This paper introduces a deep unfolding-based approach for Full Waveform Inversion (FWI) in quantitative ultrasound imaging. Our technique leverages trained deep neural networks to perform an optimized gradient step that achieves superior results and significantly reduces the number of iterations required for convergence—a crucial advantage for real-world applications. While a recently proposed deep unfolding approach, MB-QRUS, demonstrated higher efficiency than traditional FWI, our experiments on both the training dataset and out-of-distribution examples show that our method significantly outperforms classical FWI and MB-QRUS in reconstruction quality under noisy conditions, while maintaining a high level of efficiency. This work enhances the potential for real-time quantitative ultrasound imaging in clinical settings and suggests broader applicability of FWI across various domains.

The rising demand for multi-person non-contact vital signs monitoring (NCVSM) in healthcare highlights the potential of radar technology, especially in cluttered environments. Single-input multiple-output frequency-modulated continuous- wave (FMCW) radars enable multi-object localization, which is crucial for multi-person NCVSM. However, detecting and positioning humans in crowded scenarios is challenging due to resolution limitations. This work first proposes an iterative method for multi-human localization exploiting joint sparsity and cardiopulmonary properties. Then, the method is unfolded into a neural network that preserves the data’s unique features to further enhance accuracy and reduce computational cost. Simulations containing real-world data show the network’s superior performance in detecting and positioning multiple adjacent humans, outperforming existing techniques via key metrics. This approach can be integrated into advanced NCVSM systems where accuracy and computational efficiency are paramount.

Microwave imaging is a promising method for early diagnosing and monitoring brain strokes. It is portable, non-invasive, and safe to the human body. Conventional techniques solve for unknown electrical properties represented as pixels or voxels, but often result in inadequate structural information and high computational costs. We propose to reconstruct the three dimensional (3D) electrical properties of the human brain in a feature space, where the unknowns are latent codes of a variational autoencoder (VAE). The decoder of the VAE, with prior knowledge of the brain, acts as a module of data inversion. The codes in the feature space are optimized by minimizing the misfit between measured and simulated data. A dataset of 3D heads characterized by permittivity and conductivity is constructed to train the VAE. Numerical examples show that our method increases structural similarity by 14% and speeds up the solution process by over 3 orders of magnitude using only 4.8% number of the unknowns compared to the voxel-based method. This high-resolution imaging of electrical properties leads to more accurate stroke diagnosis and offers new insights into the study of the human brain.

Magnetotelluric (MT) data inversion reconstructs an electrical resistivity structure most compatible with the observed MT data, and static correction can remove the undesired static shift effect in MT data. Conventional MT data static shift correction often faces the challenge of demanding requirements, such as large data amount, additional types of data, or a deep understanding of the research area. MT inversion constrained by seismic data often has better resolution and model consistency compared with independent MT inversion. However, valuable inversion knowledge contained in geophysicists’ expertise is not effectively incorporated. In this work, we present an intelligent MT data inversion method leveraging data- and physics-driven techniques based on deep learning. A novel MT data static shift correction method is introduced based on a neural network (NN). An MT data inversion method is formulated with the constraint of the extracted seismic reflection image based on two different NNs. Experiments on synthetic and field data verify the effectiveness of the proposed method.

In this work, we apply the supervised descent method (SDM) to 3-D limited data inversion. In the measurement of the far field, the scattered field in 3-D measurement is small in magnitude and easily polluted by noise. Combining with limited observed data, the inversion problem is highly nonunique and ill-posed. To mitigate the ill-posedness, the model-based inversion is adopted by describing metallic targets based on prior information. Then, a series of generic descent directions is learned in the training stage iteratively using SDM. During inversion, the values of these model-based parameters are reconstructed directly using the learned directions. This approach is validated using both synthetic and experimental data. All simulations and experiments are conducted in a monostatic measurement setup to match real measurement conditions. The results show that by choosing proper prior information, the model-based SDM inversion can effectively compensate for the lack of data and achieve decent accuracy.

In this article, multitask learning is applied to forward modeling of 2-D magnetotellurics (MT) to predict the apparent resistivity and impedance phase of MT data. Multitask learning can learn multiple objectives simultaneously based on the shared representation, thereby improving efficiency and accuracy. The loss function is carefully designed by weighing multiple objective functions based on homoscedastic uncertainty, and the structural similarity regularization term is applied to ensure the texture of the obtained apparent resistivity and impedance phase. The proposed convolutional neural network can make accurate predictions with an average relative error of apparent resistivity and impedance phase less than 1.2% and 0.2%, respectively. The generalization ability of the proposed network is verified by applying it to cases with more complex resistivity distributions than training samples. This article shows the potential for fast and accurate computation of two highly correlated physical quantities in electromagnetic fields.

Deep learning is applied to assist the joint inversion for audio-magnetotelluric and seismic travel time data. More specifically, deep residual convolutional neural networks (DRCNNs) are designed to learn both structural similarity and resistivity-velocity relationships according to prior knowledge. During the inversion, the unknown resistivity and velocity are updated alternatingly with the Gauss-Newton method, based on the reference model generated by the trained DRCNNs. The workflow of this joint inversion scheme and the design of the DRCNNs are explained in detail. Compared with describing the resistivity-velocity relationship using empirical equations, this method can avoid the necessity in modeling the correlations in rigorous mathematical forms and extract more hidden prior information embedded in the training set, meanwhile preserving the structural similarity between different inverted models. Numerical tests show that the inverted resistivity and velocity have similar profiles, and their relationship can be kept consistent with the prior joint distribution. Furthermore, the convergence is faster, and final data misfits can be lower than separate inversion.

In this article, a new scheme based on the supervised descent method (SDM) for solving directional electromagnetic logging-while-drilling (LWD) inverse problems is proposed. The SDM provides us a new perspective to combine the classical gradient-based inversion and machine-learning-based inversion schemes. It iteratively learns a set of descent directions in the offline training process, where the training model set is generated in advance according to the prior information, and then updates the models with the learned descent directions as well as data residuals in the prediction stage, resulting in great flexibility to incorporate prior information, the capability of skipping local minima, and accelerated convergence. The generalization ability of the SDM to interrogate new models that are not contained in the training model set is also explored. By utilizing real-time information obtained from the logging process, the learned descent directions can be slightly revised with a higher efficiency to get closer to the true model. In addition, we probe the sensitivity of the SDM by adding different levels of random noise to the measurements. Numerical examples demonstrate that SDM-based inversion can achieve a higher resolution, faster convergence, and higher robustness than conventional schemes such as Occam's inversion.