Importance of phase unwrapping for the reconstruction of microwave tomographic images

3-D Microwave Tomography Using the Soft Prior Regularization Technique: Evaluation in Anatomically Realistic MRI-Derived Numerical Breast Phantoms

OBJECTIVE

Fusion of magnetic resonance imaging (MRI) breast images with microwave tomography is accomplished through a soft prior technique, which incorporates spatial information (from MRI), i.e., accurate boundary location of different regions of interest, into the regularization process of the microwave image reconstruction algorithm.

METHODS

Numerical experiments were completed on a set of three-dimensional (3-D) breast geometries derived from MR breast data with different parenchymal densities, as well as a simulated tumor to evaluate the performance over a range of breast shapes, sizes, and property distributions.

RESULTS

When the soft prior regularization technique was applied, both permittivity and conductivity relative root mean square error values decreased by more than 87% across all breast densities, except in two cases where the error decrease was only 55% and 78%. In addition, the incorporation of structural priors increased contrast between tumor and fibroglandular tissue by 59% in permittivity and 192% in conductivity.

CONCLUSION

This study confirmed that the soft prior algorithm is robust in 3-D and can function successfully across a range of complex geometries and tissue property distributions.

SIGNIFICANCE

This study demonstrates that our microwave tomography is capable of recovering accurate tissue property distributions when spatial information from MRI is incorporated through soft prior regularization.

Addressing Multipath Signal Corruption in Microwave Tomography and the Influence on System Design and Algorithm Development

In developing a microwave tomography system, we started by examining the fundamental signal measurement challenges-i.e., how to interrogate the target while suppressing unwanted multi-path signals. Beginning with a lossy coupling bath to suppress unwanted surface waves, we have developed a robust and reliable system that is both simple and low profile. However, beyond the basic measurement configuration, the lossy coupling medium concept has also informed our choice of array antenna and imaging algorithms. The synergism of these concepts has produced a novel concept which is embodied in a system that has been successfully translated to the clinic.

Two-step inversion with a logarithmic transformation for microwave breast imaging

PURPOSE

The authors have developed a new two-step microwave tomographic image reconstruction process specifically designed to incorporate logarithmic transformed microwave imaging algorithms as a means of significantly improving spatial resolution and target property recovery. Log transform eliminates the need for a priori information, but spatial filtering often integrated as part of the regularization required to stabilize image recovery, generally smooths image features and reduces object definition. The new implementation begins with this smoothed image as the first step, but then utilizes it as the starting estimate for a second step which continues the iterative process with a standard weighted Euclidean distance regularization. The penalty term of the latter restricts the new image to a multi-dimensional location close to the original but allows the algorithm to optimize the image without excessive smoothing.

METHODS

The overall approach is based on a Gauss-Newton iterative scheme which incorporates a log transformation as a way of making the reconstruction more linear. It has been shown to be robust and not require a priori information as a condition for convergence, but does produce somewhat smoothed images as a result of associated regularization. The new two-step process utilizes the previous technique to generate a smoothed initial estimate and then uses the same reconstruction process with a weighted Euclidean distance penalty term. A simple and repeatable method has been implemented to determine the weighting factor without significant computational burden. The reconstructions are assessed according to conventional parameter estimation metrics.

RESULTS

We apply the approach to phantom experiments using large, high contrast canonical shapes followed by a set of images recovered from an actual patient exam. The image improvements are substantial in regards to improved property recovery and feature delineation without inducing unwanted artifacts. Analysis of the residual vector after the reconstruction process further emphasizes that the minimization criterion is efficient with minimal biases.

CONCLUSIONS

The outcome is a novel synergism of an established stable reconstruction algorithm with a conventional regularization technique. It maintains the ability to recover high quality microwave tomographic images without the bias of a priori information while substantially improving image quality. The results are confirmed on both phantom experiments and patient exams.

Integration of microwave tomography with magnetic resonance for improved breast imaging

PURPOSE

Breast magnetic resonance imaging is highly sensitive but not very specific for the detection of breast cancer. Opportunities exist to supplement the image acquisition with a more specific modality provided the technical challenges of meeting space limitations inside the bore, restricted breast access, and electromagnetic compatibility requirements can be overcome. Magnetic resonance (MR) and microwave tomography (MT) are complementary and synergistic because the high resolution of MR is used to encode spatial priors on breast geometry and internal parenchymal features that have distinct electrical properties (i.e., fat vs fibroglandular tissue) for microwave tomography.

METHODS

The authors have overcome integration challenges associated with combining MT with MR to produce a new coregistered, multimodality breast imaging platform--magnetic resonance microwave tomography, including: substantial illumination tank size reduction specific to the confined MR bore diameter, minimization of metal content and composition, reduction of metal artifacts in the MR images, and suppression of unwanted MT multipath signals.

RESULTS

MR SNR exceeding 40 dB can be obtained. Proper filtering of MR signals reduces MT data degradation allowing MT SNR of 20 dB to be obtained, which is sufficient for image reconstruction. When MR spatial priors are incorporated into the recovery of MT property estimates, the errors between the recovered versus actual dielectric properties approach 5%.

CONCLUSIONS

The phantom and human subject exams presented here are the first demonstration of combining MT with MR to improve the accuracy of the reconstructed MT 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.

Clinical microwave tomographic imaging of the calcaneus: a first-in-human case study of two subjects

We have acquired 2-D and 3-D microwave tomographic images of the calcaneus bones of two patients to assess correlation of the microwave properties with X-ray density measures. The two volunteers were selected because each had one leg immobilized for at least six weeks during recovery from a lower leg injury. A soft-prior regularization technique was incorporated with the microwave imaging to quantitatively assess the bulk dielectric properties within the bone region. Good correlation was observed between both permittivity and conductivity and the computed tomography-derived density measures. These results represent the first clinical examples of microwave images of the calcaneus and some of the first 3-D tomographic images of any anatomical site in the living human.

Comparison of no-prior and soft-prior regularization in biomedical microwave imaging

Microwave imaging for medical applications is attractive because the range of dielectric properties of different soft tissues can be substantial. Breast cancer detection and monitoring of treatment response are areas where this technology could be important because of the contrast between normal and malignant tissue. Unfortunately, the technique is unable to achieve the high spatial resolution at depth in tissue which is available from other conventional modalities such as x-ray computed tomography (CT) or magnetic resonance imaging (MRI). We have incorporated a soft-prior regularization strategy within our microwave reconstruction algorithm and compared it with the images obtained with traditional no-prior (Levenberg-Marquardt) regularization. Initial simulation and phantom results show a significant improvement of the recovered electrical properties. Specifically, errors in the microwave property estimates were improved by as much as 95%. The effects of a false-inclusion region were also evaluated and the results show that a small residual property bias of 6% in permittivity and 15% in conductivity can occur that does not otherwise degrade the property recovery accuracy of inclusions that actually exist. The work sets the stage for integrating microwave imaging with MR for improved resolution and functional imaging of the breast in the future.