O. D. Rumyantseva

Multifrequency generalization of the Novikov algorithm for the two-dimensional inverse scattering problem

The process of reconstruction of two-dimensional refractive-absorbing scatterers by the modified Novikov algorithm is considered. A generalization of this algorithm to the multifrequency mode is proposed. The scattering data obtained at different frequencies are combined in the process of the solution using the a priori known frequency dependence of the scatterer function, which yields the constraint equations that are absent in the single-frequency version. It is shown that the problem of reconstruction instability observed in strong scatterers in the single-frequency mode can be removed by the multifrequency mode. The quality of the scatterer estimate in the multifrequency mode is significantly higher than that of the estimate obtained by straightforwardly averaging the single-frequency solutions. Interference resistance of the algorithm is sufficiently high to allow its application in practice.

Reconstruction of Fine-Scale Structure of Acoustical Scatterer on Large-Scale Contrast Background

One of the most actual medical problems is a diagnostics of different pathologies of biological tissues. It is very important to reveal a malignant pathology at the earliest stage of its growth, when the size of a disease area is a part of a millimeter. Then strict mathematical methods of the solution of inverse problems are necessary for revealing this area on the basis of experimental acoustical scattering data.

Solution of the three-dimensional acoustic inverse scattering problem. The modified Novikov algorithm

For the first time, three-dimensional model scatterers of various strengths and size are numerically reconstructed on the basis of the monochromatic functional-analytical Novikov algorithm. The algorithm allows for the multiple scattering processes and does not impose stringent constraints on the scatterer strength. The resulting scatterer estimate approaches the true value after the width of the scatterer’s spatial spectrum is restricted to a region with a radius of about 2k0. The noise robustness of the algorithm, i.e., the robustness to random errors in experimental data, is sufficiently high for diagnostic applications. However, the amount of numerical operations required by the algorithm is great.

Simulation of a functional solution to the acoustic tomography problem for data from quasi-point transducers

Two variants of a functional-analytical algorithm intended for solving inverse tomography problems are discussed and numerically carried out. The acoustic fields that are transmitted and received by transducers, which are equivalent to point ones, serve as experimental data. These data are used to calculate the classical or generalized scattering amplitude, and the scatterer characteristics are then reconstructed. The algorithm requires neither model linearization, no iterations for refining the estimates of scatterers, thus making it attractive for solving acoustic-tomography problems in different applications. The results of the numerical reconstruction of inhomogeneities in the sound velocity and absorption in a medium are presented.

Experimental modeling of the processes of active-passive thermoacoustic tomography

Experiments confirming the major results of the theoretical study of an active-passive mode of acoustic thermotomography are described. Experimental results are obtained with a setup intended for physical modeling of the processes of correlation reconstruction of the temperature, absorption, and phase velocity of sound in the object under investigation in the presence of an additionally introduced “illuminating” acoustic noise field. A possibility of reconstructing the local values of absorption and inhomogeneity of sound velocity from analyzing the correlation dependences based on difference and summary delays and also with the help of a controlled anisotropic acoustic irradiation is demonstrated.

Reconstruction of the sound velocity and absorption spatial distributions in soft biological tissue phantoms from experimental ultrasound tomography data

The paper is devoted to implementing in a specific tomographic device a two-step algorithm designed to reconstruct the spatial distributions of the sound velocity and absorption coefficient, primarily in soft biological tissues. To generate the input data of the first and second steps, a correlation algorithm is used based on determination of the time shift in the signal propagation time in the presence of an object. The results of reconstruction are presented, which are based on data measured for objects-phantoms using a developed experimental ultrasound tomograph model. We discuss problems that arise during reconstruction with a low resolution at the first step of the algorithm, and we demonstrate the high spatial resolving power achieved at the second step.

Reconstruction of the fine structure of an acoustic scatterer against the distorting influence of its large-scale inhomogeneities

In the ultrasonic diagnostics of small-size neoplasms of biological tissues at the earliest stage of their development, an efficient way to eliminate the distorting influence of high-contrast or large inhomogeneities of the biological medium is to apply the iterative technique. A simple approach is proposed, which makes it possible with only two iteration steps to achieve an efficient focusing of the tomograph array. At the first step, the unknown distribution of the large-scale inhomogeneities of sound velocity and absorption over the scatterer is reconstructed, where the large-scale inhomogeneities are those whose size exceeds several wavelengths. At the second step, the fine structure of the scatterer is reconstructed against the large-scale background, which can be performed with a high accuracy owing to the evaluation of the background at the first step. The possibility of simultaneous reconstruction of the large-scale and fine structures by the noniterative Grinevich-Novikov algorithm is considered as an alternative. This algorithm reconstructs in an explicit form two-dimensional refractive-absorbing acoustic scatterers of almost arbitrary shape and strength. Taking into account the effects of multiple scattering, this algorithm provides resolution of the fine structure almost as good as that achieved in reconstructing the same structure against an undistorting homogeneous background. The results of numerical simulations of both algorithms are presented.

Modeling of the exact solution of the inverse scattering problem by functional methods

Relations between different functional algorithms for solving the inverse scattering problem are analyzed. It is shown that the Rose algorithm does not provide a unique solution, but can be used as a means to improve the interference resistance in reconstruction algorithms that provide unique restoration of scatterer characteristics. The possibility of unique reconstruction of refractive-absorbing scatterers by the modified Rose algorithm, which includes the Sokhotsky equation, is illustrated. Results of numeric simulation of the Novikov-Grinevich-Manakov algorithm, which is efficient in reconstructing two-dimensional acoustic refractive-absorbing scatterers of actually arbitrary shape and strength, are presented. The algorithm rigorously allows for multiple scattering effects. It is promising for tomography-like application problems and features a sufficiently high interference resistance.

Acoustic tomography of the nonlinear parameter by a small number of transducers

A wave approach to solving the problem of reconstructing the acoustic nonlinear parameter distribution by a simple transmitting-receiving system with broadband modulation of primary waves is proposed. The approach uses the effect of sound scattering by sound, which makes it possible to employ a complicated time processing of signals instead of spatial processing and, consequently, to reduce the number of transmitting and receiving transducers. The possibility of practical implementation of a two-dimensional tomographic scheme based on coherent correlation processing of broadband quasi-random signals at combination frequencies is analyzed. Results of model numerical experiments on reconstructing complicated spatial distributions of the nonlinear parameter are presented.

Reconstruction of spatial distributions of sound velocity and absorption in soft biological tissues using model ultrasonic tomographic data

A two-step algorithm is used to reconstruct the spatial distributions of the acoustic characteristics of soft biological tissues-the sound velocity and absorption coefficient. Knowing these distributions is urgent for early detection of benign and malignant neoplasms in biological tissues, primarily in the breast. At the first stage, large-scale distributions are estimated; at the second step, they are refined with a high resolution. Results of reconstruction on the base of model initial data are presented. The principal necessity of preliminary reconstruction of large-scale distributions followed by their being taken into account at the second step is illustrated. The use of CUDA technology for processing makes it possible to obtain final images of 1024 × 1024 samples in only a few minutes.