The utilization of magnetic resonance (MR) imaging to guide near-infrared spectral tomography (NIRST) shows significant potential for improving the specificity and sensitivity of breast cancer diagnosis. However, the efficiency and accuracy of NIRST image reconstruction have been limited by the complexities of light propagation modeling and MRI image segmentation. To address these challenges, we developed and evaluated a deep learning-based approach for MR-guided 3D NIRST image reconstruction (DL-MRg-NIRST). Using a network trained on synthetic data, the DL-MRg-NIRST system reconstructed images from data acquired during 38 clinical imaging exams of patients with breast abnormalities. Statistical analysis of the results demonstrated a sensitivity of 87.5%, a specificity of 92.9%, and a diagnostic accuracy of 89.5% in distinguishing pathologically defined benign from malignant lesions. Additionally, the combined use of MRI and DL-MRg-NIRST diagnoses achieved an area under the receiver operating characteristic (ROC) curve of 0.98. Remarkably, the DL-MRg-NIRST image reconstruction process required only 1.4 seconds, significantly faster than state-of-the-art MR-guided NIRST methods.

Near-infrared spectral tomography (NIRST) is a non-invasive imaging technique that provides functional information about biological tissues. Due to diffuse light propagation in tissue and limited boundary measurements, NIRST image reconstruction presents an ill-posed and ill-conditioned computational problem that is difficult to solve. To address this challenge, we developed a reconstruction algorithm (Model-CNN) that integrates a diffusion equation model with a convolutional neural network (CNN). The CNN learns a regularization prior to restrict solutions to the space of desirable chromophore concentration images. Efficacy of Model-CNN was evaluated by training on numerical simulation data, and then applying the network to physical phantom and clinical patient NIRST data. Results demonstrated the superiority of Model-CNN over the conventional Tikhonov regularization approach and a deep learning algorithm (FC-CNN) in terms of absolute bias error (ABE) and peak signal-to-noise ratio (PSNR). Specifically, in comparison to Tikhonov regularization, Model-CNN reduced average ABE by 55% for total hemoglobin (HbT) and 70% water (H $_{\mathbf {{2}}}$ O) concentration, while improved PSNR by an average of 5.3 dB both for HbT and H $_{\mathbf {{2}}}$ O images. Meanwhile, image processing time was reduced by 82%, relative to the Tikhonov regularization. As compared to FC-CNN, the Model-CNN achieved a 91% reduction in ABE for HbT and 75% for H $_{\mathbf {{2}}}$ O images, with increases in PSNR by 7.3 dB and 4.7 dB, respectively. Notably, this Model-CNN approach was not trained on patient data; but instead, was trained on simulated phantom data with simpler geometrical shapes and optical source-detector configurations; yet, achieved superior image recovery when faced with real-world data.

Is it possible to find deterministic relationships between optical measurements and pathophysiology in an unsupervised manner and based on data alone? Optical property quantification is a rapidly growing biomedical imaging technique for characterizing biological tissues that shows promise in a range of clinical applications, such as intraoperative breast-conserving surgery margin assessment. However, translating tissue optical properties to clinical pathology information is still a cumbersome problem due to, amongst other things, inter- and intrapatient variability, calibration, and ultimately the nonlinear behavior of light in turbid media. These challenges limit the ability of standard statistical methods to generate a simple model of pathology, requiring more advanced algorithms. We present a data-driven, nonlinear model of breast cancer pathology for real-time margin assessment of resected samples using optical properties derived from spatial frequency domain imaging data. A series of deep neural network models are employed to obtain sets of latent embeddings that relate optical data signatures to the underlying tissue pathology in a tractable manner. These self-explanatory models can translate absorption and scattering properties measured from pathology, while also being able to synthesize new data. The method was tested on a total of 70 resected breast tissue samples containing 137 regions of interest, achieving rapid optical property modeling with errors only limited by current semi-empirical models, allowing for mass sample synthesis and providing a systematic understanding of dataset properties, paving the way for deep automated margin assessment algorithms using structured light imaging or, in principle, any other optical imaging technique seeking modeling. Code is available.

Magnetic resonance elastography (MRE) has been developed to noninvasively reconstruct mechanical properties for tissue and tissue-like materials over a frequency range of 10 ~200 Hz. In this work, low frequency (1~1.5 Hz) MRE activations were employed to estimate mechanical property distributions of simulated data and experimental phantoms. Nonlinear inversion (NLI) MRE algorithms based on viscoelastic and poroelastic material models were used to solve the inverse problems and recover images of the shear modulus and hydraulic conductivity. Data from a simulated phantom containing an inclusion with property contrast was carried out to study the feasibility of our low frequency actuated approach. To verify the stability of NLI algorithms for low frequency actuation, different levels of synthetic noise were added to the displacement data. Spatial distributions and property values were recovered well for noise level less than 5%. For the presented experimental phantom reconstructions with regularizations, the computed storage moduli from viscoelastic and poroelastic MRE gave similar results. Contrast was detected between inclusions and background in recovered hydraulic conductivity images. Results and findings confirm the feasibility of future in vivo neuroimaging examinations using natural cerebrovascular pulsations at cardiac frequencies, which can eliminate specialized equipment for high frequency actuation.

An approach using direct regularization from co-registered dynamic contrast enhanced magnetic reson- ance images was used to reconstruct near-infrared spectral tomography patient images, which does not need image segmentation. 20 patients with mammography/ultrasound confirmed breast abnormalities were involved in this paper, and the resulting images indicated that tumor total hemoglobin concentration contrast differentiated malignant from benign cases (p-value = 0.021). The approach prod- uced reconstructed images, which significantly reduced surface artifacts near the source-detector locations (p-value = 4.16e-6).

We describe an efficient gradient computation for solving inverse problems arising in magnetic resonance elastography (MRE). The algorithm can be considered as a generalized 'adjoint method' based on a Lagrangian formulation. One requirement for the classic adjoint method is assurance of the self-adjoint property of the stiffness matrix in the elasticity problem. In this paper, we show this property is no longer a necessary condition in our algorithm, but the computational performance can be as efficient as the classic method, which involves only two forward solutions and is independent of the number of parameters to be estimated. The algorithm is developed and implemented in material property reconstructions using poroelastic and viscoelastic modeling. Various gradient- and Hessian-based optimization techniques have been tested on simulation, phantom and in vivo brain data. The numerical results show the feasibility and the efficiency of the proposed scheme for gradient calculation.

The chaotic vascular network surrounding malignant tumors leads to pulsatile blood flow patterns that differ from those in benign regions of the breast. This study aimed to determine if high-speed electrical impedance tomography (EIT) is able to detect conductivity changes associated with cyclic blood-volume changes and to gauge the potential of using these signatures to differentiate malignant from benign regions within the breast. EIT imaging of pulsating latex membranes submerged in saline baths provided initial validation of its use for tracking temporally varying conductivities. Nineteen women (10 with cancer, nine without) were imaged with EIT over the course of several heartbeats in synchrony with pulse-oximetry acquisition. Eight parameters ( rs, ϕ(rt,max), rt,max, Plow:full, Phigh:full, Plow:high) relating the conductivity images and pulse-oximeter signatures were extracted and used as a means of comparing malignant and benign regions of the breast. Significant differences between malignant and benign regions of interest were noted in seven of the eight parameters. The maximum correlation between conductivity and pulse-oximeter signals, rt,max , was observed to be the optimal discriminating parameter with a receiver operating characteristic area under the curve of 0.8 and a specificity of 81% at a sensitivity of 77%. Assessing the dynamic conductivity of breast may provide additional clinical utility to that of standard imaging modalities, but further investigation is necessary to better understand the biophysical mechanisms leading to the observed conductivity changes.

Poroelastic magnetic resonance elastography is an imaging technique that could recover mechanical and hydrodynamical material properties of in vivo tissue. To date, mechanical properties have been estimated while hydrodynamical parameters have been assumed homogeneous with literature-based values. Estimating spatially-varying hydraulic conductivity would likely improve model accuracy and provide new image information related to a tissue's interstitial fluid compartment. A poroelastic model was reformulated to recover hydraulic conductivity with more appropriate fluid-flow boundary conditions. Simulated and physical experiments were conducted to evaluate the accuracy and stability of the inversion algorithm. Simulations were accurate (property errors were < 2%) even in the presence of Gaussian measurement noise up to 3%. The reformulated model significantly decreased variation in the shear modulus estimate (p << 0.001) and eliminated the homogeneity assumption and the need to assign hydraulic conductivity values from literature. Material property contrast was recovered experimentally in three different tofu phantoms and the accuracy was improved through soft-prior regularization. A frequency-dependence in hydraulic conductivity contrast was observed suggesting that fluid-solid interactions may be more prominent at low frequency. In vivo recovery of both structural and hydrodynamical characteristics of tissue could improve detection and diagnosis of neurological disorders such as hydrocephalus and brain tumors.

Tissue displacements required for mechanical property reconstruction in magnetic resonance elastography (MRE) are acquired in a magnetic resonance imaging (MRI) scanner, therefore, anatomical information is available from other imaging sequences. Despite its availability, few attempts to incorporate prior spatial information in the MRE reconstruction process have been reported. This paper implements and evaluates soft prior regularization (SPR), through which homogeneity in predefined spatial regions is enforced by a penalty term in a nonlinear inversion strategy. Phantom experiments and simulations show that when predefined regions are spatially accurate, recovered property values are stable for SPR weighting factors spanning several orders of magnitude, whereas inaccurate segmentation results in bias in the reconstructed properties that can be mitigated through proper choice of regularization weighting. The method was evaluated in vivo by estimating viscoelastic mechanical properties of frontal lobe gray and white matter for five repeated scans of a healthy volunteer. Segmentations of each tissue type were generated using automated software, and statistically significant differences between frontal lobe gray and white matter were found for both the storage modulus and loss modulus . Provided homogeneous property assumptions are reasonable, SPR produces accurate quantitative property estimates for tissue structures which are finer than the resolution currently achievable with fully distributed MRE.

Microwave breast imaging (using electromagnetic waves of frequencies around 1 GHz) has mostly remained at the research level for the past decade, gaining little clinical acceptance. The major hurdles limiting patient use are both at the hardware level (challenges in collecting accurate and noncorrupted data) and software level (often plagued by unrealistic reconstruction times in the tens of hours). In this paper we report improvements that address both issues. First, the hardware is able to measure signals down to levels compatible with sub-centimeter image resolution while keeping an exam time under 2 min. Second, the software overcomes the enormous time burden and produces similarly accurate images in less than 20 min. The combination of the new hardware and software allows us to produce and report here the first clinical 3-D microwave tomographic images of the breast. Two clinical examples are selected out of 400+ exams conducted at the Dartmouth Hitchcock Medical Center (Lebanon, NH). The first example demonstrates the potential usefulness of our system for breast cancer screening while the second example focuses on therapy monitoring.

Magnetic resonance (MR) guided optical breast imaging is a promising modality to improve the specificity of breast imaging, because it provides high-resolution quantitative maps of total hemoglobin, oxygen saturation, water content, and optical scattering. These properties have been shown to distinguish malignant from benign lesions. However, the optical detection hardware required for deep tissue imaging has poor spectral sensitivity which limits accurate water quantification; this reduces the accuracy of hemoglobin quantification. We present a methodology to improve optical quantification by utilizing the ability of Dixon MR imaging to quantitatively estimate water and fat; this technique effectively reduces optical crosstalk between water and oxyhemoglobin. The techniques described in this paper reduce hemoglobin quantification error by as much as 38%, as shown in a numerical phantom, and an experimental phantom. Error is reduced by as much 20% when imperfect MR water quantification is given. These techniques may also increase contrast between diseased and normal tissue, as shown in breast tissue in vivo. It is also shown that using these techniques may permit fewer wavelengths to be used with similar quantitative accuracy, enabling higher temporal resolution. In addition, it is shown that these techniques can improve the ability of MRI to quantify water in the presence of bias in the Dixon water/fat separation.

Magnetic resonance poroelastography (MRPE) is introduced as an alternative to single-phase model-based elastographic reconstruction methods. A 3-D finite element poroelastic inversion algorithm was developed to recover the mechanical properties of fluid-saturated tissues. The performance of this algorithm was assessed through a variety of numerical experiments, using synthetic data to probe its stability and sensitivity to the relevant model parameters. Preliminary results suggest the algorithm is robust in the presence of noise and capable of producing accurate assessments of the underlying mechanical properties in simulated phantoms. Furthermore, a 3-D time-harmonic motion field was recorded for a poroelastic phantom containing a single cylindrical inclusion and used to assess the feasibility of MRPE image reconstruction from experimental data. The elastograms obtained from the proposed poroelastic algorithm demonstrate significant improvement over linearly elastic MRE images generated using the same data. In addition, MRPE offers the opportunity to estimate the time-harmonic pressure field resulting from tissue excitation, highlighting the potential for its application in the diagnosis and monitoring of disease processes associated with changes in interstitial pressure.

In practice, most signal processing strategies for discrimination of buried objects are clutter limited. This applies even to discrimination of shallow sizable metallic objects, such as unexploded ordnance (UXO), which are to be found predominantly in the top meter of soil. The environment typically features widespread metallic clutter from detonated ordnance or other sources. Such fragments can be numerous and are often shallower than the objects of interest. Currently, the preeminent remote sensing mode for buried UXO is ultrawideband electromagnetic induction (EMI), operating over part or all of the band from some tens of hertz up to perhaps hundreds of kilohertz. Particularly because EMI fields fall off sharply with range, signals from shallow clutter may be relatively strong and can easily obscure essential scatterer signatures. To treat this, a rational theory of EMI scattering from widespread metallic clutter is formulated and tested. For dense, well-distributed clutter, analytical rules are derived for dependence of signal strength on sensor elevation, under various fundamental excitation types. For more erratic, sparse clutter distributions, signal statistics from Monte Carlo simulations show patterns like those from the analytical rules. The dependence of clutter signal magnitude on antenna elevation is determined for both thin surface layers and for volume layers of widespread small items, and for both dense and sparse clutter distributions. These are contrasted with the patterns expected from single, larger, discrete objects of interest, and the contrast is exploited in discrimination exercises for the screening problem. For sparse clutter distributions, results from inversion processing formulations that account for the patterns of clutter statistics are compared to simple least squares treatments.

Spatial unwrapping of the phase component of time varying electromagnetic fields has important implications in a range of disciplines including synthetic aperture radar (SAR) interferometry, MRI, optical confocal microscopy, and microwave tomography. This paper presents a fundamental framework based on the phase unwrapping integral, especially in the complex case where phase singularities are enclosed within the closed path integral. With respect to the phase unwrapping required when utilized in Gauss-Newton iterative microwave image reconstruction, the concept of dynamic phase unwrapping is introduced where the singularity location varies as a function of the iteratively modified property distributions. Strategies for dynamic phase unwrapping in the microwave problem were developed and successfully tested in simulations and clinical experiments utilizing large, high contrast targets to validate the approach.

Traditionally, image reconstruction in electrical impedance tomography (EIT) has been based on Laplace's equation. However, at high frequencies the coupling between electric and magnetic fields requires solution of the full Maxwell equations. In this paper, a formulation is presented in terms of the Maxwell equations expressed in scalar and vector potentials. The approach leads to boundary conditions that naturally align with the quantities measured by EIT instrumentation. A two-dimensional implementation for image reconstruction from EIT data is realized. The effect of frequency on the field distribution is illustrated using the high-frequency model and is compared with Laplace solutions. Numerical simulations and experimental results are also presented to illustrate image reconstruction over a range of frequencies using the new implementation. The results show that scalar/vector potential reconstruction produces images which are essentially indistinguishable from a Laplace algorithm for frequencies below 1 MHz but superior at frequencies reaching 10 MHz.

In this paper, the coupling and close-proximity effects arising between highly conducting and permeable metallic objects are exposed and analyzed, for the electromagnetic induction (EMI) frequency range (from tens of hertz up to several hundreds of kilohertz). To understand the physics of the interaction phenomena, a numerical technique is applied, consisting of the full method of auxiliary sources (MAS) at low frequencies and a combination of the MAS with thin-skin approximation (TSA) at high frequencies. Both numerical MAS-MAS/TSA and experimental studies have shown that the scattered field from a heterogeneous target generated as a simple superposition of independent responses from each part can be very different from the field determined from whole object with full internal interaction. A new numerical technique for fast and accurate representation of EMI responses for heterogeneous objects is pursued here, applicable to any three-dimensional heterogeneous object placed in an arbitrary time-varying EMI field. First, any primary magnetic field input is decomposed into the spheroidal modes over a fictitious surface surrounding the object. Then, for each input spheroidal mode, the full EMI problem including all interaction is solved using the MAS-MAS/TSA technique, and each modal response is reproduced using a compact reduced set of sources (RSS). Finally, the total response from the given target for any other excitation can be synthesized simply by calculating that primary field's constituent spheroidal modes and combining their stored responses. Several numerical examples are designed to show how an object's electromagnetic parameters, geometry, distance between objects, antenna positions, and orientations relative to the object affect the coupling. Comparisons between numerical and measured data for a machined composite object and for an actual unexploded ordnance demonstrate the superior accuracy and applicability of the MAS-MAS/TSA RSS model over simple dipole approximations, for certain classes of heterogeneous objects.

Current idealized forward models for electromagnetic induction (EMI) response can be defeated by the characteristic material and geometrical heterogeneity of realistic unexploded ordnance (UXO). A new, physically complete modeling system was developed that includes all effects of these heterogeneities and their interactions within the object, in both near and far fields. The model is fast enough for implementation in inversion processing algorithms. A method is demonstrated for extracting the model parameters by straightforward processing of data from a defined measurement protocol. Depending on the EMI sensor used for measurements, the process of inferring model parameters is more or less ill-posed. More complete data can alleviate the problem. For a given set of data, special numerical treatment is introduced to take the best advantage of the data and obtain reliable model parameters. The resulting fast model is implemented in a pattern matching treatment of measurements by which signals from a UXO are identified within a series of those from unknown targets. Preliminary results show that this fast model is promising for use in processing of this kind. The inherent difficulties of target identification are examined, and solutions for resolving these difficulties are discussed.

A reconstruction process featuring full parameterization of the three dimensional, time-harmonic equations of linear elasticity is developed and reconstructed property images are presented from simulation-based investigation. While interesting in its own right through the potential for increased adaptability of these reconstructive elastic imaging techniques, this study also presents a set of analysis tools used to study the poor convergence behavior found in the case of tissue like conditions (i.e. nearly incompressible materials). The choice of elastic properties for imaging in elastography research remains an open question at this point; the use of the stability and sensitivity-based analytical methods described here will help to predict and understand the value and reliability of different parameterizations of elasticity imaging. Additionally, though results indicate significant work needs to be done to achieve effective multiparameter reconstructive imaging, the methods detailed here offer the promise of increased flexibility and sophistication in elastographic imaging techniques.

Brain deformation models have proven to be a powerful tool in compensating for soft tissue deformation during image-guided neurosurgery. The accuracy of these models can be improved by incorporating intraoperative measurements of brain motion. We have designed and implemented a passive intraoperative stereo vision system capable of estimating the three-dimensional shape of the surgical scene in near real-time. This intraoperative shape is compared with the cortical surface in the co-registered preoperative magnetic resonance (MR) volume for the estimation of the cortical motion resulting from the open cranial surgery. The estimated cortical motion is then used to guide a full brain model, which updates a preoperative MR volume. We have found that the stereo vision system is accurate to within approximately 1 mm. Based on data from two representative clinical cases, we show that stereopsis guidance improves the accuracy of brain shift compensation both at and below the cortical surface.

In this paper, a new discrimination procedure is presented to enhance classification of buried metallic object. This algorithm is based on a standardized source set (SSS) approximation, applicable for an arbitrary highly conducting and permeable metallic objects placed in a low frequency (from 10's of Hertz up to several 100's of kHz) time varying electromagnetic field. The method treats accurately all near field, heterogeneity, and internal interaction effects. In the SSS approach, any input primary magnetic field is represented as a sum of magnetic fields produced by a set of sources distributed over on an auxiliary surface outside the fictitious surface. The object's response corresponding to unit amplitudes of any of these input field sources is likewise quantified in terms of a set of (responding) sources, which can be derived from measured data. Thereafter, the object's response to any excitation can be expressed just by different superpositions of these standardized inputs. The spatial distribution and frequency dependence features of responding equivalent sources are analyzed and used for target discrimination. The numerical results are given for an actual unexploded ordinance (UXO)

Operating as low as tens of hertz and as high as hundreds of kilohertz, new broadband electromagnetic induction (EMI) sensors have shown promise for classification of unseen buried metallic objects. The three-dimensional (3-D) and bodies-of-revolution (BOR) numerical studies reported here are designed to explain key scattering sensitivities that may either be useful in or may limit object classification capability. The target is excited either by a spatially uniform oscillating primary magnetic field or by the oscillating field from a loop antenna. The problem is formulated in terms of Poison's equation for scalar potential outside the object, where conductivity and electric field values are low and consequent conduction currents are generally negligible. The Helmholtz equation for vector potential applies inside the highly conducting and permeable object. In both regions, the electromagnetic phenomena of interest are magneto-quasi-static (MQS). The simulation algorithm uses the method of auxiliary sources (MAS), with auxiliary magnetic charges and auxiliary magnetic current elements distributed on auxiliary surfaces. These surfaces generally conform to but do not coincide with physical surfaces, providing extraordinarily efficient and accurate 3-D solutions. Comparisons to available analytical solutions and experimental data validate the solutions. The simulations and data illuminate broadband MQS scattering phenomenology for both magnetic and nonmagnetic metallic objects. Distinctive sensitivities are shown and signature effects analyzed relative to the scatterer's shape and aspect ratio, orientation, sharp points and edges, finite wall thickness in hollow bodies, and compound structure in which a geometrically complex body consists of a number of distinct sections, e.g., fins.

Operating in the magnetoquasistatic regime (a few hertz to perhaps a few 100 kHz), electromagnetic induction (EMI) sensing has recently emerged as one of the most promising avenues for discrimination of subsurface metallic objects, e.g., unexploded ordnance. The technique of thin-skin approximation (TSA) was devised to deal with numerical problems caused by the rapid decay of fields beneath the scatterer's surface. The rather nonintuitively broad applicability and specific error patterns of the TSA formulation are explained here by theoretical analysis based on analytical solutions and approximate Monte Carlo simulation. In the limiting case of infinitesimal skin depth (EMI perfect reflection), the scatterer aspect ratio (AR) is inferred without regard to metal type. Alternatively, the AR of some homogeneous magnetic objects is inferred from the pattern of transverse to axial response ratio over the entire EMI ultrawideband. Use of the method in inversions for electromagnetic parameters reveals fundamental nonuniqueness problems and shows their basis, which is not dependent on the method of forward solution.

This paper is built upon the assumption that in electrical impedance tomography, vectors of voltages and currents are linearly dependent through a resistance matrix. This linear relationship was confirmed experimentally and may be derived analytically under certain assumptions regarding electrodes (Isaacson, 1991). Given measurement data consisting of voltages and currents, we treat this relationship as a linear statistical model. Thus, our goal is not to reconstruct the image but directly estimate its electromagnetic properties reflected in the resistance and/or conductance matrix using electrical impedance tomography (EIT) measurements of voltages and currents on the periphery of the body. Since no inverse problem is involved the algorithm for estimation merely reduces to one matrix inversion. We estimate the impedance resistance matrix using well established statistical inference techniques for linear regression models. We provide a comprehensive treatment for a two-dimensional homogeneous body of a circular shape, by which many concepts of electrical impedance tomography, such as width of electrodes, the difference between voltage-current and current-voltage systems are illustrated. Our theory may be applied to various tests including EIT hardware calibration and whether the medium is homogeneous. These tests are illustrated on phantom agar data.

Magnetic resonance elastography can be limited by the computationally intensive nonlinear inversion schemes that are sometimes employed to estimate shear modulus from externally induced internal tissue displacements. Consequently, we have developed a parallelized partial volume reconstruction approach to overcome this limitation. In this paper, we report results from experiments conducted on breast phantoms and human volunteers to validate the proposed technique. More specifically, we demonstrate that computational cost is linearly related to the number of subzones used during image recovery and that both subzone parallelization and partial volume domain reduction decrease execution time accordingly. Importantly, elastograms computed based on the parallelized partial volume technique are not degraded in terms of either image quality or accuracy relative to their full volume counterparts provided that the estimation domain is sufficiently large to negate the effects of boundary conditions. The clinical results presented in this paper are clearly preliminary; however, the parallelized partial volume reconstruction approach performs sufficiently well to warrant more in-depth clinical evaluation.

An efficient Gauss-Newton iterative imaging technique utilizing a three-dimensional (3-D) field solution coupled to a two-dimensional (2-D) parameter estimation scheme (3-D/2-D) is presented for microwave tomographic imaging in medical applications. While electromagnetic wave propagation is described fully by a 3-D vector field, a 3-D scalar model has been applied to improve the efficiency of the iterative reconstruction process with apparently limited reduction in accuracy. In addition, the image recovery has been restricted to 2-D but is generalizable to three dimensions. Image artifacts related primarily to 3-D effects are reduced when compared with results from an entirely two-dimensional inversion (2-D/2-D). Important advances in terms of improving algorithmic efficiency include use of a block solver for computing the field solutions and application of the dual mesh scheme and adjoint approach for Jacobian construction. Methods which enhance the image quality such as the log-magnitude/unwrapped phase minimization were also applied. Results obtained from synthetic measurement data show that the new 3-D/2-D algorithm consistently outperforms its 2-D/2-D counterpart in terms of reducing the effective imaging slice thickness in both permittivity and conductivity images over a range of inclusion sizes and background medium contrasts.

Cleanup of subsurface metallic objects such as unexploded ordnance (UXO) constitutes an urgent problem worldwide. The heart of the problem is discrimination, as opposed to detection. Ultra-wideband electromagnetic induction sensors (UWB EMI), operating from a few Hz up to 100s of kHz, have shown considerable promise in subsurface discrimination of metallic objects. Unfortunately, a great many objects, including widespread clutter items, produce very broad, smooth EMI signal patterns, over a number of decades of frequency. Shape identification is complicated by the sensitivity of EMI fields to metal type. UWB ground penetrating radar (GPR) has also shown definite discrimination capability for characterizing subsurface metallic targets. Uninfluenced by metal type, GPR is capable of registering complex natural resonances from which target length can be estimated. Further, examination of the spatial patterns of GPR signals can indicate the (X,Y,Z) locations of targets, even of multiple targets present simultaneously in the incident beam. In this paper we consider potential collaborative roles of UWB GPR and UWB EMI for discrimination of multiple subsurface metallic objects. Rigorous 3-D FDTD models demonstrate GPR's ability to estimate target positions, orientations, and length even when reflections overlap. These data can then be used to constrain inversion of UWB EMI patterns. Processing of EMI measurements based on prior estimates of object location and orientation successfully extracts distinct frequency response signatures for two very closely spaced objects.

Discrimination of buried unexploded ordinance (UXO) from innocuous buried items remains a challenging, top priority problem for the electromagnetic induction (EMI) sensing community. In general, classification is an inverse problem, requiring very fast and accurate representation of the target response. To address this critical issue, this paper presents a very fast, rigorous way to compute EMI scattering from a realistically complex, composite target. Full interaction between all parts of the object are included in the calculations. The method is based on a hybrid of the full method of auxiliary source (MAS) and the MAS-thin skin depth approximation formulation (MAS-TSA), together with new modal decomposition and reduced source set techniques. For general excitation, a primary field is decomposed into the fundamental spheroidal modes on a fictitious spheroid surrounding a real target. Finally the total response from the target is reproduced using only a few auxiliary magnetic charges. A least square minimization is used for discrimination an unseen object's orientation and position. Numerical results are given and compared with experimental data.

Detection and identification of buried unexploded ordinance (UXO) is an emerging problem worldwide. Recent ultra wideband (UWB) field tests between 10s of MHz and 100s of MHz have demonstrated that certain of the target's dimensions can be estimated from analysis of complex natural resonances in the scattered signal. However, the problem becomes much more complicated at highly contaminated UXO sites where clutter items, from which subsurface UXO must be distinguished, appear simultaneously within the field of view of the sensor. This often occurs in realistic field conditions, where GPR discrimination capabilities are typically limited by ground clutter, coupling between antenna and ground, and limited view of the target due to innocuous items. Under extreme shielding by clutter, the incident field cannot excite strong currents on the target and in turn the scattered field from the object cannot easily be separated from the responses of the clutter. To investigate this, we pursue simulations here designed to test subsurface side-looking EM field scattering from multiple buried objects placed in a uniform ground. The numerical calculation is performed using the finite difference time domain (FDTD) method in conjunction with generalized perfectly matched layer GPML. The results are analyzed for a cylinder and plate placed in a uniform ground.

Estimating electric conductivity /spl sigma/ (S/m) and magnetic permeability /spl mu/ (F/m) is of great interest both for industry, mineral exploration, and for geophysical discrimination of buried objects such as unexploded ordnance (UXO). We present here a technique for inferring physical parameters of a metallic object in the EMI frequency range (from tens of Hz to several hundred kHz). Electric conductivity and magnetic permeability are inferred by an inversion algorithm operating on inphase and quadrature received components. The forward model is based on the BIE-TSA formulation, which works well over the majority of the EMI frequency range, especially for magnetic material. The formulation is organized so that most matrices related to object geometry need only be calculated once and the Jacobian matrix can be constructed easily from these matrices. Therefore, both forward solution and Jacobian matrix can be calculated quickly. For material with high magnetic permeability, forward solutions indicate that the scattered field is mostly only sensitive to the ratio of /spl sigma/ and /spl mu/. In this case the inversion algorithm becomes ill conditioned and some kind of regularization is needed. The performance of the inversion algorithm was studied under different kinds of regularization, via both theoretical analysis and numerical experiments. An optimized method for choosing regularization is suggested which may also benefit more general inverse problems.

Brain shift during open cranial surgery presents a challenge for maintaining registration with image-guidance systems. Ultrasound (US) is a convenient intraoperative imaging modality that may be a useful tool in detecting tissue shift and updating preoperative images based on intraoperative measurements of brain deformation. We have quantitatively evaluated the ability of spatially tracked freehand US to detect displacement of implanted markers in a series of three in vivo porcine experiments, where both US and computed tomography (CT) image acquisitions were obtained before and after deforming the brain. Marker displacements ranged from 0.5 to 8.5 mm. Comparisons between CT and US measurements showed a mean target localization error of 1.5 mm, and a mean vector error for displacement of 1.1 mm. Mean error in the magnitude of displacement was 0.6 mm. For one of the animals studied, the US data was used in conjunction with a biomechanical model to nonrigidly re-register a baseline CT to the deformed brain. The mean error between the actual and deformed CT's was found to be on average 1.2 and 1.9 mm at the marker locations depending on the extent of the deformation induced. These findings indicate the potential accuracy in coregistered freehand US displacement tracking in brain tissue and suggest that the resulting information can be used to drive a modeling re-registration strategy to comparable levels of agreement.

Wideband electromagnetic induction (EMI) sensing shows increasing capability and promise for characterizing subsurface metallic objects, such as UXO. While EMI has some advantages over radar, such as superior penetration of moist soil, the field problem is still difficult due to the frequent occurrence of multiple targets in close proximity. The numerical modeling problem, even for a single object, is complicated by the fact that transmitted ("primary") fields typically penetrate the target, but will often only do so slightly. In most of the established numerical treatments, the scale of discretization is dominated either by the dimensions of the thin subsurface layer of electrical activity, or, more or less equivalently, by the range over which a Green's function decays, based on the characteristics of the metal. Resolution at this scale is often computationally prohibitive, particularly for magnetic materials, even though external fields of interest have only mild gradients. We approach the problem using the Thin Skin Depth Approximation (TSA). The TSA assumes an exponential form for the internal normal magnetic field component, as a function of distance inwards from the object surface. Despite the fact that it is designed to treat a state of affairs characteristic of relatively high EMI frequencies, results based on the TSA turn out to be accurate across the entire EMI band when the relative permeability of the scatterer material is high (e.g. as for steel).

The Method of Auxiliary Sources (MAS) is formulated and applied to solution of wide-band electromagnetic induction problems involving highly conducting and possibly permeable metallic objects. Improved remote sensing discrimination of buried unexploded ordnance (UXO) motivates the study. The method uses elementary auxiliary magnetic charges and magnetic current elements to produce the unknown field. Auxiliary sources are located on virtual surfaces that usually conform to but do not coincide with the real surface of the object. Once the source coefficients are determined, the-secondary field can easily be found. The method involves no confrontations with source or Green's function singularities. It is capable of treating penetrable as well as nonpenetrable objects. Because the solution is composed of fields that automatically satisfy the governing equations, by construction, all approximation resides only in the enforcement of boundary conditions at matching (collocation) points. Accuracy in satisfying the boundary conditions can be evaluated explicitly using noncollocation points over the surface. This in turn allows one to identify problem areas on the surface and make intelligent adjustments of the source distributions, to improve solutions at minimal cost. A general 3D formulation is presented, and a version specialized to treat bodies of revolution is applied in the specific test cases discussed.

The problem of numerical modeling of electromagnetic induction (EMI) responses by metallic objects is complicated by the fact that transmitted fields may penetrate the target, but will often only do so slightly. The effect cannot be ignored, yet it is often grossly impractical to discretize the entire surface or volume of a target in space increments only on the order of a fraction of the skin depth. To deal with this problem, we retain a simple integral equation formulation in scalar potential for the region outside the target, where magnetic fields are quasi-static and irrotational. Within the target we apply only the divergence relation, /spl nabla//spl middot/H = 0. When the skin depth is small relative to the radius of curvature of the target (e.g., <0.1), we use the thin skin depth approximation (TSA), /spl part/H/sub n///spl part/n as /spl sim/-ikH/sub n/, just inside the target's surface, where k is the electromagnetic wavenumber inside the metal and n is the normal direction on the surface and pointing inside of metallic object. Examination of analytical solutions for the sphere suggests the parameter range in which this approximation might perform well and suggests ways of improving accuracy over an extended range. The fundamental TSA formulation appears to be relatively robust. Analysis indicates that it is insensitive to variation over the target's surface of primary field orientation relative to that surface, and that it is only dependent on the target's magnetic permeability through induction number. Implementing the TSA numerically, within the above divergence relation, allows us to express all quantities in terms of tangential magnetic field components and their tangential derivatives over the target surface. In principle, this closes the system completely in terms of the exterior scalar potential. Broad-band numerical simulations based on the TSA compare favorably with analytical and other numerical solutions.

Electrical impedance spectroscopy (EIS) is a potential, noninvasive technique to image women for breast cancer. Studies have shown characteristic frequency dispersions in the electrical conductivity and permittivity of malignant versus normal tissue. Using a multifrequency EIS system, we imaged the breasts of 26 women. All patients had mammograms ranked using the American College of Radiology (ACR) BIRADS system. Of the 51 individual breasts imaged, 38 were ACR 1 negative, six had ACR 4-5 suspicious lesions, and seven had ACR 2 benign findings such as fibroadenomas or calcifications. A radially translatable circular array of 16 Ag/AgCl electrodes was placed around the breast while the patient lay prone. We applied trigonometric voltage patterns at ten frequencies between 10 and 950 kHz. Anatomically coronal images were reconstructed from this data using nonlinear partial differential equation methods. Typically, ACR 1-rated breasts were interrogated in a single central plane whereas ACR 2-5-rated breasts were imaged in multiple planes covering the region of suspicion. In general, a characteristic homogeneous image emerged for mammographically normal cases while focal inhomogeneities were observed in images from women with malignancies. Using a specific visual criterion, EIS images identified 83% of the ACR 4-5 lesions while 67% were detected using a numerical criterion. Overall, multifrequency electrical impedance imaging appears promising for detecting breast malignancies, but improvements must be made before the method reaches its full potential.

Near-infrared (NIR) diffuse tomography is an emerging method for imaging the interior of tissues to quantify concentrations of hemoglobin and exogenous chromophores non-invasively in vivo. It often exploits an optical diffusion model-based image reconstruction algorithm to estimate spatial property values from measurements of the light flux at the surface of the tissue. In this study, mean-squared error (MSE) over the image is used to evaluate methods for regularizing the ill-posed inverse image reconstruction problem in NIR tomography. Estimates of image bias and image standard deviation were calculated based upon 100 repeated reconstructions of a test image with randomly distributed noise added to the light flux measurements. It was observed that the bias error dominates at high regularization parameter values while variance dominates as the algorithm is allowed to approach the optimal solution. This optimum does not necessarily correspond to the minimum projection error solution, but typically requires further iteration with a decreasing regularization parameter to reach the lowest image error. Increasing measurement noise causes a need to constrain the minimum regularization parameter to higher values in order to achieve a minimum in the overall image MSE.

Image error analysis of a diffuse near-infrared tomography (NIR) system has been carried out on simulated data using a statistical approach described in Part I of this paper (Pogue et al., 2002). The methodology is used here with experimental data acquired on phantoms with a prototype imaging system intended for characterizing breast tissue. Results show that imaging performance is not limited by random measurement error, but rather by calibration issues. The image error over the entire field of view is generally not minimized when an accurate homogeneous estimate of the phantom properties is available; however, local image error over a target region of interest (ROI) is reduced. The image reconstruction process which includes a Levenberg-Marquardt style regularization provides good minimization of the objective function, yet its reduction is not always correlated with an overall image error decrease. Minimization of the bias in an ROI which contains localized changes in the optical properties can be achieved through five to nine iterations of the algorithm. Precalibration of the algorithm through statistical evaluation of phantom studies may provide a better measure of the image accuracy than that implied by minimization of the standard objective function.

Throughout the world, the problem of buried unexploded ordnance (UXO) poses an enormous, persistent, and expensive problem. While UXO generally consists of sizable bodies of ferrous metal and can therefore be detected, with current technology it is extremely difficult to distinguish them reliably from typically widespread pieces of clutter. Thus the problem is one of subsurface discrimination. The authors previous modeling work on scattering of ground penetrating radar (GPR) from metallic objects surrounded by an infinite soil-like medium has suggested the utility of a number of key discriminants in broadband fully polarimetric sensing. In particular, resonance structure, induced field rotation and ellipticity, and bistatic observation of scattered signals were shown to offer key information about target shape and size. The authors investigate the effects on signature features of the proximity of a ground surface to the target, for the common case of shallow burial (<1 m). Overall, their analyses suggest that the key discriminants seen in scattering in an infinite medium survive the complex interactions with the ground surface. In some instances, these revealing signatures appear to be strengthened by the presence of a nearby surface. Multiposition backscatter also allows fundamental inferences about target elongation and symmetry when those cannot be obtained from single position viewing.

Reconstructing images of large high-contrast objects with microwave methods has proved difficult. Successful images have generally been obtained by using a priori information to constrain the image reconstruction to recover the correct electromagnetic property distribution. In these situations, the measured electric field phases as a function of receiver position around the periphery of the imaging field-of-view vary rapidly often undergoing changes of greater than pi radians especially when the object contrast and illumination frequency increase. In this paper, we introduce a modified form of a Maxwell equation model-based image reconstruction algorithm which directly incorporates log-magnitude and phase of the measured electric field data. By doing so, measured phase variation can be unwrapped and distributed over more than one Rieman sheet in the complex plane. Simulation studies and microwave imaging experiments demonstrate that significant image quality enhancements occur with this approach for large high-contrast objects. Simple strategies for visualizing and unwrapping phase values as a function of the transmitter and receiver positions within our microwave imaging array are described. Metrics of the degree of phase variation expressed in terms of the amount and extent of phase wrapping are defined and found to be figures-of-merit which estimate when it is critical to deploy the new image reconstruction approach. In these cases, the new algorithm recovers high-quality images without resorting to the use of a priori information on object contrast and/or size as previously required.

Model-based imaging techniques utilizing microwave signal illumination rely heavily on the ability to accurately represent the wave propagation with a suitable numerical model. To date, the highest quality images from our prototype system have been achieved utilizing a single transmitter/single receiver measurement system where both antennas are manually repositioned to facilitate multiple illuminations of the imaging region, thus requiring long data acquisition times. In an effort to develop a system that can acquire data in a real time manner, a 32-channel network has been fabricated with all ports capable of being electronically selected for either transmit or receive mode. The presence of a complete array of antenna elements at data collection time perturbs the field distributions being measured, which can subsequently degrade the image reconstruction due to increased data-model mismatch. Incorporating the nonactive antenna-compensation model from Part I of this paper into our hybrid element near field image reconstruction algorithm is shown to restore image quality when fixed antenna-array data acquisition is used. Improvements are most dramatic for inclusions located in near proximity to the antenna array itself, although cases of improvement in the recovery of centered heterogeneities are also illustrated. Increases in the frequency of illumination are found to warrant an increased need for nonactive antenna compensation. Quantitative measures of recovered inclusion shape and position reveal a systematic improvement in image reconstruction quality when the nonactive antenna-compensation model is employed. Improvements in electrical property value recovery of localized heterogeneities are also observed. Image reconstructions in freshly excised breast tissue illustrate the applicability of the approach when used with our two-dimensional microwave imaging system.

Image-guided neurosurgery relies on accurate registration of the patient, the preoperative image series, and the surgical instruments in the same coordinate space. Recent clinical reports have documented the magnitude of gravity-induced brain deformation in the operating room and suggest these levels of tissue motion may compromise the integrity of such systems. We are investigating a model-based strategy which exploits the wealth of readily-available preoperative information in conjunction with intraoperatively acquired data to construct and drive a three dimensional (3-D) computational model which estimates volumetric displacements in order to update the neuronavigational image set. Using model calculations, the preoperative image database can be deformed to generate a more accurate representation of the surgical focus during an operation. In this paper, we present a preliminary study of four patients that experienced substantial brain deformation from gravity and correlate cortical shift measurements with model predictions. Additionally, we illustrate our image deforming algorithm and demonstrate that preoperative image resolution is maintained. Results over the four cases show that the brain shifted, on average, 5.7 mm in the direction of gravity and that model predictions could reduce this misregistration error to an average of 1.2 mm.

Fixed-array microwave imaging with multisensor data acquisition can suffer from nonactive antenna element interactions which cause distortions in the measurements. In Part I of a two-part paper, we develop a nonactive antenna compensation model for incorporation in model-based near-field microwave image reconstruction methods. The model treats the nonactive members of the antenna array as impedance boundary conditions applied over a cylindrical surface of finite radius providing two parameters, the effective antenna radius and impedance factor, which can be determined empirically from measured data. Results show that the effective radius and impedance factor provide improved fits to experimental data in homogeneous phantoms where measurements are obtained with and without the presence of the nonactive antenna elements. Once deduced, these parameters are incorporated into the nonactive antenna compensation model and lead to systematic data-model match improvements in heterogeneous phantoms. While the improvements afforded by the nonactive antenna model are small on a per measurement basis, they are not insignificant. As shown in Part II, inclusion of this new model for nonactive antenna compensation produces significantly higher quality image reconstructions from measurements obtained with a fixed-array data acquisition system over the frequency band 500-900 MHz.

This paper extends basic concepts of statistical hypothesis testing and confidence intervals to images generated by a new procedure for near infrared spectroscopic tomography being developed for use in breast cancer diagnosis. By estimating the covariance matrix of the pixels of an image from data used in the image reconstruction process, confidence maps for statistical tests on individual pixels and confidence intervals for entire images are displayed as an aid to research and clinical personnel interpreting possibly noisy images. The methods are applied to simulated and phantom-based images.

Two-dimensional electromagnetic scattering from a perfectly conducting target embedded near the randomly rough surface of an isotropic lossy dielectric is investigated. The randomly rough surface is illuminated by a finite width beam from an antenna in the free space above the surface, with off-normal incidence. Standard integral equation methods are applied and include all subsurface interactions between the object and rough surface. For a chosen embedded target, Monte Carlo simulations are performed for a selection of ensembles of rough surface types intended to be suggestive of natural ground. Far field scattering coefficient distributions and corresponding synthetic images suggest when the buried object should be discernible. Sensitivities are explored in terms of surface type, polarization of the incident field, depth and orientation of target, soil characteristics, incidence angle, and beamwidth. Many of the scattering features identified should also apply in 3D.

The finite element (FE) method has found several applications in emerging imaging modalities, especially microwave imaging which has been shown to be potentially useful in a number of areas including thermal estimation. In monitoring temperature distributions, the biological phenomena of temperature variations of tissue dielectric properties is exploited. By imaging these properties and their changes during such therapies as hyperthermia, temperature distributions can be deduced using difference imaging techniques. The authors focus on a microwave imaging problem where the hybrid element (HE) method is used in conjunction with a dual mesh scheme in an effort to image complex wavenumbers, k(2). The dual mesh scheme is introduced to improve the reconstructed images of tissue properties and is ideally suited for systems using FE methods as their computational base. Since the electric fields typically vary rapidly over a given body when irradiated by high-frequency electromagnetic sources, a dense mesh is needed for these fields to be accurately represented. Conversely, k(2) may be fairly constant over subregions of the body which would allow for a less dense sampling of this parameter in those regions. In the dual mesh system employed, the first mesh, which is uniformly dense, is used for calculating the electric fields over the body whereas the second mesh, which is nonuniform and less dense, is used for representing the k(2) distribution within the region of interest. The authors examine the 2-D TM polarization case for a pair of dielectric distributions on both a large and small problem to demonstrate the flexibility of the dual mesh method along with some of the difficulties associated with larger imaging problems. Results demonstrate the capabilities of the dual mesh concept in comparison to a single mesh approach for a variety of test cases, suggesting that the dual mesh method is critical for FE based image reconstruction where rapidly varying physical quantities are used to recover smoother property profiles, as can occur in microwave imaging of biological bodies.