Detection of Multi-Layered Bond Delamination Defects Based on Full Waveform Inversion.

This study aimed to address the challenges encountered in traditional bulk wave delamination detection methods characterized by low detection efficiency. Additionally, the limitations of guided wave delamination detection methods were addressed, particularly those utilizing reflected waves, which are susceptible to edge reflections, thus complicating effective defect extraction. Leveraging the full waveform inversion algorithm, an innovative approach was established for detecting delamination defects in multi-layered structures using ultrasonic guided wave arrays. First, finite element modeling was employed to simulate guided wave data acquisition by a circular array within an aluminum-epoxy bilayer structure with embedded delamination defects. Subsequently, the full waveform inversion algorithm was applied to reconstruct both regular and irregular delamination defects. Analysis results indicated the efficacy of the proposed approach in accurately identifying delamination defects of varying shapes. Furthermore, an experimental platform for guided wave delamination defect detection was established, and experiments were conducted on a steel-cement bilayer structure containing an irregular delamination defect. The experimental results validated the exceptional imaging precision of our proposed technique for identifying delamination defects in multi-layered boards. In summary, the proposed method can accurately determine both the positions and sizes of defects with higher detection efficiency than traditional pulse-echo delamination detection methods.

Scale-Aware Edge-Preserving Full Waveform Inversion with Diffusion Filter for Crosshole Sensor Arrays.

Full waveform inversion (FWI) is recognized as a leading data-fitting methodology, leveraging the detailed information contained in physical waveform data to construct accurate, high-resolution velocity models essential for crosshole surveys. Despite its effectiveness, FWI is often challenged by its sensitivity to data quality and inherent nonlinearity, which can lead to instability and the inadvertent incorporation of noise and extraneous data into inversion models. To address these challenges, we introduce the scale-aware edge-preserving FWI (SAEP-FWI) technique, which integrates a cutting-edge nonlinear anisotropic hybrid diffusion (NAHD) filter within the gradient computation process. This innovative filter effectively reduces noise while simultaneously enhancing critical small-scale structures and edges, significantly improving the fidelity and convergence of the FWI inversion results. The application of SAEP-FWI across a variety of experimental and authentic crosshole datasets clearly demonstrates its effectiveness in suppressing noise and preserving key scale-aware and edge-delineating features, ultimately leading to clear inversion outcomes. Comparative analyses with other FWI methods highlight the performance of our technique, showcasing its ability to produce images of notably higher quality. This improvement offers a robust solution that enhances the accuracy of subsurface imaging.

High-Precision Corrosion Detection via SH1 Guided Wave Based on Full Waveform Inversion.

Corrosion detection for industrial settings is crucial for safe and efficient operations. Due to its high imaging resolution, the guided-wave full-waveform inversion tomography technique has significant potential for corrosion detection of plate metals. Limited by the long wavelengths of A0 and S0 mode waves, this method exhibits inadequate detection resolution for the earlier shallow and small corrosion defects. Based on the relatively short wavelength characteristics of the SH1 mode wave, we propose a high-precision corrosion detection method via SH1 guided wave using the full waveform inversion algorithms. By conducting finite element simulations of ultrasonic-guided waves on aluminum plates with varying corrosion defects, a comparison was made to assess the detection precision across A0, S0, and SH1 modes. The comparison results showed that, whether for regular or irregular defects, the SH1 mode wave always exhibited higher imaging accuracy than the A0 and S0 mode waves for shallow and small-sized defects. The corresponding experiments were conducted on an aluminum plate with simple or complex defects. The results of the experiments reconfirmed that the full waveform inversion method using SH1 guided wave can effectively reconstruct the shape and size of small and shallow corrosion defects within aluminum plates.

Ultrasound Computed Tomography.

This chapter presents theoretical, numerical, and experimental frameworks for the use of Ultrasound Computed Tomography (USCT) for cortical bone tissue imaging. Most of the research conducted on this topic concerns adult bone, although some work presented in this chapter is specific to the study of child bone. USCT is recognized as a powerful method for soft tissue imaging. In bone imaging, the difficulties arise from the very high impedance contrast between tissues which alters the propagation of the ultrasonic waves and limits the linear inversion algorithms used. Solutions consist in optimally assessing non-linear effects in an iterative approach aiming at local linearization. When the problem can be reduced to the study of a fluid-like cavity buried in an elastic cylinder surrounded by water, the signal processing and/or compound algorithms can be added as an extension to the linear algorithms. The main limitation of these methods is the heavy experimental costs involved. We have then suggested the introduction of purely numerical non-linear full-waveform inversion algorithms. The performances and the limitations of these linear and non-linear methods applied to cortical bone tissue imaging problems are overviewed and discussed.

A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound.

Bayesian methods are a popular research direction for inverse problems. There are a variety of techniques available to solve Bayes' equation, each with their own strengths and limitations. Here, we discuss stochastic variational inference (SVI), which solves Bayes' equation using gradient-based methods. This is important for applications which are time-limited (e.g. medical tomography) or where solving the forward problem is expensive (e.g. adjoint methods). To evaluate the use of SVI in both these contexts, we apply it to ultrasound tomography of the brain using full-waveform inversion (FWI). FWI is a computationally expensive adjoint method for solving the ultrasound tomography inverse problem, and we demonstrate that SVI can be used to find a no-cost estimate of the pixel-wise variance of the sound-speed distribution using a mean-field Gaussian approximation. In other words, we show experimentally that it is possible to estimate the pixel-wise uncertainty of the sound-speed reconstruction using SVI and a common approximation which is already implicit in other types of iterative reconstruction. Uncertainty estimates have a variety of uses in adjoint methods and tomography. As an illustrative example, we focus on the use of uncertainty for image quality assessment. This application is not limiting; our variance estimator has effectively no computational cost and we expect that it will have applications in fields such as non-destructive testing or aircraft component design where uncertainties may not be routinely estimated.

Ultrasonic Imaging of High-contrasted Objects Based on Full-waveform Inversion: Limits under Fluid Modeling.

Quantitative ultrasound techniques have been previously used to evaluate biological hard tissues, characterized by a large acoustic impedance contrast. Here, we are interested in the imaging of experimental data from different test-targets with high acoustic impedance contrast, using the Full Waveform Inversion (FWI) method to solve the inverse problem. This method is based on high-resolution numerical modeling of the forward problem of interaction between waves and medium, considering the full time series. To reduce the complexity of the numerical implementation, the model considers a fluid medium. Therefore, the aim is to evaluate the precision of the reconstruction under this assumption for materials with a different level of attenuation of shear waves, to study the limits of this hypothesis. Images of the sound speed obtained using the experimental data are presented, and the precision of the reconstruction is evaluated. Future work should include viscoelastic materials.

Deep-Learning-Driven Full-Waveform Inversion for Ultrasound Breast Imaging.

Ultrasound breast imaging is a promising alternative to conventional mammography because it does not expose women to harmful ionising radiation and it can successfully image dense breast tissue. However, conventional ultrasound imaging only provides morphological information with limited diagnostic value. Ultrasound computed tomography (USCT) uses energy in both transmission and reflection when imaging the breast to provide more diagnostically relevant quantitative tissue properties, but it is often based on time-of-flight tomography or similar ray approximations of the wave equation, resulting in reconstructed images with low resolution. Full-waveform inversion (FWI) is based on a more accurate approximation of wave-propagation phenomena and can consequently produce very high resolution images using frequencies below 1 megahertz. These low frequencies, however, are not available in most USCT acquisition systems, as they use transducers with central frequencies well above those required in FWI. To circumvent this problem, we designed, trained, and implemented a two-dimensional convolutional neural network to artificially generate missing low frequencies in USCT data. Our results show that FWI reconstructions using experiment data after the application of the proposed method successfully converged, showing good agreement with X-ray CT and reflection ultrasound-tomography images.

On-Line Corrosion Monitoring of Plate Structures Based on Guided Wave Tomography Using Piezoelectric Sensors.

Corrosion is a major safety and economic concern to various industries. In this paper, a novel ultrasonic guided wave tomography (GWT) system based on self-designed piezoelectric sensors is presented for on-line corrosion monitoring of large plate-like structures. Accurate thickness reconstruction of corrosion damages is achieved by using the dispersive regimes of selected guided waves and a reconstruction algorithm based on full waveform inversion (FWI). The system makes use of an array of miniaturised piezoelectric transducers that are capable of exciting and receiving highly dispersive A0 Lamb wave mode at low frequencies. The scattering from transducer array has been found to have a small effect on the thickness reconstruction. The efficiency and the accuracy of the new system have been demonstrated through continuous forced corrosion experiments. The FWI reconstructed thicknesses show good agreement with analytical predictions obtained by Faraday's law and laser measurements, and more importantly, the thickness images closely resemble the actual corrosion sites.

Cross-correlation adjustment full-waveform inversion with source encoding in ultrasound computed tomography.

Full-waveform inversion (FWI) is one of the leading-edge techniques in ultrasound computed tomography (USCT). FWI reconstructs the images of sound speed by iteratively minimizing the difference between the predicted and measured signals. The challenges of FWI are to improve its stability and reduce its computational cost. In this paper, a new USCT algorithm based on cross-correlation adjustment FWI with source encoding (CCAFWI-SE) is proposed. In this algorithm, the gradient is adjusted using the intermediate signals as the inversion target rather than the measured signals during iteration. The intermediate signals are generated using the travel time difference calculated by cross-correlation. In the case of conventional FWI failure, using the proposed algorithm, the estimated sound speed can converge toward the ground truth. To reduce the computational cost, an intermittent update strategy is implemented. This strategy only requires one time for the calculation of the travel time difference per stage, so that the source encoding can be used. Simulation and laboratory experiments are implemented to validate this approach. The experiment results show it has successfully recovered the sound speed model, while conventional FWI failed when the initial model greatly differed from the ground truth. This verifies that our approach improves the stability of the reconstruction in USCT. In practice, additional computational costs can be reduced by combining our approach with existing methods. The proposed approach increases the robustness of the FWI and expands its application.

In-situ sparse-array imaging for through-thickness cracks in plates with A0 Lamb waves and an efficient waveform inversion algorithm.

Structural health monitoring (SHM) requires efficient online crack detection and characterization to prevent structural failures, which mainly arise from fatigue cracks. Existing solutions for crack characterization involve analyzing sensed wave signals directly, but these approaches usually require onerous steps or many sensors to obtain sufficient and clear wave packets. An alternative strategy is a model-based inversion, which takes the full waveform into consideration and does not require analysis on a single wave packet. This approach can achieve accurate characterization with fewer sensors and simpler implementation. We propose an efficient model based on the Huygens' principle and the no-mode-conversion property of the A0 mode Lamb waves to meet the requirements of online monitoring. We then verify the proposed model-based crack imaging method through simulation and experiments on smooth and rough cracks. The proposed method is easy, cheap, and efficient, making it a desirable option for SHM tasks.

CO2 Storage Monitoring via Time-Lapse Full Waveform Inversion with Automatic Differentiation.

In the field of CO2 capture utilization and storage (CCUS), recent advancements in active-source monitoring have significantly enhanced the capabilities of time-lapse acoustical imaging, facilitating continuous capture of detailed physical parameter images from acoustic signals. Central to these advancements is time-lapse full waveform inversion (TLFWI), which is increasingly recognized for its ability to extract high-resolution images from active-source datasets. However, conventional TLFWI methodologies, which are reliant on gradient optimization, face a significant challenge due to the need for complex, explicit formulation of the physical model gradient relative to the misfit function between observed and predicted data over time. Addressing this limitation, our study introduces automatic differentiation (AD) into the TLFWI process, utilizing deep learning frameworks such as PyTorch to automate gradient calculation using the chain rule. This novel approach, AD-TLFWI, not only streamlines the inversion of time-lapse images for CO2 monitoring but also tackles the issue of local minima commonly encountered in deep learning optimizers. The effectiveness of AD-TLFWI was validated using a realistic model from the Frio-II CO2 injection site, where it successfully produced high-resolution images that demonstrate significant changes in velocity due to CO2 injection. This advancement in TLFWI methodology, underpinned by the integration of AD, represents a pivotal development in active-source monitoring systems, enhancing information extraction capabilities and providing potential solutions to complex multiphysics monitoring challenges.

Dual-Probe Transcranial Full-Waveform Inversion: A Brain Phantom Feasibility Study.

OBJECTIVE: Despite being a low-cost, portable and safe medical imaging technique, transcranial ultrasound imaging is not used widely in adults because of the severe degradation and distortion of signals caused by the skull. Full-waveform inversion (FWI) has recently been found to have potential as an effective method for transcranial ultrasound tomography to obtain high-quality, subwavelength-resolution acoustic models of the brain using low-frequency ultrasound data. In this study is the first demonstration of this method in recovering a high-resolution 2-D reconstruction of a brain and skull ultrasound imaging phantom using experimentally acquired data. METHODS: A 2:5 scale brain phantom encased within a 3-D-printed skull-mimicking layer was created to simulate a clinical transcranial imaging target. To obtain tomographic ultrasound data on the brain and skull phantom, a tomographic ultrasound acquisition system was designed and implemented using commercially available low-frequency cardiac probes. FWI reconstructions of the brain and skull phantom were performed using the acquired tomographic data and were compared with corresponding synthetic reconstructions. This comparison was used to evaluate the feasibility of the proposed imaging system when employing different transducer array configurations. RESULTS: We demonstrate the successful FWI reconstruction of the brain phantom within the skull mimic from experimentally acquired tomographic ultrasound data. To mitigate the effects of the skull-mimicking material, a reflection-matching algorithm was applied to model the morphology of the skull layer prior to performing the inversion. CONCLUSION: The findings of this study provide a promising step toward the clinical use of FWI for transcranial ultrasound imaging in adults.

Full-Waveform Inversion for Breast Ultrasound Tomography Using Line-Shape Modeled Elements.

OBJECTIVE: The objective of the work described here was to incorporate the spatial shapes of the transducer elements into the framework of the full-waveform inversion. METHODS: An element is treated as its cross-section in the 2-D imaging plane, that is, a line segment. The elements are not simply modeled as a set of point sources on their surface to avoid staircasing artifacts. By use of the Fourier collocation method, an element is spatially represented as the discrete convolution between its spatial distribution and a band-limited delta function. The excitation pulses on the emitters and recorded signals on the receivers are then weighted based on the discrete convolution results. Digital and physical experiments are implemented to validate the method. DISCUSSION: It is meaningful to model the shapes of the elements if their spatial sizes are similar to or larger than the acoustic wavelengths. It should, however, be noted that because this article focuses on 2-D imaging, the inter-plane effects are not considered. CONCLUSION: The approach helps reduce the root mean square errors and increase the structural similarity of the reconstructed images. It also helps to improve the stability of convergence and to accelerate the convergence speed.

Full waveform inversion guided wave tomography with a recurrent neural network.

Corrosion quantitative detection of plate or plate-like structure materials is crucial in industrial Non-Destructive Testing (NDT) for determining their remaining life. For doing that, a novel ultrasonic guided wave tomography method, incorporating recurrent neural network (RNN) into full waveform inversion (FWI) called as RNN-FWI, is proposed in this paper. When the wave equation of an acoustic model is solved by a forward model with the cyclic calculation units of an RNN, it is shown that the inversion of the forward model can be obtained iteratively by minimizing a waveform misfit function of quadratic Wasserstein distance between the modeled and measured data. It is also demonstrated that the gradient of the objective function can be obtained by automatic differentiation while the parameters of the waveform velocity model are updated by the adaptive momentum estimation algorithm (Adam). The U-Net deep image prior (DIP) is used as the velocity model regularization in each iteration. The final thickness maps of the plate or plate-like structure materials shown can be archived by the dispersion characteristics of guided waves. Both the numerical simulation and experimental results show that the proposed RNN-FWI tomography method performs better than the conventional time-domain FWI in terms of convergence rate, initial model requirement, and robustness.

Synthetic dataset for visco-acoustic imaging.

We provide computationally generated dataset simulating propagation of ultrasonic waves in viscous tissues in two and three dimensional domains. The dataset contains physical parameters of a human breast with a high-contrast inclusion, the acquisition setup with positions of sources and receivers, and the associated pressure-wave data at ultrasonic frequencies. We simulated the wave propagation based on seven different viscous models using the physical parameters of the breast. Furthermore, different choices of conditions for the medium's boundaries are given, namely absorbing and reflecting boundaries. The dataset allows to evaluate the performance of reconstruction methods for ultrasound imaging under attenuation model uncertainty, that is, when the precise attenuation law that characterizes the medium is unknown. In addition, the dataset enables to evaluate the robustness of inverse scheme in the context of reflecting boundary conditions where multiple reflections illuminate the sample, and/or the performance of data-processing to suppress these multiple reflections.

Ultrasound computed tomography based on full waveform inversion with source directivity calibration.

Ultrasound computed tomography based on full waveform inversion has the potential to provide high-resolution images of human tissues in a quantitative manner. A successful ultrasound computed tomography system requires the decent knowledge of acquisition array, including the spatial position and the directivity of each transducer, to meet the high-level demand of clinical applications. The conventional full waveform inversion algorithm assumes a point source with the omni-directional emission. Such assumption does not hold when the directivity of emitting transducer is not negligible. For a practical implementation, an efficient and accurate self-checking evaluation of directivity is crucial prior to the reconstruction of images. We propose to measure the directivity of each emitting transducer using the full-matrix captured data obtained with a water-immersed and target-free experiment. We introduce the weighted virtual point-source array to act as the proxy of emitting transducer during the numerical simulation. The weights of different points in the virtual array can be calculated from the observed data using the gradient-based local optimization method. Although the full waveform imaging method relies on the finite-difference solver of wave equation, such directivity estimation benefits from the introduction of analytical solver. The trick significantly reduces the numerical cost, enabling an automatic directivity self-check at boot. We verify the feasibility, efficiency, and accuracy of the virtual array method through simulated and experimental tests. For the experimental test, we also illustrate that full waveform inversion with directivity calibration can reduce the artifacts introduced by the conventional point source assumption, improving the quality of reconstructed images..

Application of full waveform inversion algorithm in Laplace-Fourier domain for high-contrast ultrasonic bone quantitative imaging.

BACKGROUND AND OBJECTIVES: Full waveform inversion (FWI) has been widely applied for the reconstruction of underground medium parameters in seismic communities and has made a great success. It is also a promising way to image hard tissues such as bones by ultrasonic FWI algorithm. However, the ultrasonic FWI methods for bone parameters imaging reported in literature so far are limited to the time domain and/or Fourier domain, and can only achieve quantitative imaging with acoustic velocity of bone less than 3000 m/s. Because the acoustic velocity of actual cortical bones can be as high as 4200 m/s, it is still a challenge for FWI to achieve higher parameter contrast bone imaging. METHODS: Here, we proposed an ultrasonic FWI algorithm in Laplace-Fourier domain (LFDFWI) for high-contrast bone quantitative imaging. Compared to Time domain and Fourier domain, the LFDFWI algorithm is more appropriate for dealing with the presence of high contrast between bone tissues, reducing the possibility of inversion falling into a local minimum, and obtaining better inversion results. We adapted the seismic FWI algorithm to make it suitable for high-frequency ultrasonic sources and small-sized bone parameter imaging. RESULTS: We conducted a series of bone models to evaluate the effectiveness of the proposed algorithm, including four kinds of bone model derived from micro computed tomography (Micro-CT) image of rat. We evaluated the experimental results based on visual analysis, error analysis and structural similarity (SSIM). The numerical simulation results showed that, when acoustic approximation is used, the proposed method can obtain accurate high-contrast images of the velocity and density parameters of bone structure, the mean relative error (MRE) in the region of interest (ROI) were all less than 2%, and the SSIM is up to 98%; when the viscoelastic approximation is used, this method can also obtain the desired high-contrast bone parameter distribution, with MRE less than 4% and SSIM higher than 74%, both of which are better than FDFWI in Fourier domain (FDFWI). CONCLUSION: The results demonstrated that the proposed FWI algorithm can obtain high resolution bone parameter models close to the Micro-CT image, which proves its clinical application potential.

Design and Construction of a Low-Frequency Ultrasound Acquisition Device for 2-D Brain Imaging Using Full-Waveform Inversion.

The main techniques used to image the brain and obtain structural data are magnetic resonance imaging and X-ray computed tomography. These techniques produce images with high spatial resolution, but with the disadvantage of requiring very large equipment with special installation needs. In addition, X-ray tomography uses ionizing radiation, which limits their use. Ultrasound imaging is a safe technology that is delivered using compact and mobile devices. However, conventional ultrasound reconstruction techniques have failed to obtain images of the brain because of, fundamentally, the presence of the skull and the distortion that it produces on ultrasound. Recent studies have indicated that full-waveform inversion, a computational technique originally from Earth science, has the potential to generate accurate 3-D images of the brain. This technology can overcome the limitations of conventional ultrasound imaging, but a prototype for transcranial applications does not yet exist. Here, we investigate different designs of an annular array of ultrasound transducers to optimize the number of elements and rotations needed to conduct transcranial imaging with full-waveform inversion. This device uses small-diameter, low-frequency transducers that readily propagate ultrasound through the skull with good signal-to-noise ratios. It also incorporates the use of rotations to produce a high-density coverage of the target and acquire redundant traces that are beneficial for full-waveform inversion. We have built a ring of 40 transducers to illustrate that this design is capable of reconstructing images of the brain, retrieving its anatomy and acoustic properties with millimeter resolution. Laboratory results reveal the ability of this device to successfully image a 2.5-D brain- and skull-mimicking phantom using full-waveform inversion. To our knowledge, this is the first prototype ever used for transcranial-like imaging. The importance of these findings and their implications for the design of a 3-D reconstruction system with possible clinical applications are discussed.

Multi-parameter reconstruction of velocity and density using ultrasonic tomography based on full waveform inversion.

In this paper, an ultrasonic tomography method based on acoustic multi-parameter full waveform inversion (FWI) is developed for high-resolution reconstructions of velocity and density in metal components. The challenging issue in multi-parameter FWI is to deal with the trade-off effects between different parameters of different natures. Moreover, different parameters have different orders of amplitudes in the wave-field which make the inversion ill-conditioned. The inverse Hessian has been shown to mitigate the coupling effects and rescale the amplitudes of different parameters, and then the reliable updates of different parameters are available. The simultaneous reconstructions of velocity and density by using the truncated Gauss-Newton method, in which the inverse Hessian can be considered through a matrix-free conjugate gradient solution of the Gauss-Newton normal equation, are investigated by simulation as well as experiment on the centred inclusions. The results show that this method can effectively alleviate the trade-off effects between velocity and density, and thus the velocity of the inclusion is accurately reconstructed and the reconstruction of the density is well achieved.

Full waveform inversion based on the ensemble Kalman filter method using uniform sampling without replacement.

Full waveform inversion (FWI) has been increasingly more and more important in seismology to better understand the interior structure of the Earth. FWI, by taking advantage of both the traveltime and amplitude in the data, provides high-resolution model parameters of the earth which can produce images with high resolution. However, this inversion method conventionally suffers from non-uniqueness due to many local minima of the objective function and large computing costs. In this study, we propose a new FWI method in a semi-random framework by integrating the ensemble Kalman filter and uniform sampling without replacement. Numerical results demonstrate that the new method can achieve high-resolution results and a wider convergence domain. Accordingly, the new method overcomes the disadvantage of conventional FWIs that depend strongly on the initial model.