On the one problem of wave diagnostic

Two approaches to solving coefficient inverse problems for wave equations are compared. One approach is based on integral representations obtained with the help of the Green's function for the wave equation. In the other approach, the gradient of the error functional is directly computed in terms of the solution of the adjoint problem for a partial differential equation. The methods developed are intended for finding inhomogeneities in homogeneous media and can be applied in medicine diag nostics, acoustic and seismic near surface exploration, engineering seismics, etc.

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“…Writing the equations for R and P separately, we obtain a nonlinear system of equations (see [13,15]) Here,…”

Section: Solution Methods For Coefficient Inverse Problems For the Wamentioning

confidence: 99%

“…Carleman estimates were addressed in [11,12], where numerical methods were proposed for solv ing a coefficient inverse problem with a source at infinity (plane wave). Coefficient inverse problems in integral representations of the Green's function were investigated in [13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Two approaches to the solution of coefficient inverse problems for wave equations

Goncharskii

Romanov

2012

Comput. Math. and Math. Phys.

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“…Model 1 describes well the effects of wave propagation in the optical, acoustic, and electromagnetic domains. The same model also describes well the effects of diffraction, refraction, and rereflection in seismic exploration and engineering seismology (Goncharskii et al 2010). For short waves the geometric optics model is used extensively, where the bulk of the energy is transferred in space along the curves that are referred to as rays in geometric optics.…”

Section: Introductionmentioning

confidence: 99%

Inverse problems of ultrasound tomography in models with attenuation

Goncharsky

Romanov²

2014

Phys. Med. Biol.

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We develop efficient methods for solving inverse problems of ultrasound tomography in models with attenuation. We treat the inverse problem as a coefficient inverse problem for unknown coordinate-dependent functions that characterize both the speed cross section and the coefficients of the wave equation describing attenuation in the diagnosed region. We derive exact formulas for the gradient of the residual functional in models with attenuation, and develop efficient algorithms for minimizing the gradient of the residual by solving the conjugate problem. These algorithms are easy to parallelize when implemented on supercomputers, allowing the computation time to be reduced by a factor of several hundred compared to a PC. The numerical analysis of model problems shows that it is possible to reconstruct not only the speed cross section, but also the properties of the attenuating medium. We investigate the choice of the initial approximation for iterative algorithms used to solve inverse problems. The algorithms considered are primarily meant for the development of ultrasound tomographs for differential diagnosis of breast cancer.

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“…To assess efficiency of the algorithms proposed in section 2.2, the model problems of reconstructing the structure of the Earth's subsurface layer have been solved [22,23]. Numerical experiments have been performed with the use of the "Chebyshev" supercomputer.…”

Section: Model Calculations Of Inverse Problems Of Wave Tomography Inmentioning

confidence: 99%

“…Section 2 discusses the integral approach to solving the inverse problem of wave tomography based on the Green function method. Using the integral approach, the inverse problems can be reduced to a system of nonlinear Fredholm integral equations of the first kind [20][21][22]. The resulting problem is ill-posed.…”

Section: Introductionmentioning

confidence: 99%

Supercomputer technologies in tomographic imaging applications

2016

JSFI

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Currently, tomographic imaging is widely used in medical and industrial non-destructive testing applications. X-ray tomography is the prevalent imaging technology. Modern medical X-ray CT scanners provide up to 1 mm of spatial resolution. The disadvantage of X-ray tomography is that it cannot be used for regular medical examinations. Early breast cancer diagnosis is one of the most pressing issues in modern healthcare. Ultrasound tomography devices are being developed in the USA, Germany and Russia to address this problem. One of the main challenges in ultrasound tomographic imaging is the development of efficient algorithms for solving inverse problems of wave tomography, which are nonlinear three-dimensional coefficient inverse problems for a hyperbolic differential equation. Solving such computationally-expensive problems requires the use of supercomputers.

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On the one problem of wave diagnostic

Cited by 9 publications

References 3 publications

Two approaches to the solution of coefficient inverse problems for wave equations

Two approaches to the solution of coefficient inverse problems for wave equations

Inverse problems of ultrasound tomography in models with attenuation

Supercomputer technologies in tomographic imaging applications

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