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Article title THE USE OF ITERATIVE METHODS OF RECONSTRUCTIVE TOMOGRAPHY FOR THE PURPOSES OF ACOUSTIC IMAGING
Authors A. Yu. Varenikova
Section SECTION II. METHODS AND DEVICES IN MEDICAL AND BIOLOGICAL PRACTICE
Month, Year 06, 2018 @en
Index UDC 534.7
DOI
Abstract The article deals with the application of methods of reconstructive tomography to restore the structural characteristics of a layered biological object. The features of implementation of integral (analytical) and iterative methods of tomographic data processing are given. The advantages and disadvantages of each group of methods are noted. It is shown that iterative methods of reconstructive tomography have a number of advantages in the study of a biological object in comparison with integrated methods. The mathematical apparatus of iterative methods of reconstructive tomography is presented. Differences of different modifications of this group of methods are given. In particular, it is reflected that the multiplicative modification of algebraic methods (MART) allows obtaining the most informative data on the distribution of structural characteristics at the boundaries of a layered biological object. The solution of the direct problem of acoustic tomography is considered. As an informative characteristic, a nonlinear parameter is proposed, which is more sensitive to structural changes of the object, the layers of which have close values of acoustic impedance. A mathematical model of the method for restoring the distribution of a nonlinear parameter is presented. This model is based on the equation for the simple wave and the point source function. Mathematical expressions are obtained to determine the value of the second-order nonlinear parameter at the point of the object under study on the basis of restoring the amplitude distribution of the vibrational velocity of the second harmonic of the ultrasonic wave. Taking into account the mathematical model of the method for determining the values of the nonlinear parameter at the point of the medium, the distribution of additives to the vibrational velocity for a layered biological object was obtained. The structure of the investigated object is described. On the basis of the data obtained, the process of obtaining projections realized by means of algebraic reconstruction methods (ART) is shown.

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Keywords Acoustic tomography; direct and inverse problems of reconstructive tomography; integral and iterative methods of reconstructive tomography; nonlinear parameter.
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