B.D. Van Veen

Localization of brain electrical activity via linearly constrained minimum variance spatial filtering

A spatial filtering method for localizing sources of brain electrical activity from surface recordings is described and analyzed. The spatial filters are implemented as a weighted sum of the data recorded at different sites. The weights are chosen to minimize the filter output power subject to a linear constraint. The linear constraint forces the filter to pass brain electrical activity from a specified location, while the power minimization attenuates activity originating at other locations. The estimated output power as a function of location is normalized by the estimated noise power as a function of location to obtain a neural activity index map. Locations of source activity correspond to maxima in the neural activity index map. The method does not require any prior assumptions about the number of active sources of their geometry because it exploits the spatial covariance of the source electrical activity. This paper presents a development and analysis of the method and explores its sensitivity to deviations between actual and assumed data models. The effect on the algorithm of covariance matrix estimation, correlation between sources, and choice of reference is discussed. Simulated and measured data is used to illustrate the efficacy of the approach.

Microwave imaging via space-time beamforming for early detection of breast cancer

A method of microwave imaging via space-time (MIST) beamforming is proposed for detecting early-stage breast cancer. An array of antennas is located near the surface of the breast and an ultrawideband (UWB) signal is transmitted sequentially from each antenna. The received backscattered signals are passed through a space-time beamformer that is designed to image backscattered signal energy as a function of location. The beamformer spatially focuses the backscattered signals to discriminate against clutter and noise while compensating for frequency-dependent propagation effects. As a consequence of the significant dielectric-properties contrast between normal and malignant tissue, localized regions of large backscatter energy levels in the image correspond to malignant tumors. A data-adaptive algorithm for removing artifacts in the received signals due to backscatter from the skin-breast interface is also presented. The effectiveness of these algorithms is demonstrated using a variety of numerical breast phantoms based on anatomically realistic MRI-derived FDTD models of the breast. Very small (2 mm) malignant tumors embedded within the complex fibroglandular structure of the breast are easily detected above the background clutter. The MIST approach is shown to offer significant improvement in performance over previous UWB microwave breast cancer detection techniques based on simpler focusing schemes.

Microwave imaging via space-time beamforming: experimental investigation of tumor detection in multilayer breast phantoms

Microwave imaging via space-time (MIST) beamforming has been proposed recently for detecting small malignant breast tumors. In this paper, we extend the previously presented two-dimensional space-time beamformer design to three-dimensional (3-D), and demonstrate its efficacy using experimental data obtained with a multilayer breast phantom. The breast phantom consists of a homogeneous normal breast tissue simulant covered by a thin layer of skin simulant. A small synthetic malignant tumor is embedded in the breast phantom. We have developed several tumor simulants that yield the range of dielectric contrasts between normal and malignant tissue that are expected in clinical scenarios. A microwave sensor comprised of a synthetic planar array of compact ultrawide-band (UWB) antennas is immersed in a coupling medium above the breast tissue phantom. At each position in the array, the antenna transmits a synthetically generated pulse (1-11 GHz) into the phantom. The received backscatter signals are processed by a data-adaptive algorithm that removes the artifact caused by antenna reverberation and backscatter from the skin-breast interface, followed by 3-D space-time beamforming to image backscattered energy as a function of location. Our investigation includes a numerical (finite difference time domain) and experimental study of the UWB antenna performance in the immersion medium, as well as a study of the influence of malignant-to-normal breast tissue dielectric contrast on dynamic range requirements and tumor detectability. This paper represents the first experimental demonstration of 3-D MIST beamforming in multilayer breast phantoms with malignant-to-normal dielectric contrasts down to 1.5 : 1 for a 4-mm synthetic tumor.

Development of Anatomically Realistic Numerical Breast Phantoms With Accurate Dielectric Properties for Modeling Microwave Interactions With the Human Breast

Computational electromagnetics models of microwave interactions with the human breast serve as an invaluable tool for exploring the feasibility of new technologies and improving design concepts related to microwave breast cancer detection and treatment. In this paper, we report the development of a collection of anatomically realistic 3-D numerical breast phantoms of varying shape, size, and radiographic density which can readily be used in finite-difference time-domain computational electromagnetics models. The phantoms are derived from T1-weighted MRIs of prone patients. Each MRI is transformed into a uniform grid of dielectric properties using several steps. First, the structure of each phantom is identified by applying image processing techniques to the MRI. Next, the voxel intensities of the MRI are converted to frequency-dependent and tissue-dependent dielectric properties of normal breast tissues via a piecewise-linear map. The dielectric properties of normal breast tissue are taken from the recently completed large-scale experimental study of normal breast tissue dielectric properties conducted by the Universities of Wisconsin and Calgary. The comprehensive collection of numerical phantoms is made available to the scientific community through an online repository.

Breast Tumor Characterization Based on Ultrawideband Microwave Backscatter

Characterization of architectural tissue features such as the shape, margin, and size of a suspicious lesion is commonly performed in conjunction with medical imaging to provide clues about the nature of an abnormality. In this paper, we numerically investigate the feasibility of using multichannel microwave backscatter in the 1-11 GHz band to classify the salient features of a dielectric target. We consider targets with three shape characteristics: smooth, microlobulated, and spiculated; and four size categories ranging from 0.5 to 2 cm in diameter. The numerical target constructs are based on Gaussian random spheres allowing for moderate shape irregularities. We perform shape and size classification for a range of signal-to-noise ratios (SNRs) to demonstrate the potential for tumor characterization based on ultrawideband (UWB) microwave backscatter. We approach classification with two basis selection methods from the literature: local discriminant bases and principal component analysis. Using these methods, we construct linear classifiers where a subset of the bases expansion vectors are the input features and we evaluate the average rate of correct classification as a performance measure. We demonstrate that for 10 dB SNR, the target size is very reliably classified with over 97% accuracy averaged over 360 targets; target shape is classified with over 70% accuracy. The relationship between the SNR of the test data and classifier performance is also explored. The results of this study are very encouraging and suggest that both shape and size characteristics of a dielectric target can be classified directly from its UWB backscatter. Hence, characterization can easily be performed in conjunction with UWB radar-based breast cancer detection without requiring any special hardware or additional data collection.

Random and pseudorandom inputs for Volterra filter identification

This paper studies input signals for the identification of nonlinear discrete-time systems modeled via a truncated Volterra series representation. A Kronecker product representation of the truncated Volterra series is used to study the persistence of excitation (PE) conditions for this model. It is shown that i.i.d. sequences and deterministic pseudorandom multilevel sequences (PRMSs) are PE for a truncated Volterra series with nonlinearities of polynomial degree N if and only if the sequences take on N+1 or more distinct levels. It is well known that polynomial regression models, such as the Volterra series, suffer from severe ill-conditioning if the degree of the polynomial is large. The condition number of the data matrix corresponding to the truncated Volterra series, for both PRMS and i.i.d. inputs, is characterized in terms of the system memory length and order of nonlinearity. Hence, the trade-off between model complexity and ill-conditioning is described mathematically. A computationally efficient least squares identification algorithm based on PRMS or i.i.d. inputs is developed that avoids directly computing the inverse of the correlation-matrix. In many applications, short data records are used in which case it is demonstrated that Volterra filter identification is much more accurate using PRMS inputs rather than Gaussian white noise inputs. >

Ultrawideband microwave breast cancer detection: a detection-theoretic approach using the generalized likelihood ratio test

Microwave imaging has been suggested as a promising modality for early-stage breast cancer detection. In this paper, we propose a statistical microwave imaging technique wherein a set of generalized likelihood ratio tests (GLRT) is applied to microwave backscatter data to determine the presence and location of strong scatterers such as malignant tumors in the breast. The GLRT is formulated assuming that the backscatter data is Gaussian distributed with known covariance matrix. We describe the method for estimating this covariance matrix offline and formulating a GLRT for several heterogeneous two-dimensional (2-D) numerical breast phantoms, several three-dimensional (3-D) experimental breast phantoms, and a 3-D numerical breast phantom with a realistic half-ellipsoid shape. Using the GLRT with the estimated covariance matrix and a threshold chosen to constrain the false discovery rate (FDR) of the image, we show the capability to detect and localize small (<0.6 cm) tumors in our numerical and experimental breast phantoms even when the dielectric contrast of the malignant-to-normal tissue is below 2:1.

Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms

The detection of early-stage tumors in the breast by microwave imaging is challenged by both the moderate endogenous dielectric contrast between healthy and malignant glandular tissues and the spatial resolution available from illumination at microwave frequencies. The high endogenous dielectric contrast between adipose and fibroglandular tissue structures increases the difficulty of tumor detection due to the high dynamic range of the contrast function to be imaged and the low level of signal scattered from a tumor relative to the clutter scattered by normal tissue structures. Microwave inverse scattering techniques, used to estimate the complete spatial profile of the dielectric properties within the breast, have the potential to reconstruct both normal and cancerous tissue structures. However, the ill-posedness of the associated inverse problem often limits the frequency of microwave illumination to the UHF band within which early-stage cancers have sub-wavelength dimensions. In this computational study, we examine the reconstruction of small, compact tumors in three-dimensional numerical breast phantoms by a multiple-frequency inverse scattering solution. Computer models are also employed to investigate the use of exogenous contrast agents for enhancing tumor detection. Simulated array measurements are acquired before and after the introduction of the assumed contrast effects for two specific agents currently under consideration for breast imaging: microbubbles and carbon nanotubes. Differential images of the applied contrast demonstrate the potential of the approach for detecting the preferential uptake of contrast agents by malignant tissues.

Eigenstructure based partially adaptive array design

A procedure is presented for designing partially adaptive arrays having nearly fully adaptive performance under steady-state conditions. Theory predicts that the required adaptive dimension is less than or equal to the rank of the spatially/temporally correlated portion of the interference correlation matrix for arbitrary linearly constrained minimum-variance beamformers. Knowledge of the eigenstructure of the interference correlation matrix is required to implement a beamformer with this adaptive dimension. To avoid adaptive estimation of the eigenstructure, the eigenstructure of an averaged correlation matrix (which spans the interference scenarios of interest) is utilized, and the adaptive dimension is given by the rank of the averaged correlation matrix. Construction of a transformation for reducing adaptive dimension is addressed. Simulations illustrating the utility of the eigenstructure approach are provided. >

Partially adaptive beamformer design via output power minimization

The computational complexity of fully adaptive arrays employing thousands of sensors is often prohibitive and, thus, one is led to processors which only use a fraction of the available adaptive degrees of freedom. We present an optimal approach to the design of a transformation that maps the fully adaptive space into a partially adaptive space based on minimization of output interference power. The design procedure allows for incorporation of a priori knowledge of interference characteristics, applies to arbitrary array geometries and interference scenarios, and results in unconstrained adaptive processor implementations. Examples are presented illustrating the effectiveness of the new partially adaptive processors against broad-band interference.