Xiao-Liang Xu

Quantitative comparisons of image registration techniques based on high-resolution MRI of the brain.

Objective A variety of methods for matching intrasubject MRI-MRI, PET-PET, or MRI-PET image pairs have been proposed. Based on the rigid body transformations needed to align pairs of high-resolution MRI scans and/or simulated PET scans (derived from these MRI scans), we obtained general comparisons of four intrasubject image registration techniques: Talairach coordinates, head and hat, equivalent internal points, and ratio image uniformity. In addition, we obtained a comparison of stereotaxic Z frames with a customized head mold for MRI-MRI image pairs. Materials and Methods and Results Each technique was quantitatively evaluated using the mean and maximum voxel registration errors for matched voxel pairs within the brain volumes being registered. Conclusion We conclude that fiducial markers such as stereotaxic Z frames that are not rigidly fixed to a patients skull are inaccurate compared with other registration techniques, Talairach coordinate transformations provide surprisingly good registration, and minimizing the variance of MRI-MRI, PET-PET, or MRI-PET ratio images provides significantly better registration than all other techniques tested. Registration optimization based on measurement of the similarity of spatial distributions of voxel values is superior to techniques that do not use such information.

Spatial-spectrum estimation in a location sector

Multiple narrowband source localization using arbitrarily configured arrays and spatial-spectrum estimation is considered. A new eigenspace-based approach which uses projections onto a particular vector or vector set in the estimated noise-only subspace is described. Several CLOSEST vector estimators are developed by using different measures of closeness. First CLOSEST is a novel full-dimensional element-space approach to spatial-spectrum estimation which has important performance advantages relative to pertinent established spatial-spectrum estimators. It incorporates a priori knowledge of the array manifold over a location sector of interest to provide SNR spectral-resolution thresholds which are lower than those of MIN-NORM (for some arrays, substantially lower). Second, relationships between the CLOSEST approach and several established approaches to spatial-spectrum estimation are established. For a linear equispaced array, MIN-NORM is shown to be a special case of the CLOSEST-approach-one which is based on projection onto a noise-only subspace vector which is close to the array manifold over the entire field of view. >

Bias analysis of the MUSIC location estimator

The authors present a rigorous bias analysis of the MUSIC location estimator, and they derive an accurate and concise bias expression. The analysis is based on the second-order Taylor series expansion of the derivative of the null spectrum, properties of the null spectrum, and statistics of the estimated signal eigenvectors. It is proven that in the derivation the remainder term in the second-order Taylor series can be dropped but the second-order terms cannot be. Simulations verify that the bias expression is valid over a wide range of signal-to-noise ratios (SNRs) extending down into the resolution threshold region of MUSIC. Although asymptotic, this expression can be accurately applied to a limited number of snapshot cases. The utility of the expression is shown by using it in a study of MUSIC location estimator characteristics. Estimate bias and standard deviation are compared for variations in SNR, numbers of sensors and snapshots, and source correlation. MUSIC resolvability and estimator performance bounds are addressed, accounting for bias. >

Statistical performance comparison of MUSIC in element-space and beam-space

Statistics of the spatial null spectra, generated from reduced-dimension beam-space (RDBS) data and MUSIC, are investigated and compared with those from element-space MUSIC. The authors consider analytically the estimated null-spectra mean and variance, particularly at critical points that determine spectral resolvability. Approximate expressions for resolution thresholds for element-space and RDBS are compared. Monte Carlo simulations are presented to support the analysis and to provide further insight. A matrix beamformer provides the transformation from element-space to RDBS. Comparisons provide insight into characteristics of the matrix beamformer that affect RDBS resolvability.<<ETX>>

A comparison of element and beam space spatial-spectrum estimation for multiple source clusters

Some of the relative advantages and disadvantages of performing eigenspace spatial-spectrum estimation in beam-space as opposed to element-space are considered. The issue of relative performance, specifically spectral-resolvability and peak position variance and bias, are addressed. It is concluded that when there are only sources impinging from a single sector (the sector selected for beam-space processing), there is no performance advantage in either element-space or beam-space processing. However, when there are out-of-sector sources beam-spacing processing has both advantages and disadvantages.<<ETX>>

Reduced-Dimension Beam-Space Broad-Band Source Localization: Preprocessor Design

Data from a set of conventional beamformers, each steered to a point in location (and frequency), are analyzed in beam-space processing. By selecting a location sector of interest, and by using only those beamformers which are steered within this sector, processing is in a Reduced-Dimension Beam-Space (RDBS). For spatial-spectrum estimation, advantages of processing in a RDBS rather than in element-space include; reduction in data and therefore computation required for spatial-spectral analysis, reduction in resolution thresholds, and attenuation of out-of-sector sources through spatial filtering. A beam-space preprocessor structure provides the element-space to RDBS transfor-mation. For broad-band source processing, its objectives are data reduction, spatial filtering and broad-band source focusing. In this paper we investigate beam-space preprocessor design.

Eigenspace based spatial-spectrum estimation for multiple beam antennas

High-resolution spatial spectrum estimation procedures in conjunction with narrowband multiple beam antenna (MBA) data are considered for source localization. The focus is on aspects of azimuth/elevation-spectrum estimation considering eigenspace estimators. Only two basic approaches to eigenspace spatial-spectrum estimators can be used with MBAs to provide unambiguous source azimuth/elevation estimates. These are the MUSIC approach and the recently developed first principal vectors (FINES) approach. Of these, FINES is recommended because it provides higher resolution.<<ETX>>

Bias analysis of source location estimates from eigenspace-based spatial-spectrum estimators

The authors rigorously derive bias expressions of source location estimates for MUSIC, MIN-NORM, and FINE for arbitrarily configured arrays. These bias expressions are a function of the null spectrum and statistics of estimated signal eigenvectors only. These expressions are valid over a wide range of signal-to-noise ratios (SNRs) extending down into the resolution threshold region. It is shown that these expressions can be accurately applied to a small number of snapshot cases.<<ETX>>

Statistical analysis of eigenspace-based source location estimates

A simple and rigorous statistical analysis of location estimates obtained from eigenspace spatial-spectrum based algorithms is presented. Concise and accurate variance expressions of location estimates for MUSIC, MIN-NORM, and FINE are derived. These expressions are valid over a wide range extending down into the resolution threshold region. It is shown that these expressions, though asymptotical, can be accurately applied to limited number of snapshot cases. Bias of location estimates is also briefly discussed. Based on the statistical analysis, a comparison among MUSIC, MIN-NORM, and FINE is made. Variance advantage of FINE over MIN-NORM, and the comparable variance between FINE and MUSIC are analytically proven.<<ETX>>

STATISTICAL PERFORMANCE ANALYSIS OF SMOOTHE MUSIC

This paper presents a statistical performance analysis of the smoothed MUSIC location estimator. Accurate asymptotical expressions for bias and variance, which are valid over a wide range of SNR extending into the resolution threshold region, are derived for multiple source cases.