Eslaminia, M., A. M. Elmeliegy, and M. N. Guddati, Full waveform inversion through double-sweeping solver, , vol. 453, pp. 110914, 2022. AbstractWebsite

An efficient method is proposed to accurately approximate the gradient and the Hessian operator for the full-waveform inversion (FWI) in large-scale problems. The key idea is an approximate solver called double-sweeping solver, which divides the domain into smaller slabs and sequentially solves the wavefields through a downward and an upward sweeping. The sequential solution is facilitated by approximating the continuity conditions that suppress the multiples, thus relaxing long-range coupling between the subdomains. The double-sweeping solver is incorporated into an inexact Gauss-Newton approach to perform FWI, where the gradient and the Hessian vector multiplication are computed more efficiently. Through numerical experiments, we show that the convergence of FWI with respect to the number of iterations does not degrade when the double-sweeping approximation is used. Given that the double-sweeping solver is computationally cheaper than full-wave simulation, the proposed method is more efficient than the standard FWI. This paper contains the complete formulation of the proposed methodology as well as an illustration of its effectiveness to problems of varying complexity including the inversion of the Marmousi model from the Geophysics community.

Eslaminia, M., A. M. Elmeliegy, and M. N. Guddati, Full waveform inversion through double-sweeping solver, , vol. 453, pp. 110914, 2022. AbstractWebsite

An efficient method is proposed to accurately approximate the gradient and the Hessian operator for the full-waveform inversion (FWI) in large-scale problems. The key idea is an approximate solver called double-sweeping solver, which divides the domain into smaller slabs and sequentially solves the wavefields through a downward and an upward sweeping. The sequential solution is facilitated by approximating the continuity conditions that suppress the multiples, thus relaxing long-range coupling between the subdomains. The double-sweeping solver is incorporated into an inexact Gauss-Newton approach to perform FWI, where the gradient and the Hessian vector multiplication are computed more efficiently. Through numerical experiments, we show that the convergence of FWI with respect to the number of iterations does not degrade when the double-sweeping approximation is used. Given that the double-sweeping solver is computationally cheaper than full-wave simulation, the proposed method is more efficient than the standard FWI. This paper contains the complete formulation of the proposed methodology as well as an illustration of its effectiveness to problems of varying complexity including the inversion of the Marmousi model from the Geophysics community.

M., E. A., and R. Y. F., "Efficient Preconditioned Soil–Foundation–Structure Interaction Approach to Compute Tall-Building Time Periods", Practice Periodical on Structural Design and ConstructionPractice Periodical on Structural Design and Construction, vol. 24, issue 3: American Society of Civil Engineers, pp. 04019007, 2019. AbstractWebsite

The present paper suggests an efficient preconditioned two-iteration substructure approach?namely, preconditioned soil?structure interaction (PSSI)?to couple the analysis of a superstructure over fixed bases (which is traditionally carried out in design companies) with the analysis of foundation plates over an elastic half-space (EHS) to obtain more accurate equivalent supporting spring stiffnesses. Hence, an accurate building time period and, consequently, lateral loads could be computed. The effectiveness of the proposed approach is illustrated in several numerical examples in terms of number of iterations and scalability followed by comparison with previous work to demonstrate the superiority of the proposed approach.The present paper suggests an efficient preconditioned two-iteration substructure approach?namely, preconditioned soil?structure interaction (PSSI)?to couple the analysis of a superstructure over fixed bases (which is traditionally carried out in design companies) with the analysis of foundation plates over an elastic half-space (EHS) to obtain more accurate equivalent supporting spring stiffnesses. Hence, an accurate building time period and, consequently, lateral loads could be computed. The effectiveness of the proposed approach is illustrated in several numerical examples in terms of number of iterations and scalability followed by comparison with previous work to demonstrate the superiority of the proposed approach.

Eslaminia, M., A. M. Elmeliegy, and M. N. Guddati, Improved least-squares migration through double-sweeping solver, , vol. 88, issue 3, pp. S131 - S141, 2023/04/07. AbstractWebsite

Based on a recently developed approximate wave-equation solver, we have developed a methodology to reduce the computational cost of seismic migration in the frequency domain. This approach divides the domain of interest into smaller subdomains, and the wavefield is computed using a sequential process to determine the downward- and upward-propagating wavefields — hence called a double-sweeping solver. A sequential process becomes possible using a special approximation of the interface conditions between subdomains. This method is incorporated into the least-squares migration framework as an approximate solver. The associated computational effort is comparable to one-way wave-equation approaches, yet, as illustrated by the numerical examples, the accuracy and convergence behavior are comparable to that of the full-wave equation.

Elmeliegy, A. M., and M. N. Guddati, "Correlation-based full-waveform shear wave elastography", Physics in Medicine & Biology, vol. 68, issue 11: IOP Publishing, pp. 115001, 2023. AbstractWebsite

Objective. With the ultimate goal of reconstructing 3D elasticity maps from ultrasound particle velocity measurements in a plane, we present in this paper a methodology of inverting for 2D elasticity maps from measurements on a single line. Approach. The inversion approach is based on gradient optimization where the elasticity map is iteratively modified until a good match is obtained between simulated and measured responses. Full-wave simulation is used as the underlying forward model to accurately capture the physics of shear wave propagation and scattering in heterogeneous soft tissue. A key aspect of the proposed inversion approach is a cost functional based on correlation between measured and simulated responses. Main results. We illustrate that the correlation-based functional has better convexity and convergence properties compared to the traditional least-squares functional, and is less sensitive to initial guess, robust against noisy measurements and other errors that are common in ultrasound elastography. Inversion with synthetic data illustrates the effectiveness of the method to characterize homogeneous inclusions as well as elasticity map of the entire region of interest. Significance. The proposed ideas lead to a new framework for shear wave elastography that shows promise in obtaining accurate maps of shear modulus using shear wave elastography data obtained from standard clinical scanners.

Guddati, M., T. Roy, A. M. Elmeliegy, and M. W. Urban, Shear wave elastography: From dispersion matching to full waveform inversion, , vol. 153, issue 3_supplement, pp. A265 - A265, 2023/03/01. AbstractWebsite

Shear Wave Elastography (SWE) involves estimating mechanical properties through inversion, i.e., matching measured and simulated propagation characteristics of shear waves in the tissue. The accuracy of the estimated properties depends significantly on the specific characteristics/responses that are being matched. These could range from simple group velocity to dispersion curves and to full-wave response (particle velocity measurements). Using specific applications of arterial, liver, and tumor elstography, we illustrate that effective SWE is performed by resorting to an inversion approach, or combination of inversion approaches, guided by the underlying physics. To this end, we present inversion approaches ranging from matching dispersion characteristics to matching full waveform responses and provide rationale for choosing the appropriate technique(s) depending on the problem at hand.

Elmeliegy, A. M., and M. Guddati, Full-waveform shear wave elastography for imaging tumors, , vol. 151, issue 4, pp. A212 - A212, 2022/04/01. AbstractWebsite

Shear wave elastography (SWE) is a method of reconstructing the stiffness of soft biological tissues by matching the observed and the simulated wavefields using an inverse optimization scheme. SWE reconstruction algorithms can be classified into two main categories, local and global methods. Global methods consider more complete physics of the waves, i.e., refraction and scattering, and, thus, have the potential to better characterize the heterogeneity of the domain. These approaches require full-waveform inversion (FWI), which is computationally expensive. More importantly, due to highly nonlinear nature, FWI has the limitation of converging to local minima, leading to erroneous reconstruction. In this work, we address this issue and propose a cost functional that not only reduces the nonlinearity of the FWI but also results in a reconstruction algorithm that is independent of push amplitudes, less sensitive to the initial guess, and has a better convergence behavior compared to the classical least-squares cost functional. In addition, we propose to utilize only a fraction of the measurements with the eventual goal of 3D reconstruction of tumors using limited ultrasound measurements. In this talk, we will present the details of the underlying formulation and examples showing the effectiveness of the proposed method.

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