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<p>In this work, the inverse problem of reconstructing the squared slowness function in the two-dimensional eikonal equation has been developed and numerically investigated. The inverse problem is reduced to the minimization of a&#xa0;travel-time misfit functional by gradient method and employs the Fast Marching Method for an efficient solution of the direct eikonal problem. A&#xa0;gradient of the functional is calculated by direct and adjoint problems, enabling the computational cost of the gradient comparable to that of a&#xa0;single direct solve. Numerical experiments on synthetic models which parameters are close to the human body with inclusions show that the method can accurately recover the spatial structure and contrast of the slowness distribution under different grid resolutions and source configurations. A comparative analysis of simple gradient and heavy ball method has shown that the use of adaptive relaxation of steps accelerates the convergence of gradient methods, including accelerated gradient methods.</p>

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Inverse kinematic problem in 2d medical acoustic travel-time tomography

  • 期刊论文

  • 发表日期：

    2026年6月16日

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  • Maxim Dudar,
  • Maxim Shishlenin

摘要

In this work, the inverse problem of reconstructing the squared slowness function in the two-dimensional eikonal equation has been developed and numerically investigated. The inverse problem is reduced to the minimization of a travel-time misfit functional by gradient method and employs the Fast Marching Method for an efficient solution of the direct eikonal problem. A gradient of the functional is calculated by direct and adjoint problems, enabling the computational cost of the gradient comparable to that of a single direct solve. Numerical experiments on synthetic models which parameters are close to the human body with inclusions show that the method can accurately recover the spatial structure and contrast of the slowness distribution under different grid resolutions and source configurations. A comparative analysis of simple gradient and heavy ball method has shown that the use of adaptive relaxation of steps accelerates the convergence of gradient methods, including accelerated gradient methods.