Estimating the Effective Permittivity for Reconstructing Accurate Microwave-Radar Images.
- 1Department of Electrical and Computer Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, T2N 1N4, Canada.
We present preliminary results from a method for estimating the optimal effective permittivity for reconstructing microwave-radar images. Using knowledge of how microwave-radar images are formed, we identify characteristics that are typical of good images, and define a fitness function to measure the relative image quality. We build a polynomial interpolant of the fitness function in order to identify the most likely permittivity values of the tissue. To make the estimation process more efficient, the polynomial interpolant is constructed using a locally and dimensionally adaptive sampling method that is a novel combination of stochastic collocation and polynomial chaos. Examples, using a series of simulated, experimental and patient data collected using the Tissue Sensing Adaptive Radar system, which is under development at the University of Calgary, are presented. These examples show how, using our method, accurate images can be reconstructed starting with only a broad estimate of the permittivity range.
- PMID: 27611785; DOI:10.1371/journal.pone.0160849
Background: Existing methods for breast cancer imaging come with associated risks (x-rays for mammograms or CT scans) or are slow and expensive (MRI scans). Because of these limitations, frequent imaging is generally not an option. Our group at the University of Calgary has been working on new imaging methods to complement these existing techniques. The systems we are developing use low-power microwave signals, and are safe and inexpensive to operate, meaning frequent imaging would be possible. Currently we are developing two systems (see Fig. 1), one that uses transmitted signals (those that pass through the tissue and are detected on the other side) and one that uses reflected signals (radar). The transmission system allows us to estimate average tissue properties and generate 2-dimensional projection maps of these average properties. The radar system cannot estimate tissue properties, but is used to reconstruct full 3-dimensional images that indicate locations of high contrast between tissue properties. We have completed scans of volunteers and patients with both systems.
To form images with the radar system, a pulse from an antenna is sent into the breast. When the pulse encounters a boundary between two different tissue types, a portion of the pulse is reflected and a portion of the pulse is transmitted. We collect and record the reflected signals with the same antenna used to send the original pulse. This process is repeated as the antenna is scanned to 140 different locations around the breast to provide a 3-dimensional view. Figure 2 shows one antenna location during a scan of an experimental model.
After the recorded signals are cleaned up to reduce unwanted noise and reflections, they are combined to form an image. Reflections from targets combine to create responses in images. Figure 3 shows an image from the radar system. The responses in the image show locations of strongly scattering objects (interfaces between tissues that reflect more energy). The image is sliced along three different planes to show the location of the largest response.
Figure 1: Left – The transmission system. Right – The radar system.
Figure 2: Single antenna position (lower left) during a scan of an experimental model. At each of the 140 positions used during a scan, the antenna is placed the same distance from the skin and perpendicular to it.
The paper featured here addresses one of the key hurdles to reconstructing reliable images with the radar system; how to estimate the speed at which the signal travels in the tissue. In order to correctly recombine the signals, the average signal speed needs to be known. Unfortunately, as breast tissue varies considerably from person to person, so does the signal speed. That means we cannot use a “standard” value for everyone. Additionally, measuring the signal speed is difficult, because we do not have access to the internal tissues. Our transmission system, mentioned earlier, provides an estimate of the bulk properties of the entire breast. However, the paths traveled by reflected signals are likely dominated by tissues near to the skin, which are predominantly fat. Therefore, the estimates of the signal speed for radar images may different from the estimates provided by the transmission system.
Method: Rather than perform more measurements to directly estimate the signal speeds, which would lead to longer scan times, we decided to examine the images themselves. We found that three main image features change when the estimate of the signal speed becomes less accurate, as the signals do not add together correctly. First, the number of artifacts (regions in the image that look like reflections from tissue interfaces, but are caused by factors such as noise) increases. These artifacts are difficult to distinguish from actual reflections and cannot be completely removed, so we look for images with a small total number of reflections and artifacts. Second, the intensity (brightness) of the reflections in the image decreases, due to poor overlap of the signals. Unfortunately, it is possible for artifacts to have very high intensity with an incorrect signal speed, so we cannot rely on this alone. Third, when the signal speed is approaches the correct value, actual reflections tend to be more spread out (smeared) compared to when the signal speed is correct. As with the intensity reduction, this is due to poor overlap of the responses when the signals are combined. Thus, we are looking for images with fewer, smaller and brighter responses.
To determine the most likely average signal speed, we compute the estimated image quality with a fitness function, based on the above criteria. We search for the image with the maximum fitness by adaptively testing a large number of possible images. A polynomial is fitted to the fitness values of the tested images in order to estimate between them. In this way, we can identify the image, or images, that are most likely to be correct.
Conclusion: We tested our method on simulated, experimental, and volunteer scans. In all cases, this method did a reasonable job of identifying the target (scatterer). Although the results presented in the paper are preliminary, we believe that this is a promising method for frequent breast imaging and are working to further improve our systems and imaging techniques.
Figure 3: An example of an image reconstructed using our radar system. This image is of an experimental model that has an inclusion to represent a tumor. The dark spot indicates the presence of high contrast tissues. The dashed circles show the expected location of the response.