DETAILED DESCRIPTION OF THE INVENTION

[0025] In one embodiment for carrying out space-time microwave imaging (MIST) in accordance with the invention, each antenna in an array of antennas sequentially transmits a low-power ultra-short microwave pulse into an object to be imaged, such as the breast, and collects the backscatter signal. The relative arrival times and amplitudes of backscattered signals received by the antennas across the antenna array provide information that can be used to detect the presence and determine the location of malignant lesions. Breast carcinomas act as significant microwave scatterers because of the large dielectric-properties contrast with the surrounding tissue. The problem of detecting and localizing scattering objects using pulsed signals and antenna arrays is similar to that encountered in radar systems, such as those used for air traffic control, military surveillance, and land-mine detection.

[0026] Data in published literature and from our measurements on freshly excised breast biopsy tissue suggest that the malignant-to-normal breast tissue contrast in dielectric constant, ε_r, and conductivity, σ, is between 2:1 and 10:1, depending on the density of the normal tissue. The higher dielectric properties of malignant breast tissue arise, in part, from increased protein hydration and a breakdown of cell membranes due to necrosis. The contrast ratio does not vary significantly with tumor age, which suggests the potential for detecting tumors at the earliest stages of development. Microwaves offer exceptionally high contrast compared to other imaging modalities, such as X-ray mammography, which exploit intrinsic contrasts on the order of a few percent. Measurements suggest typical attenuation is less than 4 dB/cm up through 10 GHz, indicating that commercial microwave instrumentation with 100 dB of dynamic range is capable of imaging through 25 cm of tissue. MIST uses microwave pulses that are on the order of 100 ps in duration, with peak powers on the order of a few milliwatts—approximately 1/100^th of the power of a typical cellular phone. Assuming a pulse repetition frequency of 1 MHz and a maximum scan depth of 10 cm, an array of 100 antennas could be sequentially scanned in 0.1 seconds.

[0027] The goal of conventional microwave tomography is the recovery of the dielectric-properties profile of an object from measurement of the transmission and scattering of microwave energy through the object. In contrast, MIST in accordance with the invention need be carried out only to identify the presence and location of strong scatterers in the breast by directly imaging backscattered signal power. Consequently, MIST avoids the need to solve a challenging, ill-conditioned nonlinear inverse-scattering problem. Early active microwave backscatter techniques were unsuccessful because they used a single antenna location for transmitting and receiving and thus had no possibility of spatially focusing the backscattered signal. The use of an antenna array and short pulses enables MIST to focus in both space and time. Thus, MIST significantly enhances the response from malignant lesions while minimizing clutter signals, thereby overcoming challenges presented by breast heterogeneity and enabling the detection of lesions as small as 1-2 mm. Note that resolution is not determined by the wavelength of the microwave excitation. Rather, the spatial extent of the array aperture measured in wavelengths and the temporal duration of the pulse are the dominant factors in determining the resolution limit.

[0028] Preliminary measurements suggest that the contrast between the dielectric properties of normal breast tissue and many benign lesions is negligible, in which case benign lesions would not act as strong microwave scatterers, allowing discrimination of benign and cancerous lesions. Furthermore, in contrast to conventional microwave tomography, MIST can also exploit morphology-dependent characteristics of lesions, such as spectral and polarization signatures, as well as the enhanced backscatter due to vascularization of malignant tumors, to further distinguish cancerous lesions from other scattering structures. In addition, change in lesion size is reflected in the backscattered spectral characteristics and signal-to-clutter ratio.

[0029] An exemplary space-time microwave imaging system in accordance with the invention which provides transmission and reception with the same antenna is shown generally at 20 in FIG. 1. The imaging system 20 includes a microwave signal generator 21 which is supplied, on a line 22, with clock pulses from a clock 23. The output of the signal generator 21, which as described below may be short broadband pulses or a signal synthesized from multiple discrete frequencies, is provided on a line 25 to a power amplifier 26, the output of which is provided on a line 27 to a directional coupler 28. The output of the directional coupler 28 is provided on a line 30 to a switching system 31 which selectively directs the power from the line 30 to lines 33 leading to each of the antennas 35 which are arranged in an array 36 of antennas (e.g., a rectangular or circular array). An array of antennas may be effectively provided by using one antenna 35 and moving it from position to position to collect data at each position, although the forming of a “virtual” array in this manner is not preferred. Further, the array may be formed to partially surround the object being imaged, for example, for use in breast imaging the array may formed to encircle the pendant breast. The antennas 35 and other microwave components should be wideband and preferably operate in the 1-10 GHz range. Examples of wideband antenna designs that may be utilized are the “bowtie” and Vivaldi type antennas and horn antennas designed for wideband operation. The switch 31 is formed to selectively provide a pulse of microwave power individually to the antennas 35 from the directional coupler 28 and to receive a signal from that antenna which is directed back through the switch 31 to the directional coupler 28. The directional coupler 28 sends the received signal on a line 38 to a low noise amplifier 40, the output of which is provided on a line 41 to a receiver 42. The receiver 42 also receives clock pulses on a line 43 from the clock 23. The clock pulses on the line 43 allow the receiver 42 to time the onset of pulses of microwave power supplied from the signal generator 21 to allow correlation in time of the received signal with respect to the transmitted signal. Alternatively, the power output from the signal generator 21 may be provided through a power splitter to the receiver 42 to allow time correlation. The signal generator 21, which may include a computer or digital processor, generates appropriately timed and shaped output pulses, discrete frequencies, etc., as required for the type of microwave transmission being utilized. The receiver 42 may be of conventional construction, providing detection of the received microwave signal and conversion of the detected signal to digitized data, e.g., with sampling of the received signal after each pulse to build up a digitized waveform, with the digitized data being provided to a digital signal processor of conventional design within the receiver 42 or to an appropriately programmed computer 44 (e.g., a general purpose PC, a dedicated digital signal processor, etc.) all of which will be referred to herein generally as a “computer.” It is understood that any type of computer that can be programmed to carry out the signal/data processing set forth herein may be utilized. The receiver 42 or the separate computer 44 processes the data to provide image data which may be displayed on a display device 45, such as a video display terminal, or which may be transmitted to a recording device 46 such as a magnetic disk or CD ROM for long-term storage, or transmitted for printout, further data processing, etc. In accordance with the invention, space-time beamforming is carried out in a computer in the receiver 42 or a separate computer 44 on the data received from the antennas, as described further below. Further, signal processing is preferably employed to carry out a reflection artifact subtraction process (e.g., for the skin interface response or the antenna response) to reduce the effect of the artifact response on the received image data. Signal processing may also be carried out to compensate for frequency dependent scattering. As an example only of commercial instruments that may be utilized, the signal generator 21, amplifiers 26 and 40, directional coupler 28, receiver 42 and clock 23 may be implemented in an Agilent Vector Network Analyzer model 8720 ES, particularly for the discrete frequency based approach, and the computer 44 may be connected to control the signal generator 21 and the switch 31.

[0030] A space-time microwave imaging system in accordance with the invention which may be utilized for simultaneous transmission from each antenna is shown generally at 50 in FIG. 2. The system 50 includes a signal generator 51 which receives a clock pulse on a line 52 from a clock 53. The output of the signal generator 51 is provided on a line 54 to signal processing circuitry 55 which distributes the microwave (e.g., pulse) output on lines 57 to power amplifiers 58. Each of the power amplifiers 58 provides its output on a line 59 to a directional coupler 60, the output of which is provided on a line 61 to an individual antenna 63. The antennas 63 are arranged to form an array 64 of antennas, e.g., a rectangular array of antennas arranged in rows and columns. The signal processing circuitry 55 distributes the pulse of microwave on each of its output lines 57 with frequency dependent filtering to provide the desired microwave radiation from the antenna array 64, e.g., focussing of radiated power from the array 64 to selected points in the target object. The signals picked up by each antenna 63 are transmitted back on the line 61 to the directional coupler 60. The directional couplers provide the received signals on lines 65 to low noise amplifiers 66, the outputs of which are provided on lines 68 to a receiver 70. The receiver 70 also receives the clock pulses from the clock 53 on a line 71 to allow the receiver 70 to time the received signals with respect to the transmitted signals. The receiver 70 detects the microwave signal on a line 68 and converts the received signal to digital waveform data which is processed by a digital signal processor or a computer 72 in accordance with the invention. The image data from the computer 72 or digital signal processor may be displayed, e.g., on a video display terminal 73, or provided to a storage device 74, e.g., CD ROM, magnetic disk, tape, etc. for long-term storage, or transmitted for other purposes.

[0031] Treatment for early-stage breast cancer typically involves a lumpectomy or partial mastectomy to remove the carcinoma and its margins, followed by radiation therapy to destroy any remaining cancer cells. For larger tumors, pre-operative chemotherapy may be used to shrink the tumor to conserve a larger portion of the breast. It is well known that the effect of radiation therapy and chemotherapy can be enhanced using microwave hyperthermia, that is, elevating the temperature of the cancerous tissue through microwave energy absorption. The persisting challenge in microwave hyperthermia, however, is to preferentially heat the cancerous tissue without harming superficial and surrounding healthy breast tissues. Sophisticated adaptive focusing algorithms have been developed for use in phased-array hyperthermia treatment, but they require the use of invasive feedback probes located within the tumor. MIST technology offers a non-invasive approach for maximizing power deposition within the tumor and minimizing power deposition elsewhere. The microwave backscatter signals obtained during a low-power MIST scan of the breast inherently contain the information needed to tightly focus a transmitted high-power microwave pulse at the site of a tumor. In this manner, space-time microwave application utilizing the system of FIG. 2, configured to focus the microwave radiation at the position of the detected tumor, can provide hyperthermia treatment to destroy small early-stage cancerous tumors without harming healthy tissue, thereby potentially eliminating the need for breast surgery and conventional radiation to the breast along with the accompanying side effects.

[0032] With reference to FIG. 3, an antenna array device which may be utilized in the microwave imaging system of the invention is shown generally at 80, having a face 81 over which are distributed multiple individual antennas 82 arranged in a two-dimensional array at known locations. The individual antenna elements 82 may have the “bow-tie” shape as shown or other shapes as desired. The array device 80 may be utilized as the antenna array 36 of FIG. 1, with the antenna elements 82 corresponding to the antennas 35, or as the antenna array 64 of FIG. 2, with the antenna elements 82 corresponding to the antennas 63. For purposes of illustration, the antenna array device 80 is also shown in FIG. 3 placed adjacent to the breast 85 or other portion of the body to be imaged, preferably utilizing a matching element 86, such as a liquid filled bag, which conforms to the contour of the breast or other part of the body being imaged to minimize air gaps and unwanted reflections of microwave energy. While the invention is illustrated herein with regard to breast imaging, it is understood that the present invention may be utilized for imaging other parts of the body of an individual.

[0033] To achieve the best resolution of the reconstructed image using the space-time focussing approach of the present invention, the radiated microwave pulse is preferably relatively short (e.g., about 100 ps), and thus has a wide band of frequency content, typically from 0 to 20 GHz and with significant energy in the frequency range of 1 GHz to 10 GHz. Thus, it is desirable to utilize antennas that are suitable for transmitting and receiving such short pulses with minimum distortion or elongation. It is desirable that the pulse radiating antenna have a constant sensitivity and a linear phase delay over the bandwidth of the incident electromagnetic pulse in the frequency domain. It is also desirable that the antenna design suppress both feed reflection and antenna ringing, and that the antenna have a smooth transition from the cable impedance at the feed point to the impedance of the immersion medium at the radiating end of the antenna. The return loss, S11, should be low in magnitude as less return loss means more power is transmitted to the antenna. Ideally, the return loss should be constant over the required bandwidth so that the spectrum of the transmitted power is flat and should have a linear phase delay across the frequency band so that the radiated waveform will not be dispersed. Other desirable properties include a well-defined polarization, constant gain, and low side lobes in the radiation pattern. Resistively loaded cylindrical and conical dipole (monopole), and bow-tie antennas can be utilized for radiating temporally short, broad bandwidth pulses. Resistive loading can be utilized to reduce the unwanted reflections that occur along the antenna and the associated distortion of the radiated signal. Spiral antennas and log-periodic antennas have also been designed to achieve wide bandwidth. Spectrum shaping and RF filtering may be needed to enhance the frequency performance of these antennas. Specialized antennas designed for pulse radiation may also be utilized. An example of a suitable antenna that is designed for short pulse radiation is shown and described in U.S. Pat. No. 6,348,898, issued Feb. 19, 2002.

[0034] As an example of the present invention, a MIST beamforming system was applied to simulated backscatter data generated from finite-difference time-domain (FDTD) computational electromagnetics simulations of microwave propagation in the breast. The anatomically realistic breast model was derived from a high-resolution 3-D breast MRI (magnetic resonance imaging) obtained during routine patient care at the University of Wisconsin Hospital and Clinics. The face-down images of the pendant breast were digitally rotated, vertically compressed, and laterally expanded to create high-resolution images of the naturally flattened breast of a patient in a supine position. Then, each voxel was assigned the appropriate values of ε_r, and σ. The 2-D model is incorporated into FDTD simulations for a co-linear 17-element monopole antenna array spanning 8 cm along the surface of the breast. Each antenna is excited with an ultrashort differentiated Gaussian pulse (temporal width of 110 ps, bandwidth of 9 GHz) and the backscattered response at the same antenna element is computed. This process is repeated for each element of the array, resulting in 17 received backscattered waveforms. The resulting FDTD-computed backscatter waveforms represent the scattering effects of heterogeneous normal breast tissue (clutter) and the malignant tumor (signal).

[0035] The skin response subtraction process estimates the skin component of the signal at each antenna as a filtered combination of the signals at all other antennas. The filter weights are chosen to minimize the residual signal over that portion of the received data dominated by the reflection from an interface with the object being imaged such as the skin-breast interface. The results show that the skin response effect is removed at the expense of energy from the tumor bleeding throughout the image. This occurs because the skin response subtraction algorithm used somewhat distorts the response from the tumor.

[0036] The beamformer algorithm utilized first time shifts the 17 received signals to approximately align the returns from a hypothesized scatterer at a candidate location. The time-aligned signals are passed through a bank of finite-impulse response (FIR) filters (one in each antenna channel), summed, and time gated and the power calculated to produce the beamformer output signal. The filters are designed using a least squares technique to present unit gain to scattered signals originating from the candidate location. This technique is described in B. Van Veen, et al., “Beamforming: A Versatile Approach to Spatial Filtering,” IEEE ASSP Magazine, Vol. Apr. 5, 1988, pp. 4-24; B. Van Veen, “Minimum Variance Beamforming, ” in Adaptive Radar Detection and Estimation, Ed. S. Haykin and A. Steinhardt, John Wiley and Sons; New York, Chapter 4, March, 1992, pp. 161-236. Hence, the beamformer output power represents an estimate of the energy scattered by that location. The beamformer is scanned to different locations in the breast by changing the time shifts, filter weights, and time gating. The output power may then be plotted as a function of scan location. Regions of large output power correspond to significant scatterers (e.g., malignant lesions).

[0037] A simulation was carried out to determine the scanned MIST output power for a 2-mm-diameter malignant tumor located 3 cm deep. For this study, the average dielectric-properties contrast between malignant and normal breast tissue in the numerical breast phantom is approximately 5:1. The heterogeneity of the normal breast tissue in the numerical breast phantom corresponds to variations in dielectric properties of ±10%, the upper bound on normal breast tissue variability that has been reported. The tumor was clearly detectable, as it stands out from the background clutter by 22 dB. MIST output power for two adjacent 2-mm-diameter tumors separated by 2 cm at a depth of 3 cm, showed two distinct scattering objects are clearly evident at the correct locations, demonstrating the potential resolving power of the present invention. A scenario under the worst-case assumption that the normal-tissue dielectric properties substantially exceed the published upper bound, thereby reducing the dielectric-properties contrast between malignant and normal tissue to less than 2:1, showed that even with significantly reduced contrast, the tumor was still easily detected, as the peak of the tumor response stands 11 dB above the largest background clutter.

[0038] The foregoing exemplary beamforming process incorporates frequency dependent propagation effects, but does not incorporate frequency dependent scattering effects. Scattering is frequency dependent due to dispersive dielectric properties and the presence of multiple scattering surfaces. Frequency dependent scattering broadens the received pulse duration, reducing resolution, and shifts the center of received energy in time, which causes scattered signal power to appear at an incorrect location. These errors may be compensated by processing the beamformer output signal from the filters prior to time gating using a parametric signal processing model for frequency dependent scattering effects. For example, autoregressive models may be used to describe the resonant behavior caused by finite tumor size.

[0039] Removal of the response from the skin-breast interface is critical for lesion detection, as this response is orders of magnitude larger than the tumor response. This response may be removed at the expense of some distortion of the tumor response. The distortion is known since it is a function of the weights used for skin response removal, allowing processing to be carried out for reducing or eliminating the tumor response distortion.

[0040] The skin response removal algorithm estimates the skin response at each antenna. The skin response is a known function of the skin thickness and the dielectric properties of the skin and breast. This fact may be exploited in processes for estimating these properties from the skin response. The average breast dielectric properties may then be used as a calibration step to choose the best beamformer design for each patient.

[0041] The methods described above assume only one antenna is transmitting and receiving at any point in time. This process involves sequentially stepping through the array. If an antenna array with multiple receive channels is used as shown in FIG. 2, then a multitude of different transmit-receive strategies are possible. Beamforming and skin response removal algorithms may be utilized in which all antennas receive simultaneously. Transmit strategies may also be utilized that focus the transmitted energy on a given region of the breast. The transmit and receive focus location is then scanned throughout the breast to form the image of scattered power. Such scanning may be utilized to improve resolution and robustness to artifacts, noise, and clutter. The signal parameters used to focus the transmission are the relative transmit time and signal amplitude in each antenna. After a lesion is located, the transmitted energy from the antennas may be focused on the lesion at a higher power level to heat and destroy the lesion.

[0042] Methods may be employed for assessing changes in lesion size from images obtained at different points in time. Both the spatial extent of the scattering region as well as the total power returned may increase from one scan to the next if the tumor undergoes angiogenesis and growth. Tracking this growth would be useful in the diagnosis of malignant lesions. Both the spatial extent of the scattering region and the total power returned may decrease if cancerous cells in the lesion are destroyed. Monitoring the decrease in lesion size would aid in assessing the effect of radiation therapy, chemotherapy, and/or thermotherapy. Use of absolute estimated tumor power is problematic due to expected variation from one measurement to the next. However, the peak tumor-to-clutter ratio should be robust to measurement variations and provide a reliable metric for assessing relative tumor size. Frequency dependent scattering effects will also vary with tumor size and provide another means for assessing changes over time.

[0043] An exemplary MIST sensor in the imaging system of the invention may include a microwave vector reflectometer (the pulse generator 21, 51 and receiver 42, 70, and may include the associated amplifiers and directional couplers) and a low-reverberation ultrawideband transmitting/receiving antenna. A low-noise commercial vector network analyzer (VNA) with a time-domain option may be used for the vector reflectometer. The dynamic range of a VNA of this type is sufficient to detect small malignant tumors up to depths of 5.0 cm in the breast.

[0044] The MIST strategy for detection is to identify the presence and location of strong scatterers in the breast, rather than to attempt to reconstruct the dielectric-properties profile of the breast interior. As a result, the MIST approach overcomes the fundamental computational limitations and related vulnerabilities to noise of conventional narrowband microwave tomography. The use of spatial and temporal focusing in MIST significantly enhances the response from malignant lesions while minimizing clutter signals, thereby overcoming challenges presented by breast heterogeneity. Space-time focusing achieves super-resolution, enabling the detection of extremely small (<5 mm in diameter) malignant lesions with harmless low-power microwave signals. In contrast to earlier examples of breast imaging using ultrawideband microwave-radar techniques, MIST employs sophisticated and robust frequency-dependent processing of microwave backscatter signals to obtain superior sensitivity for discriminating against artifacts and noise. The innovative system configuration eliminates the need for breast compression and permits the interior breast tissue to be imaged with the patient lying comfortably on her back. This uniquely enables MIST to detect tumors located near the chest wall or in the quadrant near the underarm where an estimated 50% of all breast tumors occur.

[0045] Reflection artifact removal (such as skin response removal), beam forming, and frequency-dependent scattering processes in accordance with the invention are discussed in further detail below. These processes may be carried out in a separate computer (e.g., the computer 44 of FIG. 1 or 72 of FIG. 2), or in a digital signal processor of the receiver (e.g., the receiver 42 of FIG. 1 or the receiver 70 of FIG. 2), both of which will be referred to herein as a computer, that is programmed to carry out the processing on the digitized waveform signal data for each antenna that is provided by the receiver.

[0046] The following describes the artifact removal and beamforming design method in mathematical expressions which are implemented in the computer and/or digital signal processors of the systems of FIGS. 1 and 2. Lower and upper case boldface Roman type is used to denote vector and matrix quantities, respectively. Superscript * represents the complex conjugate and superscripts T, H, and −1 represent the matrix transpose, complex conjugate transpose, and inverse, respectively.

[0047] Reflection Artifact Subtraction

[0048] A reflection artifact removal process is preferably carried out on the data received from the antennas to remove large reflection artifacts, such as the energy reflected from the ends of the antenna and feed and from the skin-breast interface. These reflections are typically orders of magnitude greater than the received backscatter signal. This reflection artifact removal or subtraction process will be described below for the example of removal of the skin-breast interface response. The skin response removal process forms an estimate of the response associated with the skin-breast interface and subtracts it from the recorded data. The response from the skin-breast interface is a function of the skin thickness, the dielectric properties of the skin, and the dielectric properties of the breast. Thus, the response from the skin-breast interface can be used to estimate these parameters. This is accomplished in general by expressing the response from the skin-breast interface as a parametric function of the unknown parameters and then choosing the unknown parameters to minimize the mean-squared error between the measured skin-breast response (the data) and the parametric function. That is, we choose the skin thickness and dielectric properties of the skin and breast so that the predicted response most closely approximates the actual measured response.

[0049] To illustrate this, consider the simple case in which the dielectric properties are assumed to be frequency independent, the skin-breast interface is assumed planar, and the transmitted signal propagates as a plane wave. To further simplify the illustration, we assume lossless propagation where the permittivity ε_r1 of the matching medium (e.g., the liquid matching medium 86 of FIG. 3) is known and the permittivity of the skin ε_r2 and the permittivity of the breast tissue ε_r3 are unknown. FIG. 4 illustrates the incident and reflected pulses at the skin/breast interface at four points in time, assuming an ultrashort microwave pulse. FIG. 5 illustrates the observed temporal waveform at the antenna which includes the pulse reflected from the matching medium/skin interface (Ref #1) and the pulse reflected from the skin/breast tissue interface (Ref #2) (in practice, these reflected pulses will overlap). Let v_inc (t)=v(t) represent the incident pulse. Then the first reflected pulse (Ref. #1) may be represented as 1

[0050] and the second reflected pulse (Ref #2) may be represented as 2

[0051] and c is the free space propagation velocity.

[0052] Hence, the observed waveform due to the incident pulse, the reflected pulse #1 and the reflected pulse #2 has the form r(t)=v(t)+a₁v(t−t₁)+a₂v(t−t₁−t₂) where v(t) is known.

[0053] We may correlate v(t) with r(t) and estimate t₁, a₁ from the second peak (in time) and a₂, t₂ from the third peak using standard time-delay/amplitude estimation techniques.

[0054] Given t₁, a₁, t₂, a₂ we may solve for d₁, d₂, {square root}{square root over (ε_r2)}, {square root}{square root over (ε_r3)} A as follows: 3$d_1=\frac{ct_1}{2\sqrt{{\varepsilon }_{\mathrm{r1}}}}\sqrt{{\varepsilon }_{\mathrm{r2<\; /mi>}}}=\frac{\left(1-a_1\right)}{\left(1+a_1\right)}\sqrt{{\varepsilon }_{\mathrm{r1}}}$

[0055] where

α=4{square root}{square root over (ε_r1)}({square root}{square root over (ε_r2)} )²β=4{square root}{square root over (ε_r1)}{square root}{square root over (ε_r2)}< /p>

δ=({square root}{square root over (ε_r1)}+{square root}{square root over (ε_r2)})^{2< /sup>}∂={square root}{square root over (ε_r2)}δ

[0056] There are many different techniques for estimating time delays and amplitudes of a known waveform that are well known. The same general methods for determining the dielectric properties may be applied to more realistic models of the skin-breast interface. The following discusses the preferred solution of the skin response removal problem in further detail.

[0057] Consider an array of N antennas and denote the received signal at the i^th antenna as b_i(t). Each received signal is converted to a sampled waveform, b_i[n], by an A/D converter in the receiver operating at a sampling frequency f_s. The received signal contains contributions from the skin-breast interface, clutter due to heterogeneity in the breast, the backscatter from lesions, and noise. The response from the skin-breast interface is orders of magnitude larger than the response from all other contributions and thus must be removed prior to performing tumor detection.

[0058] The skin artifacts in each of the N channels are similar but not identical due to local variations in skin thickness and breast heterogeneity. If the skin artifact for all channels were identical, one approach to remove it would be to subtract the average of the skin artifact across the N channels from each channel. In order to compensate for channel to channel variation in the skin artifact, the skin artifact at each antenna may be estimated as a filtered combination of the signal at all other antennas, as shown in FIG. 6. The signals from each of the other antennas are provided to FIR filters 90, the outputs of which are summed at 91 and subtracted at 92 from the signal from the particular antenna after a delay 94. The filter weights of the FIR filters 90 are chosen to minimize the residual signal mean-squared error over that portion of the received data dominated by the reflection from the skin-breast interface. Without loss of generality, suppose that the skin artifact is to be removed from the first antenna. Define the (2J+1)×1 vector of time samples in the i^th antenna channel as

b_i[n]=[b_i[n−J], . . . ,b_i[n], . . . ,b_i[n+J]] ^T, 2≦i≦N (1)

[0059] and let b_2N[n]=[b₂ ^T[n], . . . ,b_N^T [n]]^T be the concatenation of data in channels 2 through N. Similarly, let q_i be the (2J+1)×1 vector of FIR filter coefficients in the i^th channel and q=[q₂^T, . . . ,q_N^T ]^T be the concatenation of FIR (finite impulse response) filter coefficients from channels 2 through N. The optimal filter weight vector is chosen to satisfy 4

[0060] where n₀ is the time that approximates when the skin artifact begins and m is the duration of the received signal that is dominated by the skin artifact. The solution to this minimization problem is given by

q=R⁻¹p (3) 5

[0061] The fact that there is a high degree of correlation among the skin artifacts in the N channels results in the sample covariance matrix R being ill-conditioned. If R is ill-conditioned, then the matrix inversion in equation (3) can result in a solution for q that has very large norm and thus amplifies noise. In order to prevent this, we replace R with the low rank approximation 6

[0062] where λ_i,1≦i≦p, are the p significant eigenvalues and u_i,1≦i≦p, are the corresponding eigenvectors. The filter weight vector is determined by replacing R⁻¹ in equation (3) with 7

[0063] The skin artifact is then removed from the entire data record of the first channel to create artifact free data x₁[n] given by

x₁[n]=b₁[n]−q ^Tb_2N [n] (8)

[0064] This algorithm introduces a small level of distortion in the backscattered lesion signal because the backscattered lesion signals from the other N−1 channels are added back in to the first channel. This is explicitly shown by decomposing b₁[n] and b_2N[n], into a skin artifact s₁[n] and s_2N[n] and residuals d₁[n] and d_2N[n], respectively. The residual signals contain the backscattered response from the lesion. The values n₀ and m are chosen so that q is determined from a portion of the data in which the residuals are negligible and, thus,

s₁[n]−q^Ts< sub>2N[n]≈0 (9)

[0065] However, decomposing b₁[n] and b_2N[n] in equation (8) gives 8

[0066] Thus, the residual signal is distorted by q^Td_2N[n]. This term is generally small because q tends to “average” across channels and the lesion responses in d_2N[n] do not add in phase because they are not aligned in time. A simple method for reducing the distortion is to add a filtered version of the residual to obtain

{tilde over (x)}₁ [n]=x₁[n]+q^Tx _2N[n] (12)

[0067] where

x_2N[n]=[x₂[n−J], . . . ,x₂[n+J], . . . ,x_N[n−J], . . . ,x_N[n+J]] ^T (13)

[0068] is the vector containing the data from the other N-1 channels after the skin artifact has been removed from each of them. This addition of a filtered form of the residual is illustrated in FIG. 11 which includes FIR filters 145 to provide filtered signals that are summed at 146 to produce a signal added at 148 to the corrected data signal x₁[n] to provide an improved corrected signal data {tilde over (x)}₁[n].

[0069] FIG. 8 are example waveforms showing the effect of the skin response subtraction process, with the solid lines indicating the original waveforms and the dashed lines indicating the waveforms after skin artifact removal.

[0070] The artifact subtraction process can be applied only in the time domain. Thus, if frequency scanning is carried out using multiple discrete frequencies of the signals applied to the antennas, the received signal data must first be converted to the time domain (using an inverse FFT) prior to applying the artifact subtraction process.

[0071] The artifact removal process requires that all of the artifacts occur at the same relative times in the different channels. If the antennas are located at varying distances from the skin, the skin response will occur at different times. Thus, to apply the algorithm in general, the waveforms must first be time shifted so artifacts in all channels occur simultaneously. Aligning the artifacts in time is trivial because by nature the artifact is huge and it is easy to see when it starts.

[0072] The antenna reflection response will not vary in time in the different channels (assuming nearly identical antennas), so time alignment is not needed for removing it. The algorithm can simultaneously remove antenna artifact and skin reflection artifact, provided they are both time aligned in the waveforms. While this is true if the array is not the surface of the skin, it is not generally true if the distances to the skin differ for different antennas. In this case, one can apply the algorithm twice: first, to remove the antenna response, followed by time alignment of the residual skin response, and second remove the skin response.

[0073] There is one limitation with applying it twice, and that has to do with the other requirement of the algorithm, which requires the artifact to be the only contribution to the signal over a time interval that spans at least part of the artifact duration. Hence, if the antennas are varying distances from the skin, but in some channels the skin response completely overlaps (in time) the antenna response, it may not perform adequately.

[0074] Space-Time Beamforming

[0075] The image of backscattered power as a function of a location r is obtained by scanning each location with a different space-time beamformer. The beamformer for scan location r forms a weighted combination of time-delayed versions of a signal as shown in FIG. 7. Each of the signals x₁[n] from the antennas after subtraction of the skin response is passed through a time delay 97, a first time window 98, and an FIR filter 99. The outputs of the filters 99 are summed at 100. The summed output is passed through a second time window 102 to an energy calculation 103. The calculation of the energy in the signal over a consistent period of time provides a result which is proportional to power in the signal, and will be considered herein as the same as calculation of power. Preferably, the beamformer is designed to pass backscattered signals from the location r with unit gain, while attenuating signals from other locations.

[0076] For design purposes, assume that the received signal on the i^th channel is only comprised of the response due to a lesion at location r. Let this signal be denoted by x_i[n] having Fourier transform X_i(ω). Note that the received signal is

X_i(ω)=P(ω))V_i(r,ω) 1≦i≦N (14)

[0077] where P(ω) is the Fourier transform of the transmitted pulse p(t) and V_i(r,ω) is the frequency response of the electromagnetic model representing frequency dependent propagation and scattering effects. The i^th sampled waveform is then delayed by an integer number of samples n_i(r)=n_a−τ_i(r), resulting in the waveforms in each channel being approximately aligned in time. The average time τ_i(r) denotes the roundtrip propagation delay for location r in the i^th channel, computed by dividing the roundtrip path length by the average speed of propagation and rounding to the nearest sample, and n_a is the reference time to which all received signals are aligned. We choose n_a as the worst case delay over all channels and locations, that is, 9

[0078] The time aligned signals are windowed before the filtering stage, to remove interference and clutter prior to n_a that could contribute to the FIR filter outputs, using the window function 10

[0079] The FIR filter in the i^th channel has coefficients represented by the L×1 vector w_i. The FIR filters equalize path length dependent dispersion and attenuation, interpolate any fractional time delays after time shifting, and bandpass filter the signal. The frequency response of each filter can be written as 11