Inverse problems of layer-by-layer ultrasonic tomography with the data measured on a cylindrical surface


  • A.V. Goncharsky Lomonosov Moscow State University
  • S.Yu. Romanov Lomonosov Moscow State University
  • S.Yu. Seryozhnikov Lomonosov Moscow State University



ultrasonic tomography, ayer-by-layer tomography, wave equation, coefficient inverse problem, graphics processors, supercomputers


This paper is dedicated to developing efficient methods to solve inverse problems of wave tomography. The proposed new scheme of layer-by-layer tomography of 3D objects uses the experimental data measured on a cylindrical surface. This scheme provides the measurements of both the reflected and the transmitted waves and can easily be implemented in practice. The mathematical model used to solve the inverse problem takes into account the ultrasound diffraction and absorption effects. The authors developed efficient numerical methods to reconstruct the sound speed cross section using the tomographic data measured on the cylindrical surface. These methods are aimed primarily at early breast cancer diagnosis. The inverse problems of ultrasonic tomography are nonlinear and very computationally expensive. The efficiency of the developed methods is illustrated via numerical simulations. The numerical algorithm is implemented on GPU.

Author Biographies

A.V. Goncharsky

Lomonosov Moscow State University
• Head of Laboratory

S.Yu. Romanov

Lomonosov Moscow State University
• Leading Researcher

S.Yu. Seryozhnikov


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How to Cite

Гончарский А., Романов С., Серёжников С. Inverse Problems of Layer-by-Layer Ultrasonic Tomography With the Data Measured on a Cylindrical Surface // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2017. 18. 267-276. doi 10.26089/NumMet.v18r323



Section 1. Numerical methods and applications

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