Iterative Inversion Technique Research Articles

Non-destructive testing by eddy current sensor for crack orientation detection using HHO optimizer by differential probe

In this research, the design of non-destructive eddy current evaluation systems was improved using Harris Hawks optimization (HHO). To determine the orientation of cracks from eddy current data, a numerical approach was developed based finit elements methode FEM and on an iterative inversion technique that minimizes a non-linear least squares objective function that evaluates the overall difference between forecasts and observationsin axisymmetric model. In this paper the HHO optimization and steepest descent methods were compared and studied in order to minimize the objective function. To measure the precision of the estimated crack orientation, the lower bounds of the HHO optimization on crack orientation were obtained. This work explores the concept of an HHO algorithm that searches for the optimal solution within a large solution space for a specific crack orientation problem.The algorithm starts its search at any point in the solution space and looks for better solutions by searching in the "local" area surrounding the start point. The algorithm ends when it finds what it believes to be the best solution or when predetermined stopping criteria are met.

Deep learning tomographic reconstruction through hierarchical decomposition of domain transforms.

Deep learning (DL) has shown unprecedented performance for many image analysis and image enhancement tasks. Yet, solving large-scale inverse problems like tomographic reconstruction remains challenging for DL. These problems involve non-local and space-variant integral transforms between the input and output domains, for which no efficient neural network models are readily available. A prior attempt to solve tomographic reconstruction problems with supervised learning relied on a brute-force fully connected network and only allowed reconstruction with a 1284 system matrix size. This cannot practically scale to realistic data sizes such as 5124 and 5126 for three-dimensional datasets. Here we present a novel framework to solve such problems with DL by casting the original problem as a continuum of intermediate representations between the input and output domains. The original problem is broken down into a sequence of simpler transformations that can be well mapped onto an efficient hierarchical network architecture, with exponentially fewer parameters than a fully connected network would need. We applied the approach to computed tomography (CT) image reconstruction for a 5124 system matrix size. This work introduces a new kind of data-driven DL solver for full-size CT reconstruction without relying on the structure of direct (analytical) or iterative (numerical) inversion techniques. This work presents a feasibility demonstration of full-scale learnt reconstruction, whereas more developments will be needed to demonstrate superiority relative to traditional reconstruction approaches. The proposed approach is also extendable to other imaging problems such as emission and magnetic resonance reconstruction. More broadly, hierarchical DL opens the door to a new class of solvers for general inverse problems, which could potentially lead to improved signal-to-noise ratio, spatial resolution and computational efficiency in various areas.

Stress distribution in the western India-Eurasia collision zone, its kinematics and seismotectonic implications

In this study, we use iterative joint stress inversion technique on a declustered catalogue of 324 focal mechanisms to evaluate the stress distribution in the western India-Eurasia collision zone (IECZ). The stress field has been obtained for different tectonic settings, such as the Himalayan Seismic belt, Karakoram-Tibet region and the individual zones identified based on geology, tectonics and available focal mechanism solutions. The results reveal NE-SW trending principal stress (σ1) with compression for Himalayan seismic belt and strike-slip stress regime for Karakoram-Tibet. We observe that even within the Himalayan region, the western region (75°-77° E latitudes) exhibits arc-oblique compression (NE-SW) in contrast to the arc-normal compression (NNE-SSW) in central Himalaya beyond 77°E; consistent with GPS vectors. The Stress field for the aftershock sequence of 2005 Kashmir earthquake in the Hazara Syntaxis region displays dissimilarity with its adjoining regions (Pamir, Nanga Parbat, Hindukush, etc.), but exhibits similarity with the Central Himalaya. Within the Karakoram-Tibet region, the Karakoram fault exhibits NNE-SSW oriented principal stress with transpressional fault motion, while the Kaurik Chango rift shows N-S oriented principal stress with transtensional motion. The stress ratio in the western IECZ broadly varies between 0.07 and 0.9, suggesting the prominent role of the intermediate stress axis (σ2) in the areas of low-stress ratios. The inferences drawn suggest that the stress distribution in the western IECZ is heterogeneous with variable seismic hazard.

Measurement of the vertical atmospheric density profile from the X-ray Earth occultation of the Crab Nebula with Insight-HXMT

Abstract. X-ray Earth occultation sounding (XEOS) is an emerging method for measuring the neutral density in the lower thermosphere. In this paper, the X-ray Earth occultation (XEO) of the Crab Nebula is investigated using the Hard X-ray Modulation Telescope (Insight-HXMT). The pointing observation data on the 30 September 2018 recorded by the low-energy X-ray telescope (LE) of Insight-HXMT are selected and analysed. The extinction light curves and spectra during the X-ray Earth occultation process are extracted. A forward model for the XEO light curve is established, and the theoretical observational signal for light curve is predicted. The atmospheric density model is built with a scale factor to the commonly used Mass Spectrometer Incoherent Scatter Radar Extended model (MSIS) density profile within a certain altitude range. A Bayesian data analysis method is developed for the XEO light curve modelling and the atmospheric density retrieval. The posterior probability distribution of the model parameters is derived through the Markov chain–Monte Carlo (MCMC) algorithm with the NRLMSISE-00 model and the NRLMSIS 2.0 model as basis functions, and the respective best-fit density profiles are retrieved. It is found that in the altitude range of 105–200 km, the retrieved density profile is 88.8 % of the density of NRLMSISE-00 and 109.7 % of the density of NRLMSIS 2.0 by fitting the light curve in the energy range of 1.0–2.5 keV based on the XEOS method. In the altitude range of 95–125 km, the retrieved density profile is 81.0 % of the density of NRLMSISE-00 and 92.3 % of the density of NRLMSIS 2.0 by fitting the light curve in the energy range of 2.5–6.0 keV based on the XEOS method. In the altitude range of 85–110 km, the retrieved density profile is 87.7 % of the density of NRLMSISE-00 and 101.4 % of the density of NRLMSIS 2.0 by fitting the light curve in the energy range of 6.0–10.0 keV based on the XEOS method. Goodness-of-fit testing is carried out for the validation of the results. The measurements of density profiles are compared to the NRLMSISE-00 and NRLMSIS 2.0 model simulations and the previous retrieval results with NASA's Rossi X-ray Timing Explorer (RXTE) satellite. For further confirmation, we also compare the measured density profile to the ones by a standard spectrum retrieval method with an iterative inversion technique. Finally, we find that the retrieved density profile from Insight-HXMT based on the NRLMSISE-00 and NRLMSIS 2.0 models is qualitatively consistent with the previous retrieved results from RXTE. The results of light curve fitting and standard energy spectrum fitting are in good agreement. This research provides a method for the evaluation of the density profiles from MSIS model predictions. This study demonstrates that the XEOS from the X-ray astronomical satellite Insight-HXMT can provide an approach for the study of the upper atmosphere. The Insight-HXMT satellite can join the family of the XEOS. The Insight-HXMT satellite with other X-ray astronomical satellites in orbit can form a space observation network for XEOS in the future.

Efficient estimation of aquifer intrinsic permeability anisotropy using perturbation theory

Inverse modeling of aquifer measurements aims at estimating the spatial distribution of rock properties that best fits the available measurements which, in turn, allows predicting water yields and pressures to an acceptable level of accuracy. Nonlinear automatic inverse methods require multiple solutions of the diffusion equation, also known as the groundwater flow equation. Although numerical solutions to the forward problems improve the understanding of complex groundwater flow systems, they are often computationally expensive, thereby rendering the inversion process inefficient. We introduce a gradient-based inversion algorithm that leverages perturbation theory to efficiently estimate the tensorial intrinsic permeability distribution of porous media from single-phase transient pressure measurements. With a maximum of two numerical simulations, the Joint Perturbation-Superposition (JPS) method allows one to compute flow-history-dependent Intrinsic permeability Sensitivity Functions (PSF) on the spatial-temporal domain. Regardless of the gradient-based iterative inversion technique, our method efficiently adapts the sensitivity functions yielded by perturbation theory to calculate the entries of the associated Jacobian matrix at every iteration. A two-dimensional synthetic model comprising multi-well conditions is examined for an anisotropic and spatially heterogeneous groundwater flow system. The perturbation method yields accurate and efficient parameter estimation by leveraging sensitivity functions for (1) the appropriate selection of input transient pressure measurements and (2) reducing the sequential calculation of Jacobian matrices. As a result, Monte Carlo uncertainties as low as <5% are obtained for the estimated tensorial intrinsic permeability distribution, with inversion times halved when compared to conventional techniques.

Multi-channel analysis of surface waves (MASW) using dispersion and iterative inversion techniques: implications for cavity detection and geotechnical site investigation

Multi-channel analysis of surface waves (MASW) using dispersion and iterative inversion techniques: implications for cavity detection and geotechnical site investigation

On the Use of Preconditioners to Improve the Accuracy and Effectiveness of Iterative Methods to Enhance the Spatial Resolution of Radiometer Measurements

In this letter, a new approach is proposed to ameliorate the performance of iterative gradient-like regularization schemes aimed at enhancing the spatial resolution of microwave radiometer measurements in the Hilbert space. The approach consists of preconditioning the ill-conditioned discrete problem to let the iterative gradient-based inversion technique be more computer-time effective. Experiments undertaken on the simulated radiometer brightness profiles demonstrate the soundness of the proposed rationale that outperforms conventional gradient-like methods in terms of both computer-time effectiveness and accuracy in reconstructing spot-like discontinuities while resulting in larger fluctuations over the background.

A massively-parallel, unstructured overset method to simulate moving bodies in turbulent flows

An unstructured overset method capable of performing direct numerical simulation (DNS) and large eddy simulation (LES) of many (O(105)) moving bodies, utilizing many computational cores (O(105)), in turbulent, incompressible fluid flow is presented. Unstructured meshes are attached to bodies and placed within a fixed background domain. Body meshes are allowed to arbitrarily overlap and move throughout the domain. Within each mesh a high resolution, unstructured, non-dissipative finite volume method is used to solve for the flow field. Boundary conditions for each mesh are provided by interpolation from flow solutions on overlapping meshes. When many unstructured meshes of different resolution overlap, care is required in the connection between the different flow solutions. An interpolant is created which seeks to preserve volume conservation of flow quantities between meshes regardless of overlapping mesh differences. An implicit fractional step method is used for time advancement, requiring the calculation of a predicted fluid velocity and corrector pressure field. For the predictor step, the resulting interpolation is directly introduced into the implicit equations for the predicted flow field. For the corrected pressure field, the continuity between meshes is weakly enforced using a penalty formulation. The pressure formulation is symmetric, positive-definite and non-singular resulting in a formulation which is readily solvable using traditional iterative matrix inversion techniques. An Arbitrary Euler-Lagrangian (ALE) method coupled to a 6 degrees of freedom rigid body equation system (6-DOF) is used for body motion. For rotation, a quaternion representation is used to solve Euler's equations of rigid body motion. A linear spring damper model, which uses geometry information readily available from the overset assembly process, is used for collisions. Validation of the method for canonical flow fields is presented including assessment of order of accuracy and kinetic energy conservation properties. Particle-resolved direct numerical simulation (PR-DNS) of single particles in various flow fields are presented for validation. PR-DNS results of 50,000 spherical particles freely moving within turbulent channel flow are shown as a demonstration of the method at full scale. LES results of a marine propeller under crashback conditions are shown to demonstrate the ability to simulate highly unsteady turbulent flows over complex, moving geometries.

The third Sandia Fracture Challenge: peridynamic blind prediction of ductile fracture characterization in additively manufactured metal

In the context of the third Sandia Fracture Challenge (SFC3), the details of the blind predictions performed by the University of Texas team are provided in this article. Over the past two decades, the peridynamic theory has shown great promise in modeling autonomous crack nucleation and growth in materials. While peridynamics has been commonly applied to simulate failure of brittle materials, its ability in predicting ductile fracture has remained mostly untested. This fracture challenge was seen as an opportunity to assess the state of the art of the peridynamic theory in predicting the response of an additively manufactured 316L stainless steel bar with a complex geometry under the dynamic tensile experiments performed by Sandia National Laboratories. The performance of a recently proposed, generalized, ordinary finite deformation constitutive correspondence model, coupled with a recent state-based damage correspondence model was explored over this problem. For finite deformation material modeling, the classical elastoplastic framework of Simo was implemented within the ordinary correspondence theory. Damage modeling was achieved by incorporating the Johnson-Cook failure criterion using the damage correspondence framework. An iterative inverse technique was applied to calibrate the model parameters using the longitudinal and notched tensile tests data provided by Sandia National Laboratories. A blind prediction of the deformation and failure behavior of the SFC3 geometry was performed by embedding the calibrated model in a peridynamic simulation. Uncertainty was introduced into the model parameters to quantify material variability. The results are compared to the experiments conducted at Sandia National Laboratories. While our modeling approach led to qualitatively good results and a correctly predicted crack path, it underpredicted the load-carrying capacity of the structure and simulated an early fracture. Our post-experiment analysis identifies material instability issues associated with the model as the primary sources of error.

Linearized inversion methods for three-dimensional electromagnetic imaging in the multiple scattering regime

In optical or microwave computational tomography, the sample permittivity is reconstructed numerically from the measurements of its scattered field for various illuminations. When the light sample interaction involves multiple scattering, the relationship between the scattered field and the permittivity is non-linear and a direct reconstruction is not possible. Using a simple physical approach, adapted to the three-dimensional vectorial electromagnetic framework, we derive an iterative inversion technique, based on the linearization of the scattering operator, for imaging (possibly anisotropic) targets in the multiple scattering regime. We investigate the performances of different approximations of this operator accounting for more or less multiple scattering. Our method is applied to the reconstruction of targets in the microwave domain using experimental data.

Topology-optimized metasurfaces: impact of initial geometric layout.

Topology optimization is a powerful iterative inverse design technique in metasurface engineering and can transform an initial layout into a high-performance device. With this method, devices are optimized within a local design phase space, making the identification of suitable initial geometries essential. In this Letter, we examine the impact of initial geometric layout on the performance of large-angle (75deg) topology-optimized metagrating deflectors. We find that when conventional metasurface designs based on dielectric nanoposts are used as initial layouts for topology optimization, the final devices have efficiencies around 65%. In contrast, when random initial layouts are used, the final devices have ultra-high efficiencies that can reach 94%. Our numerical experiments suggest that device topologies based on conventional metasurface designs may not be suitable to produce ultra-high-efficiency, large-angle metasurfaces. Rather, initial geometric layouts with non-trivial topologies and shapes are required.

Linearized 3-D Electromagnetic Contrast Source Inversion and Its Applications to Half-Space Configurations

One of the main computational drawbacks in the application of 3-D iterative inversion techniques is the requirement of solving the field quantities for the updated contrast in every iteration. In this paper, the 3-D electromagnetic inverse scattering problem is put into a discretized finite-difference frequency-domain scheme and linearized into a cascade of two linear functionals. To deal with the nonuniqueness effectively, the joint structure of the contrast sources is exploited using a sum-of-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm optimization scheme. A cross-validation technique is used to check whether the optimization process is accurate enough. The total fields are, then, calculated and used to reconstruct the contrast by minimizing a cost functional defined as the sum of the data error and the state error. In this procedure, the total fields in the inversion domain are computed only once, while the quality and the accuracy of the obtained reconstructions are maintained. The novel method is applied to ground-penetrating radar imaging and through-the-wall imaging, in which the validity and the efficiency of the method are demonstrated.

Modeling of Source Parameters and Moment Tensors of Local Earthquakes Occurring in the Eastern Indian Shield

ABSTRACT Earthquake source parameters and crustal Q are being estimated simultaneously through the inversion of S-wave displacement spectra from three-component recordings of ten local cratonic intraplate earthquakes from 3-6 broadband stations in the eastern Indian shield, wherein, an iterative Levenberg-Marquardt inversion technique is used. The estimated seismic moment (Mo) and source radii (r) vary from 7.4 x 1012 to 7.1 x 1014 N-m and 144.2 to 211.3 m, respectively, while estimated stress drops (Δσ) and multiplicative factor (Emo) values range from 0.11 to 4.13 MPa and 1.33 to 2.16, respectively. The corner frequencies range from 6.23 to 8.62 Hz while moment magnitudes vary from 2.44 to 3.57. The radiated seismic energy and apparent stresses range from 8.3 x 106 to 2.0 x 1010 Joules and 0.06 to 0.94 MPa, respectively, wherein the estimated corner frequencies and seismic moment satisfy the relation Mo ∞ fc−(3+ε) for ε = 12.7. Thus, the source scaling of these events clearly deviates from the self-similarity i.e. f−3. Estimated Zuniga parameters reveal that all selected events satisfy the partial stress drop model, which is in good agreement with the global observations. Our estimated crustal S-wave quality factors vary from 1091 to 4926 with an average of 3006, suggesting a less heterogeneous crustal structure underlying the study region. We also perform moment tensor inversion of five selected local events using ISOLA software, which reveals that the dominant deformation mode for the eastern Indian shield is left-lateral strike slip motion with minor normal dip-slip component on an almost vertical plane. This observation suggests that neotectonic vertical movements might have played a key role in generating these earthquakes. Our modeling also depicts that the seismically mildly active Singhbhum shear zone and Eastern Ghats mobile belt are characterized by the left-lateral strike motion while two events in the Chotanagpur half graben belt suggest a normal dip-slip motion along a south dipping plane. A north-south orientation of P-axis is found to be dominant in the area, which is consistent with the prevailing north–south compression over the Indian plate.

Global adjoint tomography: first-generation model

We present the first-generation global tomographic model constructed based on adjoint tomography, an iterative full-waveform inversion technique. Synthetic seismograms were calculated using GPU-accelerated spectral-element simulations of global seismic wave propagation, accommodating effects due to 3D anelastic crust & mantle structure, topography & bathymetry, the ocean load, ellipticity, rotation, and self-gravitation. Frechet derivatives were calculated in 3D anelastic models based on an adjoint-state method. The simulations were performed on the Cray XK7 named ‘Titan’, a computer with 18,688 GPU accelerators housed at Oak Ridge National Laboratory. The transversely isotropic global model is the result of 15 tomographic iterations, which systematically reduced differences between observed and simulated three-component seismograms. Our starting model combined 3D mantle model S362ANI (Kustowski et al. 2008) with 3D crustal model Crust2.0 (Bassin et al. 2000). We simultaneously inverted for structure in the crust and mantle, thereby eliminating the need for widely used ‘crustal corrections’. We used data from 253 earthquakes in the magnitude range 5.8~ ≤ ~Mw~ ≤ ~7.0. For the first 12 iterations, we combined ∼30 s body-wave data with ∼60 s surface-wave data. The shortest period of the surface waves was gradually decreased, and in the last three iterations we combined ∼17 s body waves with ∼45 s surface waves. We started using 180 min-long seismograms after the 12th iteration and assimilated minor- and major-arc body and surface waves. The 15th iteration model features enhancements of well-known slabs, an enhanced image of the Samoa/Tahiti plume, as well as various other plumes and hotspots, such as Caroline, Galapagos, Yellowstone, and Erebus. Furthermore, we see clear improvements in slab resolution along the Hellenic and Japan Arcs, as well as subduction along the East of Scotia Plate, which does not exist in the starting model. Point-spread function tests demonstrate that we are approaching the resolution of continental-scale studies in some areas, for example underneath Yellowstone. This is a consequence of our multi-scale smoothing strategy, in which we define our smoothing operator as a function of the approximate Hessian kernel, thereby smoothing gradients less wherever we have good ray coverage, such as underneath North America.

Atomic force microscopy indentation and inverse analysis for non-linear viscoelastic identification of breast cancer cells

Breast cancer cells (MCF-7 and MCF-10A) are studied through indentation with spherical borosilicate glass particles in atomic force microscopy (AFM) contact mode in fluid. Their mechanical properties are obtained by analyzing the recorded reaction force–time response. The analysis is based on comparing experimental data with predictions from finite element (FE) simulation. Here, FE modeling is employed to simulate the AFM indentation experiment which is neither a displacement nor a force controlled test. This approach is expected to overcome many underlying problems of the widely used models such as Hertz contact model due to its capability to capture the contact behaviors between the spherical indentor and the cell, account for cell geometry, and incorporate with large strain theory. In this work, a non-linear viscoelastic (NLV) model in which the viscoelastic part is described by Prony series terms is used for the constitutive model of the cells. The time-dependent material parameters are extracted through an inverse analysis with the use of a surrogate model based on a Kriging estimator. The purpose is to automatically extract the NLV properties of the cells with a more efficient process compared to the iterative inverse technique that has been mostly applied in the literature. The method also allows the use of FE modeling in the analysis of a large amount of experimental data. The NLV parameters are compared between MCF-7 and MCF-10A and MCF-10A treated and untreated with the drug Cytochalasin D to examine the possibility of using relaxation properties as biomarkers for distinguishing these types of breast cancer cells. The comparisons indicate that malignant cells (MCF-7) are softer and exhibit more relaxation than benign cells (MCF-10A). Disrupting the cytoskeleton using the drug Cytochalasin D also results in a larger amount of relaxation in the cell’s response. In addition, relaxation properties indicate larger differences as compared to the elastic moduli like instantaneous shear modulus. These results may be useful for disease diagnosing purposes.

A comparison of direct and iterative finite element inversion techniques in dynamic elastography

As part of tissue elasticity imaging or elastography, an inverse problem needs to be solved to find the elasticity distribution from the measured displacements. The finite element method (FEM) is a common method for solving the inverse problem in dynamic elastography. This problem has been solved with both direct and iterative FEM schemes. Each of these methods has its own advantages and disadvantages which are examined in this paper. Choosing the data resolution and the excitation frequency are critical for achieving the best estimation of the tissue elasticity in FEM methods. In this paper we investigate the performance of both direct and iterative FEMs for different ranges of excitation frequency. A new form of iterative method is suggested here which requires a lower mesh density compared to the original form. Also two forms of the direct method are compared in this paper: one using the exact fit for derivatives calculation and the other using the least squares fit. We also perform a study on the spatial resolution of these methods using simulations. The comparison is also validated using a phantom experiment. The results suggest that the direct method with least squares fit is more robust to noise compared to other methods but has slightly lower resolution results. For example, for the homogenous region with 20 dB noise added to the data, the RMS error for the direct method with least squares fit is approximately half of the iterative method. It was observed that the ratio of voxel size to the wavelength should be within a specific range for the results to be reliable. For example for the direct method with least squares fit, for the case of 20 dB noise level, this ratio should be between 0.1 to 0.2. On balance, considering the much higher computational cost of the iterative method, the dependency of the iterative method on the initial guess, and the greater robustness of the direct method to noise, we suggest using the direct method with least squares fit for linear elasticity cases.

Determination of material parameters of isotropic and anisotropic hyper-elastic materials using boundary measured data

Identification of mechanical properties of isotropic and anisotropic materials that demonstrate non-linear elastic behavior, such as rubbers and soft tissues of human body, is critical for many industrial and medical purposes. In this paper, a method is presented to obtain the mechanical constants of Mooney-Rivlin and Holzapfel hyper-elastic material models which are employed to describe the behavior of isotropic and anisotropic hyper-elastic materials, respectively. By using boundary measured data from a sample with non-standard geometry, and by using an iterative inverse analysis technique, the material constants are obtained. The method uses the results of different experiments simultaneously to obtain the material parameters more accurately. The effectiveness of the proposed method is demonstrated through three examples. In the two first examples, the simulated measured data are used, while in the third example, the experimental data obtained from a polyvinyl alcohol sample are used.

CHEBYSHEV FILTER APPLIED TO AN INVERSION TECHNIQUE FOR BREAST TUMOUR DETECTION

Microwave imaging has been extensively studied in the past several years as a new technique for early stage breast cancer detection. The rationale of microwave imaging for breast tumour detection is significant contrast in the dielectric properties of normal tissue and malignant tumours. However, in practice noise present from the environments during screening/examination degrades the quality of the image. Inaccurate reconstructed image caused false/misleading interpretation of the image which leads to inappropriate diagnose or treatment to the patient. In the simulation works, noise is added to imitate the actual environment scenario. The two-dimensional (2D) object that identical to breast model is developed using numerical simulation to imitate the breast model. A filter is integrated with an iterative inversion technique for breast tumour detection to eliminate the noise. To assess the effectiveness of this approach, we consider the reconstruction of the electrical parameter profiles of 2D objects from measurements of the transient total electromagnetic field data contaminated with noise. Additive white Gaussian noise is utilized to mimic the effect of random processes that occur in the nature. This paper presents the filter settings and characteristics that affect the reconstruction of the image in order to obtain the most reliable and closer to the actual image. Selection of filter settings or design is important in order to achieve desired signal, most accurate image and provide reliable information of the object. Chebyshev low pass filter is applied in the Forward-Backward Time-Stepping (FBTS) algorithm to filter the noisy data and to improve the quality of reconstructed image.

Visible light tomography of MHD eigenmodes in the H-1NF stellarator using magnetic coordinates

A tomographic reconstruction technique is described for the inversion of a set of limited-angle high-resolution 2D visible light emission projections of global MHD eigenmodes in the H-1NF heliac. The technique is well suited to limited viewing access in toroidal devices and the strong shaping of optimized stellarator/heliotron configurations. Fluctuations are represented as a finite sum of Fourier modes characterized by toroidal and poloidal mode numbers having fixed amplitude and phase in a set of nested flux volumes in Boozer coordinates (Boozer 1980 Phys. Fluids 23 904–8). Iterative tomographic inversion techniques and standard linear least-squares methods are used to solve for the complex amplitudes. The method is applied to synchronous camera images of singly charged carbon impurity ion emission at 514 nm obtained at three discrete poloidal viewing orientations (Haskey et al 2014 Rev. Sci. Instrum. 85 033505). The 2D amplitude and phase projections provide high quality reconstructions of the radial structure of the fluctuations that are compact in Boozer space and allow clear determination of the poloidal mode number as well as some degree of toroidal mode number differentiation.

A practical, robust approach to high resolution ultrasonic breast tomography

Breast ultrasound tomography is considered a potentially safer, more reliable, and more sensitive alternative to the widely used mammography for breast cancer diagnosis and screening. Vital to achieving this potential is the development of imaging algorithms to unravel the complex anatomy of the breast. Bent Ray Tomography (BRT) is the most prominent algorithm, producing sound-speed maps, but the underlying approximation of ray theory means that the algorithm is unsuitable for structures where significant diffraction is present. Accordingly, the maximum resolution of the BRT algorithm is not sufficient to image the details of the breast on the scale of a few millimeters. Therefore, iterative full-wave inversion techniques are often applied to improve the resolution of the BRT image, but they are typically slow or fail because of the uncertainties such as 3D effects, noise, or transducer characteristics. Presented here is a solution where the BRT algorithm is combined with diffraction tomography (DT), avoiding iterations yet producing a high resolution sound-speed image. It is demonstrated with both numerical and experimental data how this can successfully—and robustly—deal with a range of phenomena present in breast ultrasound experiments such as attenuation, density, 3D effects, and transducer directivity while maintaining a high resolution.