As global groundwater levels continue to decline rapidly, there is a growing need for advanced techniques to monitor and manage aquifers effectively. This study focuses on validating a numerical model using seismic data from a small-scale experimental setup designed to estimate water volume in a porous reservoir. Expanding on previous work with synthetic data, we analyze seismic data acquired from a controlled experimental site in Laukaa, Finland. By employing neural networks, we directly estimate water volume from seismic responses, bypassing the traditional need for separate determinations, for example, of reservoir water-table level and porosity. The study models wave propagation through a coupled poroviscoelastic-viscoelastic medium using a three-dimensional discontinuous Galerkin method. The proposed methodology is validated against experimental data, aiming to improve precision in mapping current water volumes and contributing to the development of sustainable groundwater management practices.

Purpose Iterative model-based image reconstruction algorithms in cone beam computed tomography (CBCT) require repetitive forward and backward projection operations. We compare the quality of the branchless distance-driven (BDD) projector in iterative CBCT reconstruction with ray- and voxel-based methods in both regular and low-dose examinations, and introduce a hybrid approach that aims at faster computation by using the BDD as the backprojector only. We also demonstrate the potential of the BDD in FDK reconstructions.Approach Two measured and one simulated datasets are used. Contrast-to-noise ratio (CNR) and modulation transfer function values are computed for one measured dataset. The structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR) are computed with the simulated data.Results Based on our results, BDD has reduced noise and better CNR compared to the other methods, with the quality dependent on the scanner geometry. The CNR is improved by 21% with the BDD and 4% with the hybrid method. BDD improves SSIM values by approximately 3.3% in the lowest dose case and 1% in the highest dose case, while for PSNR the values are 5% - 10% better. For the hybrid method, the SSIM improvements range from 0.8% - 2.2%, and the PSNR from 3.7% - 6.6 %. The hybrid method with the BDD as a backprojector can be computationally twice faster with similar image quality.Conclusions The hybrid projector is a good choice as a compromise between image quality and computation time. Furthermore, BDD and the hybrid projector are better choices in low-dose CBCT reconstructions.

Model-based image reconstruction algorithms are known to produce high-accuracy images but are still rarely used in cone beam computed tomography. One of the reasons for this is the computational requirements of model-based iterative algorithms, as it can take hundreds of iterations to obtain converged images. In this work, we present a measurement space-based preconditioner applied to the primal-dual hybrid gradient (PDHG) algorithm. The method is compared with the regular PDHG, FISTA, and OS-SART algorithms, as well as to a PDHG algorithm where the step-size parameters are adaptively computed. All tested algorithms utilize subsets for acceleration. The presented filtering-based preconditioner can obtain convergence in 10 iterations with 20 subsets, compared to a hundred or more iterations required by the other tested methods. The presented method is also computationally fast and has only a 15% increase in computation time per iteration compared to PDHG without the preconditioner.

Mining environments involve complex hydro-bio-geochemical systems. Reactive transport modeling (RTM) is essential to rigorously describe these processes. Yet, process-based RTM is computationally intensive and limited in practical applications. To mitigate such challenges, this paper provides a novel deep learning-based surrogate accelerator, hidden-reactive-transport-neural-network (HRTNet), to simulate pyrite oxidation, a process of key importance for acid mine drainage. HRTNet relies on a flexible two-network architecture integrating chemical and physical equations. The model can effectively capture the desired spatio-temporal dynamics in a considerably reduced computation time (almost eight-fold). Additionally, HRTNet shows a good generalization capability covering a wide range of conditions beyond the training datasets.

Reactive transport models (RTMs) are essential tools to describe and integrate a wide range of physical and biogeochemical processes in natural and engineered porous media. However, the high computational cost often limits their applications for many practical purposes. These challenges mainly stem from the solution of a set of coupled partial differential equations (PDEs), describing multicomponent transport and geochemical reactions along with their multilevel coupling across different spatial and temporal scales. To mitigate this issue, we propose and develop a surrogate modeling approach, hidden reactive transport neural network (HRTNet). The proposed model relies on a flexible architecture based on two networks, which share a common loss function and allows incorporating both data‐driven and physics‐chemistry‐informed contributions. We consider pyrite oxidation in a 1‐D geochemically heterogeneous domain as a model example to investigate and demonstrate the capability of HRTNet as well as to analyze the performance of the developed surrogate modeling approach. HRTNet was trained based on the training data generated from the process‐based reactive transport simulations, and, successively, the trained model was used as a surrogate to predict the behavior of the reactive transport system. The results reveal that the predictions obtained by the trained surrogate model agree well with those from mechanistic RTMs in a considerably reduced computation time. Furthermore, the physics‐ and chemistry‐informed learning was promising to achieve a good generalization capability, because HRTNet could predict the desired spatio‐temporal dynamics for a wide range of initial concentrations beyond the training data sets.

Accurately estimating phase flow rates in multiphase systems is crucial for many industries, where precise measurements are essential for operational efficiency and safety. Addressing this issue, this paper introduces an approach that employs deep learning-assisted dual-modal electromagnetic flow tomography (EMFT) and electrical tomography (ET) to predict both oil and water flow rates in two-phase oil-water flows. To facilitate the generation of the data, we first simulate diverse flow conditions using COMSOL Multiphysics software and the convection-diffusion equation, aiming to create a realistic representation of two-phase oil-water flows. The dual-modal system measurement data, generated from these simulations and simulated by using a dense finite element mesh, provide reliable inputs for the deep learning model. Moreover, this study also integrates experimental data into both the training and testing phases, improving the ability of the proposed approach to estimate flow rates accurately in practical investigations. The results from laboratory experiments demonstrate the potential of the deep learning-assisted dual-modal ET and EMFT approach in effectively resolving the challenges of estimating flow rates in two-phase oil-water flow systems. By combining the deep learning capabilities with dual-modal tomography, this study offers valuable insights for future applications and represents a significant step forward in the field of multiphase flow rate estimation.

Objective . In this paper, we propose positron emission tomography image reconstruction using a multi-resolution triangular mesh. The mesh can be adapted based on patient specific anatomical information that can be in the form of a computed tomography or magnetic resonance imaging image in the hybrid imaging systems. The triangular mesh can be adapted to high resolution in localized anatomical regions of interest (ROI) and made coarser in other regions, leading to an imaging model with high resolution in the ROI with clearly reduced number of degrees of freedom compared to a conventional uniformly dense imaging model. Approach. We compare maximum likelihood expectation maximization reconstructions with the multi-resolution model to reconstructions using a uniformly dense mesh, a sparse mesh and regular rectangular pixel mesh. Two simulated cases are used in the comparison, with the first one using the NEMA image quality phantom and the second the XCAT human phantom. Main results. When compared to the results with the uniform imaging models, the locally refined multi-resolution mesh retains the accuracy of the dense mesh reconstruction in the ROI while being faster to compute than the reconstructions with the uniformly dense mesh. The locally dense multi-resolution model leads also to more accurate reconstruction than the pixel-based mesh or the sparse triangular mesh. Significance. The findings suggest that triangular multi-resolution mesh, which can be made patient and application specific, is a potential alternative for pixel-based reconstruction.

A potential framework to estimate the volume of water stored in a porous storage reservoir from seismic data is neural networks. In this study, the man-made groundwater reservoir is modeled as a coupled poroviscoelastic-viscoelastic medium, and the underlying wave propagation problem is solved using a three-dimensional discontinuous Galerkin method coupled with an Adams-Bashforth time stepping scheme. The wave problem solver is used to generate databases for the neural network-based machine learning model to estimate the water volume. In the numerical examples, we investigate a deconvolution-based approach to normalize the effect from the source wavelet in addition to the network's tolerance for noise levels. We also apply the SHapley Additive exPlanations method to obtain greater insight into which part of the input data contributes the most to the water volume estimation. The numerical results demonstrate the capacity of the fully connected neural network to estimate the amount of water stored in the porous storage reservoir.

Summary In this study, the neural network is used to estimate the amount of water stored in a porous reservoir from seismic data. To generate the training data for the neural network, a coupled poroviscoelastic-viscoelastic wave propagation model is solved using a three-dimensional (3D) discontinuous Galerkin method coupled with an Adams-Bashforth time stepping scheme. In addition, the effect of the unknown source wavelet is normalized using a deconvolution- based approach. Results indicate that the proposed neural network approach is applicable to estimate the wave content of a porous reservoir with a variety of noise amplitudes while uninteresting parameters can be successfully ignored.

Summary Neural networks provide an attractive framework to monitor the water table level and the volume of stored water in porous media from seismic data in an automated, fast and cost-efficient manner. In this work, a subsurface reservoir is modeled as a coupled three-dimensional poroviscoelastic-viscoelastic medium. The wave propagation from source to receiver(s) is numerically simulated using a nodal discontinuous Galerkin method coupled with an Adams-Bashforth time-stepping scheme on a graphics processing unit cluster. The wave field solver is used to generate databases for the neural network model to estimate the water table level and actual volume of water. We use a deconvolution-based approach to normalize the effect from the source wavelet. The results demonstrate the capacity of the fully connected neural network for estimating both the water table level and the volume of stored water in the porous storage reservoir from both synthetic and measured data.

A multi-parameter joint reconstruction method is proposed for electrical impedance tomography (EIT) and ultrasonic transmission tomography (UTT) dual-modality tomography based on statistical joint inversion framework. The inherent correlation of two imaging modalities is that the conductivity and sound speed parameters share the same structure, which can be defined by the structural similarity of the spatial distributions of conductivity and sound speed. The structural similarity between conductivity and sound speed is quantitatively characterized by a joint prior model with total variation and cross-gradient functionals. The multi-parameter joint reconstruction problem is constructed by Bayesian joint inverse model, and solved by maximum a posterior method with alternate solution strategy. Numerical and experimental tests are carried out to evaluate the performance of the proposed method. The results show that the proposed EIT/UTT dual-modality tomography method with structural similarity promoting can improve the reconstruction accuracy of conductivity and sound speed compared with the traditional single-modality EIT and UTT methods.

Monitoring, control and design of industrial processes involving multiphase flows often call for analysis of data from multiple sensors which give information on different quantities of the flowing materials. An example of such case is the problem of monitoring the flow of oil–water mixture: the phase fractions of oil and water, their velocities and volumetric flow rates cannot be retrieved from measurements given by a single sensing/imaging modality. For this reason, multi-modal tomographic imaging systems have been developed. In multi-phase flows, the quantities retrieved from different tomographic instruments are often interconnected—for example, the evolutions of the phase fractions depend on their velocities and vice versa. However, the analysis of data from different tomographic modalities is usually done separately—without taking into account physics that link the quantities of interest. In this paper, we propose a novel approach to image reconstruction in dual-modal tomography of multiphase flows. The governing idea is to combine the two modalities via Bayesian state estimation, that is, we write models that approximate connections between different quantities involved in the process and use sequential measurements from both modalities to jointly estimate these temporally evolving quantities. As an example case, we consider a dual-modal system comprising the electromagnetic flow tomography (EMFT) and electrical tomography (ET). While the EMFT is sensitive to the velocity field but also depends on the phase fractions of fluids, ET measurements are directly linked to phase fractions only. We study the performance of state estimation in EMFT-ET tomography with a set of numerical simulations. The results demonstrate that it outperforms the conventional stationary reconstruction approach, and also provides means for uncertainty quantification in multiphase flow imaging.

Accurate measurement of two-phase flow quantities is essential for managing production in many industries. However, the inherent complexity of two-phase flow often makes estimating these quantities difficult, necessitating the development of reliable techniques for quantifying two-phase flow. In this paper, we investigated the feasibility of using state estimation for dynamic image reconstruction in dual-modal tomography of two-phase oil–water flow. We utilized electromagnetic flow tomography (EMFT) to estimate velocity fields and electrical tomography (ET) to determine phase fraction distributions. In state estimation, the contribution of the velocity field to the temporal evolution of the phase fraction distribution was accounted for by approximating the process with a convection–diffusion model. The extended Kalman filter (EKF) and fixed-interval Kalman smoother (FIKS) were used to reconstruct the temporally evolving velocity and phase fraction distributions, which were further used to estimate the volumetric flow rates of the phases. Experimental results on a laboratory setup showed that the FIKS approach outperformed the conventional stationary reconstructions, with the average relative errors of the volumetric flow rates of oil and water being less than 4%. The FIKS approach also provided feasible uncertainty estimates for the velocity, phase fraction, and volumetric flow rate of the phases, enhancing the reliability of the state estimation approach.

When using the statistical inversion framework in microwave tomography (MWT), generally, the real and imaginary parts of the unknown dielectric constant are treated as uncorrelated and independent random variables. Thereby, in the maximum a posteriori estimates, the two recovered variables may show different structural changes inside the imaging domain. In this work, a correlated sample-based prior model is presented to incorporate the correlation of the real part with the imaginary part of the dielectric constant in the statistical inversion framework. The method is used to estimate the inhomogeneous moisture distribution (as dielectric constant) in a large cross section of polymer foam. The targeted application of MWT is in industrial drying to derive intelligent control methods based on tomographic inputs for selective heating purposes. One of the features of the proposed method shows how to integrate lab-based dielectric characterization, often available in MWT application cases, in the prior modeling. The method is validated with numerical and experimental MWT data for the considered moisture distributions.

We propose a state estimation approach to time-varying magnetic resonance imaging utilizing a priori information. In state estimation, the time-dependent image reconstruction problem is modeled by separate state evolution and observation models. In our method, we compute the state estimates by using the Kalman filter and steady-state Kalman smoother utilizing a data-driven estimate for the process noise covariance matrix, constructed from conventional sliding window estimates. The proposed approach is evaluated using radially golden angle sampled simulated and experimental small animal data from a rat brain. In our method, the state estimates are updated after each new spoke of radial data becomes available, leading to faster frame rate compared with the conventional approaches. The results are compared with the estimates with the sliding window method. The results show that the state estimation approach with the data-driven process noise covariance can improve both spatial and temporal resolution.

With the ongoing digitalization of industry, imaging sensors are becoming increasingly important for industrial process control. In addition to direct imaging techniques such as those provided by video or infrared cameras, tomographic sensors are of interest in the process industry where harsh process conditions and opaque fluids require non-intrusive and non-optical sensing techniques. Because most tomographic sensors rely on complex and often time-multiplexed excitation and measurement schemes and require computationally intensive image reconstruction, their application in the control of highly dynamic processes is often hindered. This article provides an overview of the current state of the art in fast process tomography and its potential for use in industry.

This paper compares three different projectors for the iterative image reconstruction in cone beam computed tomography (CBCT), used to compute both the forward projection as well as the backprojection in practically all iterative reconstruction algorithms. The tested projectors are an improved version of the Siddon's algorithm, an interpolation-based projector, and the branchless distance-driven projector. For the forward projection of the interpolation-based projector, the effect of the sampling distance is also examined. The improved Siddon projector is a ray-driven projector while the interpolation and branchless projectors are ray-driven in forward projection and voxel-driven in backprojection. All projectors were implemented for GPUs using OpenCL and the interpolation-based and branchless distance-driven projector utilized the built-in hardware-based interpolation available in GPUs. The projectors were tested using experimental phantom data from Planmeca CBCT scanner. The results show that quality-wise the differences between the interpolation-based and branchless projectors are small, while the improved Siddon tends to cause aliasing artifacts and Moiré pattern unless sufficient sampling or point spread function blurring is used. Computationally the interpolation-based projector is fastest while the improved Siddon is the slowest. The branchless distance-driven projector can also exhibit noise pattern if the dynamic range of the integral image used with the projector is too wide. Thus the interpolation-based projector is both the computationally fastest method, while also providing very similar quality in CBCT as well as being more robust than the branchless distance-driven method. The sampling distance of the interpolation-based projector, on the other hand, has quite a small effect on the final image quality and thus distances of even four voxels can be used without noticeable effect on image quality.