Article International workshop “Inverse Problems and Integral Geometry” Immanuel Kant Baltic Federal University, Kaliningrad, Russia October 13–16, 2014 was published on October 1, 2015 in the journal Journal of Inverse and Ill-posed Problems (volume 23, issue 5).

Given a bounded domain M in with a conformally Euclidean metric , we consider the inverse problem of recovering a semigeodesic neighborhood of a domain and the conformal factor ρ in the neighborhood from the travel time data (defined below) and the Cartesian coordinates of Γ . We develop an explicit reconstruction procedure for this problem. The key ingredient is the relation between the reconstruction procedure and a Cauchy problem of the conformal Killing equation.

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