Qianqian Fang

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.

Microwave image reconstruction of tissue property dispersion characteristics utilizing multiple-frequency information

A multiple-frequency-dispersion reconstruction algorithm utilizing a Gauss-Newton iterative strategy is presented for microwave imaging. This algorithm facilitates the simultaneous use of multiple-frequency measurement data in a single image reconstruction. Using the stabilizing effects of the low-frequency measurement data, higher frequency data can be included to reconstruct images with improved resolution. The parameters reconstructed in this implementation are now frequency-independent dispersion coefficients instead of the actual properties and may provide new diagnostic information. In this paper, large high-contrast objects are successfully constructed utilizing assumed simple dispersion models for both simulation and phantom cases for which the traditional single-frequency algorithm previously failed. Consistent improvement in image quality can be observed by involving more frequencies in the reconstruction; however, there appears to be a limit to how closely spaced the frequencies can be chosen while still providing independent new information. Possibilities for fine-tuning the image reconstruction performance in this context include: 1) variations of the assumed dispersion model and 2) Jacobian matrix column and row weighting schemes. Techniques for further reducing the forward solution computation time using time-domain solvers are also briefly discussed. The proposed dispersion reconstruction technique is quite general and can also be utilized in conjunction with other Gauss-Newton-based algorithms including the log-magnitude phase-form algorithm.

Viable Three-Dimensional Medical Microwave Tomography: Theory and Numerical Experiments

Three-dimensional microwave tomography represents a potentially very important advance over 2D techniques because it eliminates associated approximations which may lead to more accurate images. However, with the significant increase in problem size, computational efficiency is critical to making 3D microwave imaging viable in practice. In this paper, we present two 3D image reconstruction methods utilizing 3D scalar and vector field modeling strategies, respectively. Finite element (FE) and finite-difference time-domain (FDTD) algorithms are used to model the electromagnetic field interactions in human tissue in 3D. Image reconstruction techniques previously developed for the 2D problem, such as the dual-mesh scheme, iterative block solver, and adjoint Jacobian method are extended directly to 3D reconstructions. Speed improvements achieved by setting an initial field distribution and utilizing an alternating-direction implicit (ADI) FDTD are explored for 3D vector field modeling. The proposed algorithms are tested with simulated data and correctly recovered the position, size and electrical properties of the target. The adjoint formulation and the FDTD method utilizing initial field estimates are found to be significantly more effective in reducing the computation time. Finally, these results also demonstrate that cross-plane measurements are critical for reconstructing 3D profiles of the target.

Singular value analysis of the Jacobian matrix in microwave image reconstruction

For non-linear inverse scattering problems utilizing Gauss-Newton methods, the Jacobian matrix encodes rich information concerning the system performance and algorithm efficiency. In this paper, we perform an analytical evaluation of a single-iteration Jacobian matrix based on a previously derived nodal adjoint representation. Concepts for studying linear ill-posed problems, such as the degree-of-ill-posedness, are used to assess the impact of important system parameters on the expected image quality. Analytical singular value decomposition (SVD) of the Jacobian matrix for a circular imaging domain is derived along with the numerical SVD for optimizing imaging system configurations. The results show significant reductions in the degree-of-ill-posedness when signal frequency, antenna array density and property parameter sampling are increased. Specifically, the decay rate in the singular spectrum of the Jacobian decreases monotonically with signal frequency being approximately 1/3 of its 0.1 GHz value at 3 GHz, is improved with antenna array density up to about 35 equally-spaced circumferentially positioned elements and drops significantly with increased property parameter sampling to more than twice the amount of measurement data. These results should serve as useful guidelines in the development of design specifications for an optimized hardware installation

The Multidimensional Phase Unwrapping Integral and Applications to Microwave Tomographical Image Reconstruction

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

Microwave thermal imaging: initial in vivo experience with a single heating zone

The deployment of hyperthermia as a routine adjuvant to radiation or chemotherapy is limited largely by the inability to devise treatment plans which can be monitored through temperature distribution feedback during therapy. A non-invasive microwave tomographic thermal imaging system is currently being developed which has previously exhibited excellent correlation between the recovered electrical conductivity of a heated zone and its actual temperature change during phantom studies. To extend the validation of this approach in vivo, the imaging system has been re-configured for small animal experiments to operate within the bore of a CT scanner for anatomical and thermometry registration. A series of 5–7 day old pigs have been imaged during hyperthermia with a monopole antenna array submerged in a saline tank where a small plastic tube surgically inserted the length of the abdomen has been used to create a zone of heated saline at pre-selected temperatures. Tomographic microwave data over the frequency range of 300–1000 MHz of the pig abdomen in the plane perpendicular to the torso is collected at regular intervals after the tube saline temperatures have settled to the desired settings. Images are reconstructed over a range of operating frequencies. The tube location is clearly visible and the recovered saline conductivity varies linearly with the controlled temperature values. Difference images utilizing the baseline state prior to heating reinforces the linear relationship between temperature and imaged saline conductivity. Demonstration of in vivo temperature recovery and correlation with an independent monitoring device is an important milestone prior to clinical integration of this non-invasive imaging system with a thermal therapy device.

Image accuracy improvements in microwave tomographic thermometry: phantom experience

Evaluation of a laboratory-scale microwave imaging system for non-invasive temperature monitoring has previously been reported with good results in terms of both spatial and temperature resolution. However, a new formulation of the reconstruction algorithm in terms of the log-magnitude and phase of the electric fields has dramatically improved the ability of the system to track the temperature-dependent electrical conductivity distribution. This algorithmic enhancement was originally implemented as a way of improving overall imaging capability in cases of large, high contrast permittivity scatterers, but has also proved to be sensitive to subtle conductivity changes as required in thermal imaging. Additional refinements in the regularization procedure have strengthened the reliability and robustness of image convergence. Imaging experiments were performed for a single heated target consisting of a 5.1 cm diameter PVC tube located within 15 and 25 cm diameter monopole antenna arrays, respectively. The performance of both log-magnitude/phase and complex-valued reconstructions when subjected to four different regularization schemes has been compared based on this experimental data. The results demonstrate a significant accuracy improvement (to 0.2° C as compared with 1.6° C for the previously published approach) in tracking thermal changes in phantoms where electrical properties vary linearly with temperature over a range relevant to hyperthermia cancer therapy.

Microwave breast imaging with an under-determined reconstruction parameter mesh

Microwave imaging has been proposed as a method for detecting breast tumors because of the high electrical property contrast between tumors and normal tissue. We are currently developing a tomographic system which can generally be treated as an ill-conditioned inverse problem and utilize a Gauss-Newton iterative algorithm to handle its nonlinear nature. The ill-conditioning is generally related to the number of parameters being reconstructed with respect to the amount of measurement data. Our initial implementation restricted the number of parameters to close to that of the measurement data. However, this sparse discretization of the imaging zone severely limited the resolution and required a high degree of spatial filtering to stabilize the algorithm convergence. We are currently exploring significantly increasing the number of reconstruction parameters to the point of making the problem considerably under-determined. Initial results indicate that the benefit in terms of increased degrees of freedom has resulted in dramatically improved resolution without compromising stability.

3D scalar microwave image reconstruction algorithm

We have recently implemented a microwave imaging algorithm which incorporates scalar 3D wave propagation while reconstructing a 2D dielectric property profile. This is a preliminary step in reaching a full 3D image reconstruction approach but allows us to investigate important issues associated with speed of reconstruction and problem size. Key concepts developed during our 2D system evaluations have also proved to be translatable to the 3D approach and have accelerated the overall implementation.

Initial experience with a microwave imaging system for monitoring temperature change in an animal model

We are developing a microwave system for non-invasively monitoring temperature distributions in human tissue during thermal therapy. Central to our approach is a microwave antenna array and switching matrix which allows tomographic data collection over a wide range of frequencies (300 MHz-1 GHz). The measured field values are processed by a reconstruction algorithm that creates electrical property maps which vary with temperature and show changes in temperature as a function of time through difference imaging. Initial phantom investigations suggested that our imaging device was sufficiently sensitive to thermally induced electrical property changes to expand the studies to animal models. The results presented here are from our initial experiments conducted with a saline-coupled microwave imaging system on a 5-day old live piglet. The heating was accomplished using a heated tube of water surgically implanted in the piglets abdomen. Fiber optic temperature sensors were inserted at various positions for comparison with recovered conductivity values and the entire experiment was performed in a CT scanner to facilitate localization of the probes with respect to the heating tube, piglet geometry and microwave antenna array.