Focusing of hydroacoustic images based on multiangle sounding data |
E. O. Kovalenko, A. A. Sushchenko |
2024, issue 2, P. 193-199 DOI: https://doi.org/10.47910/FEMJ202418 |
Abstract |
In this paper we prove a convergent part of inhomogeneous Groshev type theorem for non-degenerate curves in Euclidean space where an error function is not necessarily monotonic. Our result naturally incorporates and generalizes the homogeneous measure theorem for non-degenerate curves. In particular, the method of Inhomogeneous Transference Principle and Sprindzuk's method of essential and inessential domains are used in the proof. |
Keywords: radiation transfer equation, inverse problem, bottom and volume scattering, multibeam sensing. |
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References |
[1] Turner J. A., Weaver R. L., “Radiative transfer of ultrasound”, The Journal of the Acoustical Society of America, 96:6, (1994), 3654–3674. [2] Quijano J. E., Zurk L. M., “Radiative transfer theory applied to ocean bottom modeling”, The Journal of the Acoustical Society of America, 126:4, (2009), 1711–1723. [3] Prokhorov I. V., Zolotarev V. V., Agafonov I. B., “The problem of acoustic sounding in a fluctuating ocean”, Dal’nevost. Mat. Zh., 11:1, (2011), 76–87. [4] Prokhorov I. V., Sushchenko A. A., “Studying the problem of acoustic sounding of the seabed using methods of radiative transfer theory”, Acoustic journal, 61:3, (2015), 400–408. [5] Prokhorov I. V., Sushchenko A. A., Kan V. A., “On the problem of reconstructing the floor topography of a fluctuating ocean”, Journal of Applied and Industrial Mathematics, 9:3, (2015), 412–422. [6] Kovalenko E. O., Sushchenko A. A., Prokhorov I. V., “Processing of the information from side-scan sonar”, Proceedings of SPIE, 10035, (2016), 100352C. [7] Kovalenko E. O., Sushchenko A. A., Kan V. A., “Focusing of sonar images as an inverse problem for radiative transfer equation”, Proceedings of SPIE, 10833, (2018), 108336D. [8] Prokhorov I. V., Sushchenko A. A., Kim A., “Initial boundary value problem for the radiative transfer equation with diffusion matching conditions”, Journal of Applied and Industrial Mathematics, 11:1, (2017), 115–124. [9] Prokhorov I. V., Sushchenko A. A., “The Cauchy problem for the radiatve transfer equation in an unbounded medium”, Dal’nevost. Mat. Zh., 18:1, (2018), 101–111. [10] Prokhorov I. V., Kovalenko E. O., “Determination of the bottom scattering coefficient in multi-beam probing of the ocean”, Far Eastern Mathematical Journal, 19:2, (2019), 206–222. [11] Amosov A. A., “Initial-Boundary Value Problem for the Non-Stationary Radiative Transfer Equation with Fresnel Reflection and Refraction Conditions”, Journal of Mathematical Sciences, 231:3, (2018), 279–337. [12] Amosov A. A., “Initial-Boundary Value Problem for the Non-stationary Radiative Transfer Equation with Diffuse Reflection and Refraction Conditions”, Journal of Mathematical Sciences, 235:2, (2018), 117–137. [13] Amosov A. A., “Nonstationary radiation transfer through a multilayered medium with reflection and refraction conditions”, Mathematical Methods in the Applied Sciences, 41:17, (2018), 8115–8135. [14] Prokhorov I. V., “The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions”, Math. Notes, 105:1, (2019), 80–90. [15] Kim A., Prokhorov I. V., “Initial-boundary value problem for a radiative transfer equation with generalized matching conditions”, Siberian Electronic Mathematical Reports, 16, (2019), 1036–1056. |