Geodesic
Computing magnifier for refining the position and shape of three-dimensional objects in acoustic sensing
Matematičeskoe modelirovanie, Tome 34 (2022) no. 5, pp. 3-26

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A computational procedure is proposed for refining the position and shape of threedimensional acoustic inhomogeneities during sound sounding of the medium. The procedure, called a computational magnifier, is based on a high-speed algorithm for solving the inverse problem of acoustic sounding in areas of a special structure (threedimensional space, cylindrical area, etc.) with a complex wave field amplitude as data recorded “in a thin layer”. The computational magnifying procedure consists in "fast" solving the inverse problem using the specified algorithm on a fixed grid in the original three-dimensional region, narrowing the original region to a nested new region containing inhomogeneities, and then solving the inverse problem in this new region on a grid of the same size. Repeating this procedure several times, one can significantly refine the position and shape of the investigated zoomed inhomogeneities. The computational magnifying procedure works much faster than solving the inverse problem on fine threedimensional grids in the original domain. This makes it easy to implement the procedure on personal computers (PCs) of average performance. The article proposes a method for the numerical assessment of the quality of clarification of the position and shape of the studied inhomogeneities, based on the use of histograms. A number of numerical model PC experiments on the use of a computational magnifier in a cylindrical region are presented. These include: analysis of the quality of position and shape refinement using histograms when solving an inverse problem with accurate and noisy data, the effect of averaging noisy data for determining the position and shape, experiments to assess the resolution of a computational magnifier, etc. The operating time of the computational magnifier in these three-dimensional numerical experiments was about 10 seconds.
Keywords: acoustic sounding, 3D-inverse problem of determining inhomogeneities, fast regularizing algorithm
Mots-clés : computational magnifier. 
@article{MM_2022_34_5_a0,
     author = {A. B. Bakushinsky and A. S. Leonov},
     title = {Computing magnifier for refining the position and shape of three-dimensional objects in acoustic sensing},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--26},
     publisher = {mathdoc},
     volume = {34},
     number = {5},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2022_34_5_a0/}
}
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A. B. Bakushinsky; A. S. Leonov. Computing magnifier for refining the position and shape of three-dimensional objects in acoustic sensing. Matematičeskoe modelirovanie, Tome 34 (2022) no. 5, pp. 3-26. http://geodesic.mathdoc.fr/item/MM_2022_34_5_a0/