Confocal microwave imaging for breast cancer detection: delay-multiply-and-sum image reconstruction algorithm

A new image reconstruction algorithm, termed as delay-multiply-and-sum (DMAS), for breast cancer detection using an ultra-wideband confocal microwave imaging technique is proposed. In DMAS algorithm, the backscattered signals received from numerical breast phantoms simulated using the finite-difference time-domain method are time shifted, multiplied in pair, and the products are summed to form a synthetic focal point. The effectiveness of the DMAS algorithm is shown by applying it to backscattered signals received from a variety of numerical breast phantoms. The reconstructed images illustrate improvement in identification of embedded malignant tumors over the delay-and-sum algorithm. Successful detection and localization of tumors as small as 2 mm in diameter are also demonstrated.     

A confocal microwave imaging algorithm for breast cancer detection

We present a computationally efficient and robust image reconstruction algorithm for breast cancer detection using an ultrawideband confocal microwave imaging system. To test the efficacy of this approach, we have developed a two-dimensional (2-D) anatomically realistic MRI-derived FDTD model of the cancerous breast. The image reconstruction algorithm is applied to FDTD-computed backscatter signals, resulting in a microwave image that clearly identifies the presence and location of the malignant lesion. These simulations demonstrate the feasibility of detecting and imaging small breast tumors using this novel approach     

A simplified first-order reconstruction algorithm for microwave tomography

A first-order reconstruction algorithm for microwave tomographic imaging has been developed considering the wave nature of the probing signal. The algorithm has been simplified by neglecting mutual interaction terms. The traditional ray theory which is successfully applied in X-ray and ultrasound tomography, is totally inadequate to explain different electromagnetic phenomena, for example, scattering, diffraction and boundary reflections. A beam concept has been introduced in developing the algorithm. The results of applying the algorithm on a small biological model containing bone, muscle and muscle-like materials have been extremely encouraging indicating the possibility of development of a microwave imaging scheme. The image, however, at present is not as perfect as it should have been from clinical point of view, most probably due to the simplifying assumptions made in developing the algorithm.     

Experimental validation of a PO-based shape reconstruction algorithm

The effectiveness of a linear inverse scattering algorithm for the shape reconstruction of perfectly conducting objects is experimentally validated by processing measured data. The data are collected via an automatic system for free-space measurements under reflection mode geometry. The amplitude and phase of the scattered field is measured in a multistatic and multifrequency configuration for different locations (views) of the transmitting antenna. The reliability of the measurement setup is shown by a comparison with simulated data. No a priori knowledge of the shape of the scatterers is assumed. The results of inversions of experimental data collected under single-view illumination agree well with those of inversions of synthetic data, so showing the robustness of the algorithm.     

A reconstruction algorithm for breast cancer imaging with electrical impedance tomography in mammography geometry

The conductivity and permittivity of breast tumors are known to differ significantly from those of normal breast tissues, and electrical impedance tomography (EIT) is being studied as a modality for breast cancer imaging to exploit these differences. At present, X-ray mammography is the primary standard imaging modality used for breast cancer screening in clinical practice, so it is desirable to study EIT in the geometry of mammography. This paper presents a forward model of a simplified mammography geometry and a reconstruction algorithm for breast tumor imaging using EIT techniques. The mammography geometry is modeled as a rectangular box with electrode arrays on the top and bottom planes. A forward model for the electrical impedance imaging problem is derived for a homogeneous conductivity distribution and is validated by experiment using a phantom tank. A reconstruction algorithm for breast tumor imaging based on a linearization approach and the proposed forward model is presented. It is found that the proposed reconstruction algorithm performs well in the phantom experiment, and that the locations of a 5-mm-cube metal target and a 6-mm-cube agar target could be recovered at a target depth of 15 mm using a 32 electrode system.     

基于轨迹位置形状相似性的隐私保护算法

为了降低轨迹数据发布产生的隐私泄露风险,提出了多种轨迹匿名算法。然而,现有的轨迹匿名算法在计算轨迹相似性时忽略了轨迹的形状因素对轨迹相似性的影响,因此产生的匿名轨迹集合的可用性相对较低。针对这一问题,提出了一种新的轨迹相似性度量模型,在考虑轨迹的时间和空间要素的同时,加入了轨迹的形状因素,可以在多项式时间内计算定义在不同时间跨度上的轨迹的距离,能够更加准确、快速地度量轨迹之间的相似性;在此基础上,提出了一种基于轨迹位置形状相似性的隐私保护算法,最大限度地提高了聚类内部轨迹的相似性,并且使用真实的原始位置信息形成数据"面罩",满足了轨迹k-匿名,在有效地保护轨迹数据的同时,提高了轨迹数据的可用性;最后,在合成轨迹数据集和真实轨迹数据集上的实验结果表明,本算法花费更少的时间代价,具有更高的数据可用性。     

Spherical harmonics and Earth-rotation synthesis in radio astronomy

That spherical harmonic functionsY_{nm}(theta,phi)can be used to advantage in the Earth-rotation synthesis of radio astronomy maps is shown in this paper. As Earth rotates the baseline of a radio interferometer generates a cone whose angletheta, measured from theN-Spolar axis, can be varied by changing the baseline's azimuthal direction on the surface of Earth. A series of Earth-rotation measurements, at different cone angles but with baselines of equal lengthb, can be regarded as being made on a baseline sphere of radiusb, the analog of theuvplane in Fourier-type synthesis. The measured output distribution can be expanded as a spherical harmonic series on the baseline sphere. The coefficients of the series are related to the coefficients of the spherical harmonic series expansion of the source distribution on the celestial sphere by a matrix transformation. The matrix [B] is a function only of the baseline configuration (it does not vary with source declination). Inversion of the matrix leads to the solution for the source coefficients, from which a spherical harmonic map is formed of the source distribution.     

Nonlinear extension to a moment method iterative reconstruction algorithm for microwave tomography

An iterative nonlinear algorithm for microwave image reconstruction based on moment method solutions to field problems has been suggested. The algorithm has been simplified significantly considering the effects due to the dominant nonlinear terms only. The results obtained using it have been compared with those reported earlier using a simpler algorithm.     

Multistatic adaptive microwave imaging for early breast cancer detection

We propose a new multistatic adaptive microwave imaging (MAMI) method for early breast cancer detection. MAMI is a two-stage robust Capon beamforming (RCB) based image formation algorithm. MAMI exhibits higher resolution, lower sidelobes, and better noise and interference rejection capabilities than the existing approaches. The effectiveness of using MAMI for breast cancer detection is demonstrated via a simulated 3-D breast model and several numerical examples.     

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.     

A constrained modulus reconstruction technique for breast cancer assessment

A reconstruction technique for breast tissue elasticity modulus is described. This technique assumes that the geometry of normal and suspicious tissues is available from a contrast-enhanced magnetic resonance image. Furthermore, it is assumed that the modulus is constant throughout each tissue volume. The technique, which uses quasi-static strain data, is iterative where each iteration involves modulus updating followed by stress calculation. Breast mechanical stimulation is assumed to be done by two compressional rigid plates. As a result, stress is calculated using the finite element method based on the well-controlled boundary conditions of the compression plates. Using the calculated stress and the measured strain, modulus updating is done element-by-element based on Hooke's law. Breast tissue modulus reconstruction using simulated data and phantom modulus reconstruction using experimental data indicate that the technique is robust.     

Solutions to the two-dimensional boundary value problem for microwave breast tumor detection

This letter presents a noninvasive microwave application method for breast tumor detection. Forward equations are developed using the signals' scattering effect at the presence of an object inside the breast model. It is shown how the complex backscattered signals which characterize the internal material properties are analyzed using cylindrical coordinates to obtain required information. The algorithm developed to solve the inverse problem can compute the unknown tumor size and its location inside the breast model.     

Predicting tumor location by modeling the deformation of the breast

Breast cancer is one of the biggest killers in the western world, and early diagnosis is essential for improved prognosis. The shape of the breast varies hugely between the scenarios of magnetic resonance (MR) imaging (patient lies prone, breast hanging down under gravity), X-ray mammography (breast strongly compressed) and ultrasound or biopsy/surgery (patient lies supine), rendering image fusion an extremely difficult task. This paper is concerned with the use of the finite-element method and nonlinear elasticity to build a 3-D, patient-specific, anatomically accurate model of the breast. The model is constructed from MR images and can be deformed to simulate breast shape and predict tumor location during mammography or biopsy/surgery. Two extensions of the standard elasticity problem need to be solved: an inverse elasticity problem (arising from the fact that only a deformed, stressed, state is known initially), and the contact problem of modeling compression. The model is used for craniocaudal mediolateral oblique mammographic image matching, and a number of numerical experiments are performed.     

Novel EIS postprocessing algorithm for breast cancer diagnosis

A new postprocessing algorithm was developed for the diagnosis of breast cancer using electrical impedance scanning. This algorithm automatically recognizes bright focal spots in the conductivity map of the breast. Moreover, this algorithm discriminates between malignant and benign/normal tissues using two main predictors: phase at 5 kHz and crossover frequency, the frequency at which the imaginary part of the admittance is at its maximum. The thresholds for these predictors were adjusted using a learning group consisting of 83 carcinomas and 378 benign cases. In addition, the algorithm was verified on an independent test group including 87 carcinomas, 153 benign cases and 356 asymptomatic cases. Biopsy was used as gold standard for determining pathology in the symptomatic cases. A sensitivity of 84% and a specificity of 52% were obtained for the test group.     

Time reversal with the FDTD method for microwave breast cancer detection

The feasibility of microwave breast cancer detection with a time-reversal (TR) algorithm is examined. This algorithm is based on the finite-difference time-domain method, and compensates for the wave decay and, therefore, is suitable for lossy media. In this paper, we consider a two-dimensional breast model based on magnetic resonance imaging data, and examine the focusing abilities of a TR mirror comprised of an array of receivers with a single ultra-wideband pulse excitation. In order to resolve small 3-mm-diameter tumors, a very short duration pulse is necessary, and this requirement may restrict the applicability of the system due to hardware limitations. We propose a way to overcome this obstacle based on the observation that the amplitude and phase information of the tumor response is sufficient to achieve focusing. The robustness of the TR algorithm with respect to breast inhomogeneities is demonstrated, and the good performance of the method suggests it is a promising technique for microwave breast cancer detection.     

A matched-filter FDTD-based time reversal approach for microwave breast cancer detection

Based on the finite-difference time-domain (FDTD) method, a numerical time-reversal (TR) algorithm for microwave breast cancer detection, already presented in previous work , , is further examined. In , we assumed that the exact field scattered from the tumor-like anomaly is available for backpropagation, and it was shown that the time reversal process is robust to breast inhomogeneities and uncertainties of the skin thickness or electric properties. In this paper, we use the same time reversal mirror (TRM) and two-dimensional (2-D) breast model based on magnetic resonance imaging (MRI) data, but examine the realistic situation where the target response is not known and can only be estimated from the total signal, which is dominated by clutter. A matched-filter approach to solve this signal processing problem is proposed and applied to the TRM data. Detection and localization is achieved for different target locations, and the ability of the time reversal algorithm to avoid false alarms is demonstrated.     

Computational modeling of three-dimensional microwave tomography of breast cancer

Microwave tomographic approach is proposed to detect and image breast cancers. Taking into account the big difference in dielectrical properties between normal and malignant tissues, we have proposed using the microwave tomographic method to image a human breast. Because of the anatomical features of the objects, this case has to be referred to the tomography with a limited angle of observation. As a result of computer experiments we have established that multiview cylindrical configurations are able to provide microwave tomograms of the breast with a small size tumor inside. Using the gradient method, we have developed a computer code to create images of the three-dimensional objects in dielectrical properties on microwave frequencies.     

Measurement of magnitude and phase of harmonics generated innonlinear microwave two-ports

A method for simultaneously measuring the magnitude and phase of the harmonics generated by a microwave two-port is reported. The two-port under test is driven with a sinusoidal microwave signal strong enough to force it into nonlinear operation. Its output harmonics are measured in the frequency domain with a setup that includes a vector network analyzer. For phase calibration at the harmonic frequencies, a millimeter-wave Schottky diode is used as a reference device. The system allows the measurement of harmonics with a phase accuracy of about ±10° at 20 GHz (referred to f₁=5 GHz). It can be built for any frequency (<40 GHz) at which a vector network analyzer and a suitable signal generator with multiplier are available. For low-amplitude harmonics, higher sensitivity compared to time-domain measurements with a sampling scope results in better measurement accuracy. The accuracy should improve further if the nonideality of the diode reference circuit is characterized more precisely     

Microwave holograms and microwave reconstruction

Microwave holographic reconstruction of the metal objects inside a purse was achieved by a nonscanning method. A microwave field was used for both constructing and reconstructing the holographic image. The visualisation of the microwave field was performed by both Polaroid and liquid-crystal techniques. The frequency used was 34.26GHz.     

乳腺癌检测的三维时域微波断层成像方法

应用泛函分析和变分法,改进拉格朗日(Lagrange)乘子算法为一种三维时域微波断层成像方法,用于检测早期乳腺癌。该方法首先以最小二乘准则构造目标函数,将反演问题表示为约束最小化问题;接着应用罚函数法转化为无约束最小化问题;然后基于变分计算导出闭式的拉格朗日函数关于相对介电常数和电导率的Fréchet导数;最后借助梯度算法和时域有限差分(FDTD)法迭代求解。为了对抗噪声污染和逆问题的病态特性,采用了一阶的吉洪诺夫(Tikhonov)正则化方法。利用FDTD和PRP共轭梯度(CG)法,对三维半球乳房模型进行了仿真计算,仿真结果显示了方法的可行性。