Contrast-enhanced microwave imaging of breast tumors: a computational study using 3-D 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.

Maximum likelihood dipole fitting in spatially colored noise.

We evaluated a maximum likelihood dipole-fitting algorithm for somatosensory evoked field (SEF) MEG data in the presence of spatially colored noise. The method exploits the temporal multiepoch structure of the evoked response data to estimate the spatial noise covariance matrix from the section of data being fit, which eliminates the stationarity assumption implicit in prestimulus based whitening approaches. The performance of the method, including its effectiveness in comparison to other localization techniques (dipole fitting, LCMV and MUSIC) was evaluated using the bootstrap technique. Synthetic data results demonstrated robustness of the algorithm in the presence of relatively high levels of noise when traditional dipole fitting algorithms fail. Application of the algorithm to adult somatosensory MEG data showed that while it is not advantageous for high SNR data, it definitely provides improved performance (measured by the spread of localizations) as the data sample size decreases.

Linearly constrained minimum variance source imaging using cortical bases.

An approach is presented for representing spatially extended cortical activity using a basis function expansion. The bases are designed to represent patches on the cortical surface. The basis function expansion coefficients are estimated for each patch by scanning modified linearly constrained minimum variance (LCMV) spatial filters over the entire surface. Next, a generalized likelihood ratio test (GLRT) is performed to detect patches with significant activity. In the last step, an image of the activity within each patch is reconstructed using a minimum norm solution to a local inverse problem. We show that the basis function representation enables the LCMV approach to identify patches of coherent activity that are missed by the conventional LCMV method and has potential for extended source detection and localization.

Nonlinear functional modeling of scalp recorded auditory evoked responses to maximum length sequences.

The purpose of this study was to model the adult human's scalp recorded evoked response to auditory pulses separated by varying inter pulse intervals (IPIs). The responses modeled probably reflect auditory nerve and brainstem generators. The subjects were 10 young adult humans with normal hearing. They were presented pseudo random sequences of pulses (maximum length sequences, MLSs) in order to characterize their system response. For the stimuli and the responses modeled accounting for temporal nonlinearities (interactions among the pulses) improved model performance only marginally. Nonlinear contributions to the models decreased with increasing interval between the input pulses. Increasing the memory of the model beyond 20 ms did not increase modeled performance dramatically. Model performance varied as a function of minimum IPI (MIPI) of the MLSs. At the shortest MIPI overall model performance deteriorated (due, in part, to a decrease in SNR), but nonlinear effects became relatively more important. At the longest MIPI performance also deteriorated, possibly due to the increasing influence of longer latency, more variable evoked potential components. Modeled performance generalized to responses recorded in the same recording session to the same and different MLSs. This study confirms the similarity between MLS linear kernels and conventionally averaged evoked responses--both are adapted responses reflecting the IPIs of the evoking stimuli.

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.

A spatial feature extraction and regularization model for the head-related transfer function.

A functional representation is proposed for complex valued (amplitude and phase) head-related transfer functions (HRTFs), including both frequency and spatial dependence. The frequency variation is spanned by a set of eigentransfer functions (EFs) that are generated using the Karhunen-Loève expansion. Any HRTF is represented as a weighted combination of the EFs where the weights are functions of the HRTFs spatial location and are termed spatial characteristic functions (SCFs). Samples of the SCFs are obtained by projecting the measured HRTFs onto the EFs. A regularization framework is employed to obtain a functional representation for the SCFs by fitting each set of SCF samples with a two-dimensional spline. Acoustic validation of the model's fidelity and predictive capability is provided using 2188 measured HRTFs from a KEMAR manikin and 1816 measured HRTFs from an anesthetized live cat. Errors between measured and modeled HRTFs are generally less than one percent. Larger errors occur in the contralateral regions for KEMAR and lower back regions for the cat as a consequence of the relatively small HRTF amplitudes resulting from head shadowing. Methods for reducing these errors are discussed.

A framework for assessing the relative efficiency of stimulus sequences in evoked response measurements.

A general matrix-based framework for characterizing the performance of cross-correlation techniques for recovering the response to an arbitrary stimulus sequence is presented. In general an infinite number of recovery sequences can be identified for any given stimulus sequence. The recovery sequence that minimizes the noise in the recovered response is derived and the effect of the recovery operation on the noise is analyzed. This general framework is employed to develop analytic expressions for the relative efficiencies of conventional signal averaging and binary MLS based methods for the most commonly used recovery operation and the one that optimizes SNR assuming the background noise is uncorrelated. The results depend on the ratio of response length to MLS minimum pulse interval and the amplitude loss as a function of stimulus rate. Examples based on measured amplitude loss functions for ABR recordings are employed to evaluate the relative efficiencies of MLS techniques. When the noise is uncorrelated conventional signal averaging is from two to five times as efficient as MLS techniques. The relative advantage of averaging is shown to decrease when the noise is dominated by low-frequency components.

External ear transfer function modeling: a beamforming approach.

In this article, a beamformer is proposed as a functional model for the spatial and temporal filtering characteristics of the external ear. The output of a beamformer is a weighted combination of the data received at an array of spatially distributed sensors. The beamformer weights and array geometry determine its spatial and temporal filtering characteristics. A procedure is described for choosing the weights to minimize the mean-squared error between the beamformer response and the measured response of the external ear. The effectiveness of the model is demonstrated by designing a beamformer of several hundred weights that duplicates and interpolates the measured external ear response of a cat over broad ranges of frequency and direction. A limited investigation of modeling performance as a function of array geometry is reported.

Auditory space expansion via linear filtering.

A signal-processing algorithm that modifies the interaural time delays associated with directional sources is described. Signals received at two microphones are processed by four linear filters arranged in a lattice configuration to produce two outputs, one for each ear. Since the processing is linear, the method is equally applicable to single or multiple directional sources. The filters are designed to minimize the average squared error between a user specified desired space warping function and the actual warping function that they implement. Two classes of filters are considered: filters whose frequency response is unconstrained and filters constrained to be causal with finite impulse response. In both cases the solution of the least-squares problem is given and properties of the actual space warping function are examined. Perceptual experiments and analysis of acoustic waveforms are utilized to demonstrate the effectiveness of the algorithm. Extension of this method for utilizing more than two microphones is described.