Envelope Inversion with Source encoding for Ultrasound Computed Tomography

Ultrasound computed tomography (USCT) is an emerging imaging modality that holds great promise for breast imaging. Full-waveform inversion (FWI)-based image reconstruction methods incorporate accurate wave physics to produce high spatial resolution quantitative images of speed of sound or other acoustic properties of the breast tissues. However, FWI reconstruction is computationally expensive, which limits its application in a clinical setting. This contribution investigates using the use of a convolutional neural network (CNN) to learn a mapping from USCT data to speed of sound estimates. The CNN was trained using a supervised approach that employed a large set of anatomically and physiologically realistic numerical breast phantoms (NBPs) and simulated USCT measurements. Once trained, this CNN can then be evaluated for real-time FWI image reconstruction from USCT data. The performance of the proposed method was assessed and compared against FWI using a hold-out sample of 41 NBPs and corresponding USCT images. Accuracy was measured using relative mean square error (RMSE) and structural self-similarity index measure (SSIM). This numerical experiment demonstrates that a supervised learning model can achieve accuracy comparable to FWI, while significantly reducing computational time and memory requirements.

Ultrasound imaging of musculoskeletal tissue has long been a challenge. As a novel medical ultrasound computed tomography (UCT) technique, full-waveform inversion (FWI) provides a promising solution for musculoskeletal imaging with high spatial resolution. However, FWI suffers from a substantial computational burden, primarily due to the multiple wavefield calculations involved in the inversion process, especially when dealing with a large number of sources. In order to minimize the number of wavefield calculations, we propose a source encoding technology for musculoskeletal FWI. In detail, based on the ring-shaped array within the UCT configuration, a novel vortex encoding strategy is developed and applied to FWI. Given the orthogonal properties of acoustic vortices, this strategy effectively mitigates the cross talk artifacts between the encoding sources. This vortex-encoded full-waveform inversion (VE-FWI) significantly reduces computation load by an order of magnitude compared to the conventional FWI. Besides, the vortex encoding strategy enhances the quality of reconstructed images, with a 2.9% increase in peak signal-to-noise ratio and a 4.7% increase in structure similarity index measure compared to other traditional encoding strategies. VE-FWI not only accelerates musculoskeletal UCT but also maintains high imaging quality, presenting a promising solution for practical applications with both accuracy and computational efficiency.

In the linearized seismic full waveform inversion (FWI), it is well known that a good initial model is needed to avoid cycle-skipping issue, especially when the low-frequency components of data are lacking. To solve the problem, we develop a joint first-arrival traveltime and early arrival envelope inversion method (JTE) to build a good near-surface velocity model with low-wavenumber components. The JTE method combines the robustness of nonlinear traveltime inversion and the low-frequency information embedded in the waveform envelope. In two synthetic experiments, we confirm that traveltime inversion constrains the top near-surface velocity structures tightly, while the envelope inversion recovers the low-wavenumber structures with low-velocity objects or layers. Using the results of JTE as starting models, we find that FWI can produce accurate solutions for complex numerical models. In a real-data example, JTE followed by FWI resolves a near-surface velocity model to improve statics corrections for the subsurface stacking image.

<p>The seismic full waveform inversion (FWI), as one of important ways to obtain the seismic wave velocity, has made rapid development in the last decade. In response to problems of cycle-skipping artifacts, dependence on the initial model, and low-frequency information in FWI, researchers have made many improvements, such as multi-scale envelope inversion and low-frequency extension. Recently, deep learning has been also adopted seismic data processing and interpretation, because of its strong nonlinear mapping ability. However, these works depend on labels used for training heavily, especially for the velocity model in the inversion, which prevents them from real application. Referring to these studies, this work combines low-frequency extension commonly as well as multiscale inversion with deep learning, and proposes a multi-scale FWI gradient optimization method based on CNN. CNN we designed is trained to predict the inversion gradient corresponding to the low-frequency band data in FWI, so that multi-scale gradient optimization can be directly used in multi-scale inversion, expanding the low-frequency information in the actual data and reducing the calculation in FWI. With a specially designed dataset, CNN is trained to optimize the gradients computed from the high-frequency band data by predicting the gradients corresponding to the low-frequency band data and the gradients corresponding to the mid-frequency band data, respectively. The predicted gradients are used in different stages of the multi-scale inversion. The low-frequency gradients are used to invert the initial structural construction so as not to rely on a good initial model, and the high-frequency gradients are used to improve the accuracy of the inversion results. In this way, low-frequency expansion and multiscale inversion can be achieved simultaneously. Our method achieves good results on the initial model for a given uniform wave velocity, effectively alleviating the reliance on the initial model in FWI. This study provides a new idea of combining deep learning and full waveform inversion, which will be effectively used in seismic data processing.</p>

Envelope inversion (EI) is an efficient tool to mitigate the nonlinearity of conventional full waveform inversion (FWI) by utilizing the ultralow-frequency component in the seismic data. However, the performance of envelope inversion depends on the frequency component and initial model to some extent. To improve the convergence ability and avoid the local minima issue, we propose a convolution-based envelope inversion method to update the low-wavenumber component of the velocity model. Besides, the multi-scale inversion strategy (MCEI) is also incorporated to improve the inversion accuracy while guaranteeing the global convergence. The success of this method relies on modifying the original envelope data to expand the overlap region between observed and modeled envelope data, which in turn expands the global minimum basin of misfit function. The accurate low-wavenumber component of the velocity model provided by MCEI can be used as the migration model or an initial model for conventional FWI. The numerical tests on simple layer model and complex BP 2004 model verify that the proposed method is more robust than EI even when the initial model is coarse and the frequency component of data is high.

Inspired by the large number of applications for symmetric nonlinear equations, an improved full waveform inversion algorithm is proposed in this paper in order to quantitatively measure the bone density and realize the early diagnosis of osteoporosis. The isotropic elastic wave equation is used to simulate ultrasonic propagation between bone and soft tissue, and the Gauss–Newton algorithm based on symmetric nonlinear equations is applied to solve the optimal solution in the inversion. In addition, the authors use several strategies including the frequency-grid multiscale method, the envelope inversion and the new joint velocity–density inversion to improve the result of conventional full-waveform inversion method. The effects of various inversion settings are also tested to find a balanced way of keeping good accuracy and high computational efficiency. Numerical inversion experiments showed that the improved full waveform inversion (FWI) method proposed in this paper shows superior inversion results as it can detect small velocity–density changes in bones, and the relative error of the numerical model is within 10%. This method can also avoid interference from small amounts of noise and satisfy the high precision requirements for quantitative ultrasound measurements of bone.

Ultrasound computed tomography (UCT) is considered to have great potential for the early diagnosis of knee joint injuries. Combining prior knowledge and sound speeds of tissues, UCT can diagnose a variety of symptoms and the extent of tissue lesion. However, no existing studies can reconstruct the sound speed distributions of knee joints in UCT. Therefore, in this study, sound speed distributions of knee joints are reconstructed to provide an imaging basis for the formulation of a treatment plan. In addition, Full waveform inversion (FWI) methods are utilized to estimate highresolution images. However, for media with large variations in sound speeds, traditional FWI methods may lead to a cycle-skipping phenomenon and incorrect convergence direction. Hence, this study proposes a multi-centerfrequency source based FWI method to overcome the above limitations. A penalized least-squares optimization problem is constructed to obtain a numerical solution of the sound speed distribution. Computer simulations are conducted to prove the effectiveness and robustness of the proposed method. Furthermore, the reasons for selecting the center frequencies of sources are analyzed. Two numerical knee joint phantoms are used to evaluate the performance. The results suggest that the biases of the reconstructed images are less than 1% under a 5% noise condition.

Ultrasound computed tomography (USCT) is an emerging imaging modality that holds great promise for breast imaging. Full-waveform inversion (FWI)-based image reconstruction methods leverage accurate wave physics to generate high spatial resolution quantitative images of the breast tissue’s acoustic properties, such as speed of sound, from USCT measurement data. However, the significant computational demand for FWI reconstruction poses a considerable challenge to its widespread adoption in clinical settings. Data-driven machine learning approaches offer a faster and more efficient means of translating waveform data into images. Yet, the effectiveness of machine learning methods is constrained by the diversity and quality of the training data. Given the heterogeneous distribution of breast tissue characteristics, such as fat content and size, the performance of machine learning varies across different sizes. This variability is problematic, particularly in medical diagnostics, where precision is crucial. In response to the limited data in certain categories, we propose utilizing generative AI to augment data samples, thereby enhancing FWI’s performance on limited-sample data and addressing issues of AI fairness.

In seismic exploration, 3D acoustic full waveform inversion (FWI) is nowadays commonly used to estimate large-to-intermediate scale velocity features with low-frequency and wide-aperture data. Velocity maps estimated with this technique can have higher resolution than the ones obtained by travel-time inversion. However, since full waveform inversion fits both the phases and the amplitudes of seismic data, the acoustic assumption may not be adequate to reproduce the data's amplitude versus offset variations in presence of hard velocity contrasts. This could limit the applications of acoustic FWI and put some constrains on the choice of the initial model reducing model's resolution. To better understand the behaviour of acoustic FWI in presence of hard layers and study the potential elastic effects, we built a synthetic model that mimics the geology of North Oman. Then we inverted the data generated with this model starting from an almost exact initial model and also from a smooth one. We show that acoustic FWI diverges when starting from an initial model with too high resolution. The inversion over-fits the elastic data leading to erroneous velocity updates. This synthetic experiment illustrates the limitations of acoustic FWI when used to obtain a high resolution velocity image in complex geology.

Summary Full-waveform inversion can be severely compromised by problems of cycle skipping; this occurs when predicted and observed data differ by more than half a cycle, and it leads the inversion to recover a local rather than the global minimum model. Overcoming cycle skipping normally requires both a good starting model and low-frequency content in the field data. Here we present a scheme that uses a non-linear extrapolation to add missing low- frequencies into the field data. We demonstrate the scheme using a 3D OBC field dataset, and show that it can invert to recover the global minimum model even when the original un-extrapolated field dataset is significantly cycle skipped. Introduction Full-waveform inversion (FWI) is an optimization scheme that seeks to find the global minimum of the misfit between field seismic data and synthetic data generated by a model. It proceeds towards the global minimum by a series of local linearized iterations from a starting model. The true relationship between model and data however is non-linear, and several of these non-linearities can lead the inversion scheme to become trapped within local minima rather than reaching the desired global solution. Amongst these non-linearities, the most important is that produced by the oscillatory nature of the seismic data themselves. A cycle-skipped starting model, that is one that produces data that differ by more than half a cycle with respect to the field data, will normally lead the inversion in entirely the wrong direction towards a local minimum. This problem is well known; its practical solution typically requires a highly accurate starting model combined with low-frequency field data. In these circumstances, the predicted starting data are not cycle skipped at the lowest frequencies, and the global solution can be found by starting FWI using the lowest frequencies in the field data. In this paper, we present a FWI scheme that relaxes the requirement for low-frequency field data and a good starting model, and that is able to reach the global minimum solution even when the starting data are cycle skipped. We do this by using the observed field data to synthesize low-frequency data that were not present in the original field data. We then invert these invented low- frequencies, which has the effect of dragging the starting model towards the global minimum. We then switch to invert the true field data which are now no longer cycle skipped, and so reach the global minimum.

Summary While full waveform inversion (FWI) can provide high resolution velocity models, the method is often let down by the cycle skipping problem. Several solutions based on the estimation of the time shifts have been proposed. Among them, dynamic warping FWI (D-FWI) combines the dynamic warping for the computation of the time shifts between the observed and the predicted data, and a technique which partially warps the observed data to connect the predicted data in a cycle skipping-free way. However, the D-FWI still risks falling into local minima, in particular when the initial model is inaccurate and low-frequency data are missing. Here, we propose a more robust process for estimating the time shifts in which dynamic warping is repeated with offset dependent constraints. The more reliably detected time shifts, can be used in D-FWI with a waveform-based or a traveltime-based objective function to better manage the cycle-skipping problem. We demonstrate the method with a synthetic data from the Marmousi model as well as one challenging OBC dataset from Indonesia.

Ultrasound Computer Tomography (USCT) is a promising new imaging method for breast cancer diagnosis. We developed a 3D USCT system and tested it in a pilot study with encouraging results: 3D USCT was able to depict two carcinomas, which were present in contrast enhanced MRI volumes serving as ground truth. To overcome severe differences in the breast shape, an image registration was applied. We analyzed the correlation between average sound speed in the breast and the breast density estimated from segmented MRIs and found a positive correlation with R=0.70. Based on the results of the pilot study we now carry out a successive clinical study with 200 patients. For this we integrated our reconstruction methods and image post-processing into a comprehensive workflow. It includes a dedicated DICOM viewer for interactive assessment of fused USCT images. A new preview mode now allows intuitive and faster patient positioning. We updated the USCT system to decrease the data acquisition time by approximately factor two and to increase the penetration depth of the breast into the USCT aperture by 1 cm . Furthermore the compute-intensive reflectivity reconstruction was considerably accelerated, now allowing a sub-millimeter volume reconstruction in approximately 16 minutes. The updates made it possible to successfully image first patients in our ongoing clinical study.

Ultrasound computed tomography (USCT) receives increasing attention because of its capability to reconstruct quantitative information about the material property distribution as images with superior resolution. However, one roadblock for the wide adoption of relevant techniques is the high demand for computational resources and the long processing time for solving a large inverse problem in imaging. To alleviate the associated challenges, a two-stage inversion scheme is proposed: 1) the ultrasound scanning signals are first processed using a full waveform inversion (FWI) technique with a single iteration to rapidly create a model (image) with embedded wave speed distribution; 2) the corresponding image will be further improved by feeding into a pre-trained deep neural network. The deep learning models presented in this paper are built upon two architectures to instantaneously solve the associated inverse problems and to produce a high-resolution image in real-time. The first is based on 1D convolutional neural network (1D-CNN) layers with an autoencoder structure. The second implements additional layers and skip connections inspired by a U-Net architecture. The resultant superior reconstructions from both CNNs demonstrate that the proposed framework produces a high-resolution image from a rapidly-generated, low-resolution image in real-time, with dramatically improved results.

Seismic full waveform inversion (FWI) is able to build high-resolution velocity model based on the full information carried by seismic wave. However, FWI requires an accurate enough initial model to ensure convergence. In this paper, we propose a new nonlinear FWI method to mitigate the initial model dependence problem. Specifically, we firstly propose a nonlinear operator within the hybrid model- and data-driven framework based on the frequency controllable envelope operator (FCEO) and a deep learning architecture U-Net. FCEO is used to obtain the envelope of a band-limited data and U-Net realizes the mapping from this envelope to that corresponding to a lower frequency band. The U-Net is trained in a self-supervised manner that avoids the reliance on labeled data and benefits the generalization ability. Based on the nonlinear operator, a nonlinear FWI method is proposed by defining a new misfit function. In addition, the calculation of gradient is derived using the adjoint-state method. Using numerical examples, we investigate the performance of the proposed nonlinear operator and the new nonlinear FWI method. The results clearly demonstrate that the proposed nonlinear operator is effective in obtaining low-frequency envelope data, and the new nonlinear FWI method has advantages over common method in mitigating cycle-skipping and building an initial model for conventional FWI.

Full-waveform inversion (FWI) is a highly nonlinear and nonconvex problem. To mitigate the dependence of FWI on the quality of starting model and on the low frequencies in the data, we apply the gradient sampling algorithm (GSA) introduced for nonsmooth, nonconvex optimization problems to FWI. The search space is hugely expanded to have more freedom to accommodate large velocity errors in the starting model. The original implementation of GSA requires explicit calculation of the gradient at each sampled vector, which is prohibitively expensive. Based on the observation that a slight perturbation in the velocity model causes a small spatial shift of the wavefield, we have approximated the sampled gradients by crosscorrelating the space-shifted source- and receiver-side wavefields. Theoretical derivation suggests that the two wavefields should be shifted in the same direction to obtain reasonable low-wavenumber updates. The final descent search direction is obtained by summing all the shifted gradients. For practical implementation, we only take one random space shift at each time step during the gradient calculation. This simplification provides an efficient realization in which the computational costs and memory requirements are the same as conventional FWI. Multiple numerical examples demonstrate that the proposed method alleviates the cycle-skipping problem of conventional FWI when starting from very crude initial velocity models without low-frequency data.