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SENSITIVITY OF inversion algorithms FOR RECOVERING ELASTIC-CONSTANTS OF ANISOTROPIC SOLIDS FROM LONGITUDINAL WAVESPEED DATA

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ULTRASONICS 1992年第1期30卷 43-48页

作者： EVERY, AG SACHSE, W CORNELL UNIV DEPT THEORET & APPL MECHITHACANY 14853

This paper discusses the sensitivity of inversion algorithms for recovering the elastic constants of moderately anisotropic solids using only ultrasonic longitudinal wavespeed data measured for various directions in a medium. This investigation is motivated, in part, by experience with the recently developed point source/point receiver technique, in which longitudinal wave arrivals are clearer and easier to measure accurately than the later transverse wave arrivals. A perturbation method is presented which shows that for a medium of triclinic symmetry, the longitudinal wavespeeds are most sensitive to the partial set of elastic constants C-11, C22, C33, (C-12 + 2C66), (C23 + 2C44) and (C-13 + 2C55), and it is these constants which can therefore be most accurately recovered from longitudinal wavespeed data. A number of illustrative numerical examples are presented which demonstrate the lack of sensitivity to certain constants and illustrate the recovery of elastic constants from simulated longitudinal mode data. These show that there is good convergence for the partial set of elastic constants, whereas the remaining elastic constants are much less accurately recovered.

关键词： inversion algorithms ELASTIC CONSTANTS LONGITUDINAL WAVESPEEDS

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A performance comparison of inversion algorithms for the retrieval of the aerosol size distribution

A performance comparison of inversion algorithms for the ret...

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作者： Estellés, V. Utrillas, M.P. Gómez-Amo, J.L. Martínez-Lozano, J.A. Grupo de Radiación Solar Dept. Termodinàmica Universitat de València C/ Dr. Moliner 50 46100 Burjassot Valencia Spain

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Tensor tomography using V-line transforms with vertices restricted to a circle

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ANALYSIS AND MATHEMATICAL PHYSICS 2025年第1期15卷 1-23页

作者： Mishra, Rohit Kumar Purohit, Anamika Zamindar, Indrani Indian Inst Technol Gandhinagar Dept Math Gandhinagar 382355 Gujarat India

In this article, we study the problem of recovering symmetric m-tensor fields (including vector fields) supported in a unit disk D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {D}}$$\end{document} from a set of generalized V-line transforms, namely longitudinal, transverse, and mixed V-line transforms, and their integral moments. We work in a circular geometric setup, where the V-lines have vertices on a circle, and the axis of symmetry is orthogonal to the circle. We present two approaches to recover a symmetric m-tensor field from the combination of longitudinal, transverse, and mixed V-line transforms. With the help of these inversion results, we are able to give an explicit kernel description for these transforms. We also derive inversion algorithms to reconstruct a symmetric m-tensor field from its first (m+1) integral moment longitudinal/transverse V-line transforms.

关键词： Inverse problems V-line transform Tensor tomography inversion algorithms Integral moments

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V-Line Tensor Tomography: Numerical Results\ast

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SIAM JOURNAL ON IMAGING SCIENCES 2025年第1期18卷 597-630页

作者： Ambartsoumian, Gaik Mishra, Rohit Kumar Zamindar, Indrani Univ Texas Arlington Dept Math Arlington TX 76019 USA Indian Inst Technol Gandhinagar Dept Math Gandhinagar 382355 Gujarat India

This article presents the numerical verification and validation of several inversion algorithms for V-line transforms (VLTs) acting on symmetric 2-tensor fields in the plane. The analysis of these transforms and the theoretical foundation of their inversion methods were studied in the recent demonstrate the efficient recovery of an unknown symmetric 2-tensor field from various combinations of the longitudinal, transverse, and mixed VLTs, their corresponding first moments, and the star VLT. The paper examines the performance of the proposed algorithms in different settings and illustrates the results with numerical simulations on smooth and nonsmooth phantoms.

关键词： inverse problems V-line transform broken ray transform star transform tensor tomography numerical simulations inversion algorithms numerical solution of PDEs

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A modification of the Dewilde-van der Veen method for inversion of finite structured matrices

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LINEAR ALGEBRA AND ITS APPLICATIONS 2002年 343卷 419-450页

作者： Eidelman, Y Gohberg, I Tel Aviv Univ Raymond & Beverly Sackler Fac Exact Sci Sch Math Sci IL-69978 Tel Aviv Israel

We study a class of block structured matrices R = {R-ij}(i,j=1)(N) with a property that the solution of the corresponding system Rx = y of linear algebraic equations may be performed for O(N) arithmetic operations. In this paper for finite invertible matrices we analyze in detail factorization and inversion algorithms. These algorithms are related to those suggested by P.M. Dewilde and A.J. van der Veen (Time-varying Systems and Computations, Kluwer Academic Publishers, New York, 1998) for a class of finite and infinite matrices with a small Hankel rank. The algorithms presented here are more transparent and are a modification of the algorithms from the above reference, The approach and the proofs are essentially different from those in the above-mentioned reference. The paper contains also analysis of complexity and results of numerical experiments. (C) 2002 Elsevier Science Inc. All rights reserved.

关键词： structured matrices linear complexity algorithms inversion algorithms factorization algorithms solution of linear equations

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A neural networks inversion-based algorithm for multiobjective design of a high-field superconducting dipole magnet

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IEEE TRANSACTIONS ON MAGNETICS 2007年第4期43卷 1557-1560页

作者： Cau, F. Di Mauro, M. Fanni, Alessandra Montisci, A. Testoni, P. Univ Cagliari Elect & Elect Engn Dept I-09123 Cagliari Italy

In this paper, an original algorithm to solve multiobjective design problems, which makes use of a neural network (NN) inversion method, is presented. The proposed approach allows us to explore the solutions directly in the objectives space, rather than in the parameters space, with a great saving of computation time in the reconstruction of the Pareto front. A multilayer perceptron NN is first trained to solve the analysis design problem. The inversion of the neural model allows us to obtain the design parameters, starting from the desired requirements on all the conflicting multiple objectives. The performance of the method is demonstrated by its application to the design of a high-field superconducting dipole magnet, where a tradeoff between the superconductors volumes is required in order to obtain a prescribed magnetic field value in the dipole axis.

关键词： inversion algorithms multiobjective design neural networks (NNs) Pareto front superconducting dipole

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Spatio-temporal directional filtering for improved inversion of MR elastography images

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MEDICAL IMAGE ANALYSIS 2003年第4期7卷 465-473页

作者： Manduca, A Lake, DS Kruse, SA Ehman, RL Mayo Clin & Mayo Fdn Rochester MN 55901 USA

Dynamic magnetic resonance elastography can visualize and measure propagating shear waves in tissue-like materials subjected to harmonic mechanical excitation. This allows the calculation of local values of material parameters such as shear modulus and attenuation. Various inversion algorithms to perform such calculations have been proposed, but they are sensitive to areas of low displacement amplitude (and hence low SNR) that result from interference patterns due to reflection and refraction. A spatio-temporal directional filter applied as a pre-processing step can separate interfering waves so they can be processed separately. Weighted combinations of inversions from such directionally separated data sets can significantly improve reconstructions of shear modulus and attenuation. (C) 2003 Elsevier B.V. All rights reserved.

关键词： elasticity elastography inversion algorithms shear modulus tissue characterization

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Semi-empirical inversion technique for retrieval of quantitative attenuation profiles with underwater scanning LiDAR system 7

Semi-empirical inversion technique for retrieval of quantita...

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Conference on Ocean Sensing and Monitoring VII

作者： Vuorenkoski, Anni K. Dalgleish, Fraser R. Twardowski, Michael S. Ouyang, Bing Trees, Charles C. Florida Atlantic Univ Harbor Branch Oceanog Inst Ft Pierce FL 34946 USA WET Labs Inc Narragansett RI 02882 USA STO NATO CMRE La Spezia Italy

ISBN: (纸本)9781628415759

A fine structure underwater imaging LiDAR (FSUIL) has recently been developed and initial field trials have been conducted. The instrument, which rapidly scans an array of closely spaced, narrow, collimated laser pulses into the water column produces two-dimensional arrays of backscatter profiles, with fine spatial and temporal resolution. In this paper a novel method to derive attenuation profiles is introduced. This approach is particularly attractive in applications where primary on-board processing is required, and other applications where conventional model-based approaches are not feasible due to a limited computational capacity or lack of a priori knowledge of model input parameters. The paper also includes design details regarding the new FSUIL instrument are given, with field results taken in clear to moderately turbid water being presented to illustrate the various effects and considerations in the analysis of the system data. LiDAR waveforms and LiDAR derived attenuation coefficients are analyzed and compared to calibrated beam attenuation, particulate scattering and absorption coefficients. The system was field tested during the NATO Ligurian Sea LIDAR & Optical Measurements Experiment (LLOMEx) cruise in March 2013, during the spring bloom conditions. Throughout a wide range of environmental conditions, the FSUIL was deployed on an in situ profiler obtaining thousands of three-dimensional LiDAR scans from the near surface down to the lower thermocline. Deployed concurrent to the FSUIL was a range of commercially available off-the-shelf instruments providing side-by-side in-situ attenuation measurement.

关键词： LiDAR multiple scattering attenuation profiles inversion algorithms

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Improved inversion of MR elastography images by spatio-temporal directional filtering

Improved inversion of MR elastography images by spatio-tempo...

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Medical Imaging 2003 Conference

作者： Manduca, A Lake, DS Ehman, RL Mayo Clin & Mayo Fdn Dept Physiol & Biophys & Biomath Resource Rochester MN 55905 USA

ISBN: (纸本)0819448338

MR e0lastography can visualize and measure propagating shear waves in tissue-like materials subjected to harmonic mechanical excitation. This allows the calculation of local values of material parameters such as shear modulus and attenuation. Various inversion algorithms to perform such calculations have been proposed, but they are sensitive to areas of low displacement amplitude (and hence low SNR) that result from interference patterns due to reflection and refraction. A spatio-temporal directional filter applied as a pre-processing step can separate interfering waves so they can be processed separately. Weighted combinations of inversions from such directionally separated data sets can significantly improve reconstructions of shear modulus and attenuation.

关键词： elasticity elastography shear modulus tissue characterization inversion algorithms digital filters wave propagation shear wave

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Water properties derived from water color versus measured from water sample: application of a new color-inversion algorithm

Water properties derived from water color versus measured fr...

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Conference on Ocean Remote Sensing and Applications

作者： Lee, ZP Carder, KL Patch, J Barnard, A Otis, D Trees, CC USN Res Lab Stennis Space Ctr MS 39529 USA

ISBN: (纸本)0819446785

Apply a newly developed ocean-color inversion algorithm to measurements made in the west Florida Shelf and off the California coast, we derived the particle backscattering coefficient and the total absorption coefficient. From the derived total absorption coefficient, we calculated the absorption coefficients of the phytoplankton pigments and that of the gelbstoff (Colored Dissolved Organic Matter). From the derived pigment absorption coefficients, we further calculated the chlorophyll-a concentrations. These derived values were compared with those measured from water samples. It is found that the derived values are very consistent with those measured ones, suggesting that the inversion methods work very well for these coastal waters, and can be applied to satellite data for wide observations.

关键词： optical properties inversion algorithms chlorophyll-a concentrations

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