Three-dimensional microwave tomography: initial experimentalimaging of animals

The purpose of this study was to construct a microwave tomographic system capable of conducting experiments with whole scale biological objects and to demonstrate the feasibility of microwave tomography for imaging such objects using a canine model. Experiments were conducted using a three-dimensional (3-D) microwave tomographic system with working chamber dimensions of 120 cm in diameter and 135 cm in height. The operating frequency was 0.9 GHz. The object under study was located in the central area of the tomographic chamber filled with a salt solution. Experimentally measured attenuation of the electromagnetic field through the thorax was about -120 dB. To obtain images, we used various two-dimensional and 3-D reconstruction schemes. Images of the canine were obtained. In spite of imperfections, the images represent a significant milestone in the development of microwave tomography for whole body imaging and demonstrate its feasibility.     

Microwave tomography: two-dimensional system for biological imaging

Microwave tomographic imaging is one of the new technologies which has the potential for important applications in medicine. Microwave tomographically reconstructed images may potentially provide information about the physiological state of tissue as well as the anatomical structure of an organ. A two-dimensional (2-D) prototype of a quasi real-time microwave tomographic system was constructed. It was utilized to reconstruct images of physiologically active biological tissues such as an explanted canine perfused heart. The tomographic system consisted of 64 special antennae, divided into 32 emitters and 32 receivers which were electronically scanned. The cylindrical microwave chamber had an internal diameter of 360 mm and was filled with various solutions, including deionized water. The system operated on a frequency of 2.45 GHz. The polarization of the incident electromagnetic field was linear in the vertical direction. Total acquisition time was less than 500 ms. Both accurate and approximation methods of image reconstruction were used. Images of 2-D phantoms, canine hearts, and beating canine hearts have been achieved. In the worst-case situation when the 2-D diffraction model was used for an attempt to “slice” three-dimensional (3-D) object reconstruction, the authors still achieved spatial resolution of 1 to 2 cm and contrast resolution of 5%     

Microwave image reconstruction from 3-D fields coupled to 2-D parameter estimation

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.     

Quantitative microwave imaging with a 2.45-GHz planar microwavecamera

This paper presents microwave tomographic reconstructions of the complex permittivity of lossy dielectric objects immersed in water from experimental multiview near-field data obtained with a 2.35-GHz planar active microwave camera. An iterative reconstruction algorithm based on the Levenberg-Marquardt method was used to solve the nonlinear matrix equation which results when applying a moment method to the electric field integral representation. The effects of uncertainties in experimental parameters such as the exterior medium complex permittivity the imaging system geometry and the incident field at the object location are illustrated by means of reconstructions from synthetic data. It appears that the uncertainties in the incident field have the strongest impact on the reconstructions. A receiver calibration procedure has been implemented and some ways: to access to the incident field at the object location have been assessed     

基于哈特曼波前探测层析重建三维温度场

基于哈特曼波前探测的流场层析测量技术结合了光学波前探测技术和计算机层析重建技术。系统由哈特曼传感器探测平行光束穿过流场后的投影波前，提取流场在多方向上的投影数据，采用计算机层析技术重建流场物理量的空间分布。为了验证系统的可行性和标定系统重建精度，首先对静态圆对称折射率场进行层析重建，折射率重建误差为10^-3。任静仑标定的基础上．对实际火焰温度场进行了层析重建，获得了火焰温度场的三维温度分布，取得了较好的实验结果。     

A cone-beam reconstruction algorithm for circle-plus-arc data-acquisition geometry

In cone-beam computerized tomography (CT), projections acquired with the focal spot constrained on a planar orbit cannot provide a complete set of data to reconstruct the object function exactly. There are severe distortions in the reconstructed noncentral transverse planes when the cone angle is large. In this work, a new method is proposed which can obtain a complete set of data by acquiring cone-beam projections along a circle-plus-arc orbit. A reconstruction algorithm using this circle-plus-arc orbit is developed, based on the Radon transform and Grangeat's formula. This algorithm first transforms the cone-beam projection data of an object to the first derivative of the three-dimensional (3-D) Radon transform, using Grangeat's formula, and then reconstructs the object using the inverse Radon transform. In order to reduce interpolation errors, new rebinning equations have been derived accurately, which allows one-dimensional (1-D) interpolation to be used in the rebinning process instead of 3-D interpolation. A noise-free Defrise phantom and a Poisson noise-added Shepp-Logan phantom were simulated and reconstructed for algorithm validation. The results from the computer simulation indicate that the new cone-beam data-acquisition scheme can provide a complete set of projection data and the image reconstruction algorithm can achieve exact reconstruction. Potentially, the algorithm can be applied in practice for both a standard CT gantry-based volume tomographic imaging system and a C-arm-based cone-beam tomographic imaging system, with little mechanical modification required.     

Microwave Imaging in Layered Media: 3-D Image Reconstruction From Experimental Data

A prototype microwave imaging system for imaging 3-D targets in layered media is developed to validate the capability of microwave imaging with experimental data and with 3-D nonlinear inverse scattering algorithms. In this experimental prototype, the transmitting and receiving antennas are placed in a rectangular tub containing a fluid. Two plastic slabs are placed in parallel in the fluid to form a five-layer medium. The microwave scattering data are acquired by mechanically scanning a single transmitting antenna and a single receiving antenna, thus avoiding the mutual coupling that occurs when an array is used. The collected 3-D experimental data in the fluid are processed by full 3-D nonlinear inverse scattering algorithms to unravel the complicated multiple scattering effects and produce 3-D digital images of the dielectric constant and conductivity of the imaging domain. The image reconstruction is focused on the position and dimensions of the unknown scatterers. Different dielectric and metallic objects have been imaged effectively at 1.64 GHz.      

基于太赫兹相干层析成像系统色散补偿的研究

为了提高太赫兹相干层析成像系统的纵向分辨率,采用色散补偿方法解决了宽带光源做成像光源带来的色散问题。基于评价函数的迭代补偿算法对降噪滤波后的原始信号进行色散补偿,得到了较为清晰的3维重构图像。结果表明,在迭代补偿算法的计算中,无需预知样品的厚度信息以及色散特性,即可获得高精度的3维重构图像,纵向分辨率高达100μm。该研究在高精度的材料无损探测领域具有较大的研究价值和广泛的应用前景。     

Microwave tomography: theoretical and experimental investigation ofthe iteration reconstruction algorithm

Results of experiments on the two-dimensional (2-D) quasi real-time microwave tomographic system have been reported. Various reconstruction possibilities of this system have been demonstrated on phantoms and canine hearts. The early utilized Rytov approximation is appropriate for low-contrast inverse problems. A new iterative reconstruction algorithm is proposed in this paper. The iterations converge to an accurate solution of the scalar Helmholtz-equation inverse problem in the case of higher contrasts. The goal of the reported study is an experimental and theoretical investigation of the proposed iteration algorithm. The influence on the quality of the reconstructed images and on the spatial resolution of such factors as the number of receivers, the accuracy of the scattered field measurements, and the dielectric contrast have been investigated     

Medical imaging with a microwave tomographic scanner

A microwave tomographic scanner for biomedical applications is presented. It consists of a 64-element circular array with a useful diameter of 20 cm. Electronically scanning the transmitting and receiving antennas allows multiview measurements with no mechanical movement. Imaging parameters-a spatial resolution of 7 mm and a contrast resolution of 1% for a measurement time of 3 s-are appropriate for medical use. Measurements on tissue-simulating phantoms and volunteers, together with numerical simulations, are presented to assess the system for absolute imaging of tissue distribution and for differential imaging of physiological, pathological, and induced changes in tissues     

An Improved SIRT-Style Reconstruction Algorithm for Microwave Tomography

An improved SIRT-style reconstruction algorithm has been suggested using a beam concept for linear first-order microwave tomographic imaging. The results of applying the algorithm on a small-scale model having a simplified data-collecting arrangement have been extremely encouraging and indicate the possibility for achieving a high-resolution microwave imaging system. However, the contrast in the picture that is obtained is a bit poor mainly due to the simplifying assumptions made to linearize the algorithm and to some extent due to some other reasons, e. g., 1) insufficient number of projections, 2) improper selection of initial trial solution, 3) small object size, and 4) failure of the fan-beam concept in electromagnetic imaging.     

Multipolar laminated electromagnet for low-field magnetic resonanceimaging and electron paramagnetic resonance imaging

A cylindrical 16-pole electromagnet (EM) for electron paramagnetic resonance imaging (EPRI) and low-field magnetic resonance imaging (MRI) has been designed by means of two-dimensional and three-dimensional (3-D) finite element analysis (FEA). The use of an automatic procedure that combines FEA with a minimization routine allowed the optimization of the design, in order to improve the homogeneity along the axis of the EM. A prototype has been built by using electrical steel sheets that were cut by laser; this solution reduced significantly the manufacturing cost. The EM operates with a maximum flux density, in the bore, of 0.08 T and has a homogeneity along the axis of about 40 parts per million (ppm) in a spherical region 10 cm in diameter. It generates the main field and two of the three field gradients required in the 3-D image reconstruction. Good agreement was found between the results of simulation and the measured values     

Electrical conductivity imaging via contactless measurements

A new imaging modality is introduced to image electrical conductivity of biological tissues via contactless measurements. This modality uses magnetic excitation to induce currents inside the body and measures the magnetic fields of the induced currents. In this study, the mathematical basis of the methodology is analyzed and numerical models are developed to simulate the imaging system. The induced currents are expressed using the A-phi formulation of the electric field where A is the magnetic vector potential and phi is the scalar potential function. It is assumed that A describes the primary magnetic vector potential that exists in the absence of the body. This assumption considerably simplifies the solution of the secondary magnetic fields caused by induced currents. In order to solve phi for objects of arbitrary conductivity distribution a three-dimensional (3-D) finite-element method (FEM) formulation is employed. A specific 7 x 7-coil system is assumed nearby the upper surface of a 10 x 10 x 5-cm conductive body. A sensitivity matrix, which relates the perturbation in measurements to the conductivity perturbations, is calculated. Singular-value decomposition of the sensitivity matrix shows various characteristics of the imaging system. Images are reconstructed using 500 voxels in the image domain, with truncated pseudoinverse. The noise level is assumed to produce a representative signal-to-noise ratio (SNR) of 80 dB. It is observed that it is possible to identify voxel perturbations (of volume 1 cm3) at 2 cm depth. However, resolution gradually decreases for deeper conductivity perturbations.     

Microwave-tomographic imaging of the high dielectric-contrast objects using different image-reconstruction approaches

Microwave tomography is an imaging modality based on differentiation of dielectric properties of an object. The dielectric properties of biological tissues and its functional changes have high medical significance. Biomedical applications of microwave tomography are a very complicated and challenging problem, from both technical and image reconstruction point-of-views. The high contrast in tissue dielectric properties presenting significant advantage for diagnostic purposes possesses a very challenging problem from an image-reconstruction prospective. Different imaging approaches have been developed to attack the problem, such as two-dimensional (2-D) and three-dimensional (3-D), minimization, and iteration schemes. The goal of this research is to study imaging performance of the Newton and the multiplicative regularized contrast source inversion (MR-CSI) methods in 2-D geometry and gradient and MR-CSI methods in 3-D geometry using high-contrast, medium-size phantoms, and biological objects. Experiments were conducted on phantoms and excised segment of a pig hind-leg using a 3-D microwave-tomographic system operating at frequencies of 0.9 and 2.05 GHz. Both objects being of medium size (10-15 cm) possess high dielectric contrasts. Reconstructed images were obtained using all imaging approaches. Different approaches are evaluated and discussed based on its performance and quality of reconstructed images.     

Fast 3-d tomographic microwave imaging for breast cancer detection

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.     

Three-dimensional myocardial strain reconstruction from tagged MRI using a cylindrical B-spline model

In this paper, we present a new method for reconstructing three-dimensional (3-D) left ventricular myocardial strain from tagged magnetic resonance (MR) image data with a 3-D B-spline deformation model. The B-spline model is based on a cylindrical coordinate system that more closely fits the morphology of the myocardium than previously proposed Cartesian B-spline models and does not require explicit regularization. Our reconstruction method first fits a spatial coordinate B-spline displacement field to the tag line data. This displacement field maps each tag line point in the deformed myocardium back to its reference position (end-diastole). The spatial coordinate displacement field is then converted to material coordinates with another B-spline fit. Finally, strain is computed by analytically differentiating the material coordinate B-spline displacement field with respect to space. We tested our method with strains reconstructed from an analytically defined mathematical left ventricular deformation model and ten human imaging studies. Our results demonstrate that a quadratic cylindrical B-spline with a fixed number of control points can accurately fit a physiologically realistic range of deformations. The average 3-D reconstruction computation time is 20 seconds per time frame on a 450 MHz Sun Ultra80 workstation.     

Deep tissue photoacoustic imaging using a miniaturized 2-D capacitive micromachined ultrasonic transducer array

In this paper, we demonstrate 3-D photoacoustic imaging (PAI) of light absorbing objects embedded as deep as 5 cm inside strong optically scattering phantoms using a miniaturized (4 mm × 4 mm × 500 μm), 2-D capacitive micromachined ultrasonic transducer (CMUT) array of 16 × 16 elements with a center frequency of 5.5 MHz. Two-dimensional tomographic images and 3-D volumetric images of the objects placed at different depths are presented. In addition, we studied the sensitivity of CMUT-based PAI to the concentration of indocyanine green dye at 5 cm depth inside the phantom. Under optimized experimental conditions, the objects at 5 cm depth can be imaged with SNR of about 35 dB and a spatial resolution of approximately 500 μm. Results demonstrate that CMUTs with integrated front-end amplifier circuits are an attractive choice for achieving relatively high depth sensitivity for PAI.     

Analytical calculation of volumes-of-intersection for iterative, fully 3-D PET reconstruction

Use of iterative algorithms to reconstruct three-dimensional (3-D) positron emission tomography (PET) data requires the computation of the system probability matrix. The pure geometrical contribution can easily be approximated by the length-of-intersection (LOI) between lines-of-response (LOR) and individual voxels. However, more accurate geometrical projectors are desirable. Therefore, we have developed a fast method for the analytical calculation of the 3-D shape and volume of volumes-of-intersection (VOI). This method provides an alternative robust projector with a uniformly continuous sampling of the image space. The enhanced calculation effort is facilitated by using several speedup techniques. Exploiting intrinsic symmetry relations and the sparseness of the system matrix allows to create an efficiently compressed matrix which can be precomputed and completely stored in memory. In addition, a new voxel addressing scheme has been implemented. This scheme avoids time-consuming symmetry transformations of voxel addresses by using an octant-wise symmetrically ordered field of voxels. The above methods have been applied for a fully 3-D, iterative reconstruction of 3-D sinograms recorded with a Siemens/CTI ECAT HR+ PET scanner. A comparison of the performance of the reconstruction using LOI weighting and VOI weighting is presented.     

Reconstruction quality and spectral content of an electromagnetic time-domain inversion algorithm

A tomographic time-domain reconstruction algorithm for solving the inverse electromagnetic problem is described. The application we have in mind is dielectric breast cancer detection but the results are of general interest to the field of microwave tomography. Reconstructions have been made from experimental and numerically simulated data for objects of different sizes in order to investigate the relation between the spectral content of the illuminating pulse and the quality of the reconstructed image. We have found that the spectral content is crucial for a successful reconstruction. The work has further shown that when imaging objects with different scale lengths it is an advantage to use a multiple step procedure. Low frequency content in the pulse is used to image the large structures and the reconstruction process then proceed by using higher frequency data to resolve small scale lengths. Good agreement between the results obtained from experimental data and simulated data has been achieved.     

Kinematic and deformation analysis of 4-D coronary arterial trees reconstructed from cine angiograms

In the cardiovascular arena, percutaneous catheter-based interventional (i.e., therapeutic) procedures include a variety of coronary and other vascular system interventions. These procedures use two-dimensional (2-D) X-ray-based imaging as the sole or the major imaging modality for procedure guidance and quantification of key parameters. Coronary vascular curvilinearity is one key parameter that requires a four-dimensional (4-D) format, i.e., three-dimensional (3-D) anatomical representation that changes during the cardiac cycle. A new method has been developed for reconstruction and analysis of these patient-specific 4-D datasets utilizing routine cine angiograms. The proposed method consists of three major processes: 1) reconstruction of moving coronary arterial tree throughout the cardiac cycle; 2) establishment of temporal correspondence with smoothness constraints; and 3) kinematic and deformation analysis of the reconstructed 3-D moving coronary arterial trees throughout the cardiac cycle.