R.M. Leahy

Publications of R.M. Leahy

• Optimal Rebinning of Time-of-Flight PET Data

  Authors: Sangtae Ahn, Sanghee Cho, Quanzheng Li, Yanguang Lin, R.M. Leahy

  Medical Imaging, IEEE Transactions on. 11/2011;

  Time-of-flight (TOF) positron emission tomography (PET) scanners offer the potential for significantly improved signal-to-noise ratio (SNR) and lesion detectability in clinical PET. However, fully 3DTime-of-flight (TOF) positron emission tomography (PET) scanners offer the potential for significantly improved signal-to-noise ratio (SNR) and lesion detectability in clinical PET. However, fully 3D TOF PET image reconstruction is a challenging task due to the huge data size. One solution to this problem is to rebin TOF data into a lower dimensional format. We have recently developed Fourier rebinning methods for mapping TOF data into non-TOF formats that retain substantial SNR advantages relative to sinograms acquired without TOF information. However, mappings for rebinning into non-TOF formats are not unique and optimization of rebinning methods has not been widely investigated. In this paper we address the question of optimal rebinning in order to make full use of TOF information. We focus on FORET-3D, which approximately rebins 3D TOF data into 3D non-TOF sinogram formats without requiring a Fourier transform in the axial direction. We optimize the weighting for FORET-3D to minimize the variance, resulting in H ²-weighted FORET-3D, which turns out to be the best linear unbiased estimator (BLUE) under reasonable approximations and furthermore the uniformly minimum variance unbiased (UMVU) estimator under Gaussian noise assumptions. This implies that any information loss due to optimal rebinning is as a result only of the approximations used in deriving the rebinning equation and developing the optimal weighting. We demonstrate using simulated and real phantom TOF data that the optimal rebinning method achieves variance reduction and contrast recovery improvement compared to nonoptimized rebinning weightings. In our preliminary study using a simplified simulation setup, the performance of the optimal rebinning method was comparable to that of fully 3D TOF MAP.

• PET Image Reconstruction Using Information Theoretic Anatomical Priors

  Authors: S. Somayajula, C. Panagiotou, A. Rangarajan, Quanzheng Li, S.R. Arridge, R.M. Leahy

  Medical Imaging, IEEE Transactions on. 04/2011;

  We describe a nonparametric framework for incorporating information from co-registered anatomical images into positron emission tomographic (PET) image reconstruction through priors based onWe describe a nonparametric framework for incorporating information from co-registered anatomical images into positron emission tomographic (PET) image reconstruction through priors based on information theoretic similarity measures. We compare and evaluate the use of mutual information (MI) and joint entropy (JE) between feature vectors extracted from the anatomical and PET images as priors in PET reconstruction. Scale-space theory provides a framework for the analysis of images at different levels of detail, and we use this approach to define feature vectors that emphasize prominent boundaries in the anatomical and functional images, and attach less importance to detail and noise that is less likely to be correlated in the two images. Through simulations that model the best case scenario of perfect agreement between the anatomical and functional images, and a more realistic situation with a real magnetic resonance image and a PET phantom that has partial volumes and a smooth variation of intensities, we evaluate the performance of MI and JE based priors in comparison to a Gaussian quadratic prior, which does not use any anatomical information. We also apply this method to clinical brain scan data using Fallypride, a tracer that binds to dopamine receptors and therefore localizes mainly in the striatum. We present an efficient method of computing these priors and their derivatives based on fast Fourier transforms that reduce the complexity of their convolution-like expressions. Our results indicate that while sensitive to initialization and choice of hyperparameters, information theoretic priors can reconstruct images with higher contrast and superior quantitation than quadratic priors.

• Anatomical structural network analysis of human brain using partial correlations of gray matter volumes

  Authors: A.A. Joshi, S.H. Joshi, I. Dinov, D.W. Shattuck, R.M. Leahy, A.W. Toga

  Biomedical Imaging: From Nano to Macro, 2010 IEEE International Symposium on; 05/2010

  Structural connectivity in human brain has been studied by modeling the statistical dependence between features of cortical regions, such as gray matter thickness. Statistical correlations betweenStructural connectivity in human brain has been studied by modeling the statistical dependence between features of cortical regions, such as gray matter thickness. Statistical correlations between gray matter thickness have been mainly used as a metric to study this dependence. In this paper, we propose the use of partial correlations instead of Pearson correlation for inferring the brain structural connectivity using gray matter volumes from a large population of 466 subjects. We argue that partial-correlation is a better measure for extracting connectivity matrix from multivariate data because it removes the effects of confounding correlations that get introduced due to canonical dependence between data. Our experimental results on gray-matter volumes from a large population of brains compare and contrast the connectivities obtained by applying both correlation and partial correlation analysis.

• Statistically optimal graph partition method based on modularity

  Authors: Yu-Teng Chang, D. Pantazis, H.B. Hui, R.M. Leahy

  Biomedical Imaging: From Nano to Macro, 2010 IEEE International Symposium on; 05/2010

  Graph theory provides a formal framework to investigate the functional and structural connectome of the brain. We extend previous work on modularity-based graph partitioning methods that are able toGraph theory provides a formal framework to investigate the functional and structural connectome of the brain. We extend previous work on modularity-based graph partitioning methods that are able to detect network community structures. We estimate the conditional expected network, provide exact analytical solutions for a Gaussian random network, and also demonstrate that this network is the best unbiased linear estimator even when the Gaussian assumption is violated. We use the conditional expected network to partition graphs, and demonstrate its performance in simulations, a real network dataset, and a structural brain connectivity network.

• Canonical correlation analysis applied to functional connectivity in MEG

  Authors: J.L.P. Soto, D. Pantazis, K. Jerbi, S. Baillet, R.M. Leahy

  Biomedical Imaging: From Nano to Macro, 2010 IEEE International Symposium on; 05/2010

  We present a multivariate method based on canonical correlation analysis for the study of functional connectivity in the brain with MEG data. We obtain a time-frequency representation of the brainWe present a multivariate method based on canonical correlation analysis for the study of functional connectivity in the brain with MEG data. We obtain a time-frequency representation of the brain activity on the cortical surface, and use the signal power at specific frequency bands as inputs to our model. Our measure of interaction between two spatial locations is the canonical correlation, and the vectors associated with it indicate the contribution of each individual frequency band to the interaction. The resulting canonical correlation maps are thresholded for significance using false discovery rate. We further provide a novel way to control for linear mixing by testing whether the correlation vectors are collinear. We apply our method to simulations and experimental data from an MEG visuomotor study, and demonstrate that it is able to detect functional interactions across space as well as the frequency bands that contribute to these interactions.

• Optimized weighting for Fourier rebinning of three-dimensional time-of-Flight PET data to non-time-of-flight

  Authors: Sangtae Ahn, Sanghee Cho, Quanzheng Li, R.M. Leahy

  Nuclear Science Symposium Conference Record (NSS/MIC), 2009 IEEE; 12/2009

  Time-of-flight (TOF) PET scanners provide the potential for significantly improved signal-to-noise ratio (SNR) and lesion detectability in clinical PET. Therefore, it is likely that TOF will becomeTime-of-flight (TOF) PET scanners provide the potential for significantly improved signal-to-noise ratio (SNR) and lesion detectability in clinical PET. Therefore, it is likely that TOF will become the standard for clinical whole body PET in the near future. However, fully 3D TOF PET image reconstruction is a challenging task due to the huge data size. One solution to this problem is to rebin TOF data into a lower dimensional format. We have recently developed Fourier rebinning methods for mapping TOF data into non-TOF formats and achieved substantial SNR advantages over sinograms acquired without TOF information. However, such mappings for rebinning into non-TOF formats are not unique and optimization of rebinning methods has not been widely investigated. In this paper we address the question of optimal rebinning in order to make full use of TOF information and consequently to maximize image quality. We focus on FORET-3D, which rebins 3D TOF data into 3D non-TOF sinogram formats without requiring a Fourier transform in the axial direction. We optimize the weighting for FORET-3D using a uniformly minimum variance unbiased (UMVU) estimator under reasonable approximations. We show that the rebinned data with optimal weights are a sufficient statistic for the unknown image, implying that any information loss due to rebinning is as a result only of the approximations used in developing the optimal weighting. We demonstrate using simulated and real phantom TOF data that the optimal rebinning method achieves significant variance reduction and better contrast recovery compared to other rebinning weightings.

• Controlling Familywise Error Rate for Matched Subspace Detection in Dynamic FDG PET

  Authors: Zheng Li, Quanzheng Li, D. Pantazis, Xiaoli Yu, P.S. Conti, R.M. Leahy

  Medical Imaging, IEEE Transactions on. 11/2009;

  Detection of small lesions in fluorodeoxyglucose (FDG) positron emission tomography (PET) is limited by image resolution and low signal to noise ratio. We have previously described a matched subspaceDetection of small lesions in fluorodeoxyglucose (FDG) positron emission tomography (PET) is limited by image resolution and low signal to noise ratio. We have previously described a matched subspace detection method that uses the time activity curve to distinguish tumors from background in dynamic FDG PET. Applying this algorithm on a voxel by voxel basis throughout the dynamic image produces a test statistic image or ldquomaprdquo which on thresholding indicates the potential locations of secondary or metastatic tumors. In this paper, we describe a thresholding method that controls familywise error rate (FWER) for the matched subspace detection statistical map. The method involves three steps. First, the PET image is segmented into several homogeneous regions. Then, the statistical map is normalized to a zero mean unit variance Gaussian random field. Finally, the images are thresholded at a fixed FWER by estimating their spatial smoothness and applying a random field theory maximum statistic approach. We evaluate this thresholding method using digital phantoms generated from clinical dynamic images. We also present an application of the proposed approach to clinical PET data from a breast cancer patient with metastatic disease.

• Generalized sidelobe canceller for magnetoencephalography arrays

  Authors: J.C. Mosher, M.S. Hamalainen, D. Pantazis, H.B. Hui, R.C. Burgess, R.M. Leahy

  Biomedical Imaging: From Nano to Macro, 2009. ISBI '09. IEEE International Symposium on; 08/2009

  In the last decade, large arrays of sensors for magnetoencephalography (MEG) (and electroencephalography (EEG)) have become more common place, allowing new opportunities for the application ofIn the last decade, large arrays of sensors for magnetoencephalography (MEG) (and electroencephalography (EEG)) have become more common place, allowing new opportunities for the application of beamforming techniques to the joint problems of signal estimation and noise reduction. We introduce a new approach to noise cancellation, the generalized sidelobe canceller (GSC), itself an alternative to the linearly constrained minimum variance (LCMV) algorithm. The GSC framework naturally fits within the other noise reduction techniques that employ real or virtual reference arrays. Using expository human subject data with strong environmental and biological artifacts, we demonstrate a straightforward sequence of steps for practical noise filtering, applicable to any large array sensor design.

• Diffusion optical tomography using entropic priors

  Authors: C. Panagiotou, S. Somayajula, A.P. Gibson, M. Schweiger, R.M. Leahy, S.R. Arridge

  Biomedical Imaging: From Nano to Macro, 2009. ISBI '09. IEEE International Symposium on; 08/2009

  Diffuse optical tomography (DOT) is a functional imaging modality which aims to retrieve the optical characteristics of the probed tissue, namely light absorption and diffusion. The accurateDiffuse optical tomography (DOT) is a functional imaging modality which aims to retrieve the optical characteristics of the probed tissue, namely light absorption and diffusion. The accurate retrieval of the spatial distribution for each optical characteristic involves the solution of a highly-ill posed, non-linear inverse problem, thus employing a regularization is essential. In this work, we propose an entropic regularization scheme for DOT reconstruction that uses a priori structural information through mutual information (MI) and joint entropy (JE).We compare MI and JE through simulations that illustrate their behavior when the reference and DOT images are not identical in structure. We propose an efficient implementation of these regularizers based on fast Fourier transforms. The method is tested through numerical simulations.

• Direct estimation of patlak parameters from list mode PET data

  Authors: Quanzheng Li, R.M. Leahy

  Biomedical Imaging: From Nano to Macro, 2009. ISBI '09. IEEE International Symposium on; 08/2009

  We describe a method to directly estimate Patlak parameters from list mode data. Based on the Patlak model, the uptake rate function of each voxel can be written as a linear combination of the bloodWe describe a method to directly estimate Patlak parameters from list mode data. Based on the Patlak model, the uptake rate function of each voxel can be written as a linear combination of the blood input function and its integral, with the slope and intercept of the Patlak model as the corresponding weight. The positron emission rate in each voxel is then modeled as an inhomogeneous Poisson process with this rate function. The Patlak parameters are estimated directly from list mode data by maximizing the objective function, formed by the sum of the likelihood of arrival times and a spatial smoothness penalty, using a convergent four dimensional incremental gradient algorithm. Fully four dimensional simulations in a liver phantom demonstrate application of this method to realistic time activity curves.

• Optimal illumination patterns for fluorescence tomography

  Authors: J. Dutta, Sangtae Ahn, A.A. Joshi, R.M. Leahy

  Biomedical Imaging: From Nano to Macro, 2009. ISBI '09. IEEE International Symposium on; 08/2009

  Fluorescence tomography has become increasingly popular for detecting molecular targets for imaging gene expression and other cellular processes in vivo in small animal studies. In this imagingFluorescence tomography has become increasingly popular for detecting molecular targets for imaging gene expression and other cellular processes in vivo in small animal studies. In this imaging modality, multiple sets of data are acquired by illuminating the animal surface with different excitation patterns, each of which produces a distinct spatial pattern of fluorescence. This work addresses one of the most intriguing, yet unsolved, problems of fluorescence tomography, which is to determine how to optimally illuminate the animal surface so as to maximize the information content in the acquired data. The key idea of this work is to parameterize the illumination pattern and to maximize the information content in the data by improving the conditioning of the Fisher information matrix. We formulate our problem as a constrained optimization problem. We compare the performance of different geometric illumination schemes with those generated by this optimization approach using the Digimouse atlas.

• Posture matching and elastic registration of a mouse atlas to surface topography range data

  Authors: A.A. Joshi, A.J. Chaudhari, Changqing Li, D.W. Shattuck, J. Dutta, R.M. Leahy, A.W. Toga

  Biomedical Imaging: From Nano to Macro, 2009. ISBI '09. IEEE International Symposium on; 08/2009

  Estimation of internal mouse anatomy is required for quantitative bioluminescence or fluorescence tomography. However, only surface range data can be recovered from all-optical systems. These dataEstimation of internal mouse anatomy is required for quantitative bioluminescence or fluorescence tomography. However, only surface range data can be recovered from all-optical systems. These data are at times sparse or incomplete. We present a method for fitting an elastically deformable mouse atlas to surface topographic range data acquired by an optical system. In this method, we first match the postures of a deformable atlas and the range data of the mouse being imaged. This is achieved by aligning manually identified landmarks. We then minimize the asymmetric L² pseudo-distance between the surface of the deformable atlas and the surface topography range data. Once this registration is accomplished, the internal anatomy of the atlas is transformed to the coordinate system of the range data using elastic energy minimization. We evaluated our method by using it to register a digital mouse atlas to a surface model produced from a manually labeled CT mouse data set. Dice coefficents indicated excellent agreement in the brain and heart, with fair agreement in the kidneys and bladder. We also present example results produced using our method to align the digital mouse atlas to surface range data.

• POSTURE MATCHING AND ELASTIC REGISTRATION OF A MOUSE ATLAS TO SURFACE TOPOGRAPHY RANGE DATA.

  Authors: A A Joshi, A J Chaudhari, Changqing Li, D W Shattuck, J Dutta, R M Leahy, A W Toga

  Proceedings / IEEE International Symposium on Biomedical Imaging: from nano to macro. IEEE International Symposium on Biomedical Imaging. 08/2009; 2009:366-369.

  Estimation of internal mouse anatomy is required for quantitative bioluminescence or fluorescence tomography. However, only surface range data can be recovered from all-optical systems. These dataEstimation of internal mouse anatomy is required for quantitative bioluminescence or fluorescence tomography. However, only surface range data can be recovered from all-optical systems. These data are at times sparse or incomplete. We present a method for fitting an elastically deformable mouse atlas to surface topographic range data acquired by an optical system. In this method, we first match the postures of a deformable atlas and the range data of the mouse being imaged. This is achieved by aligning manually identified landmarks. We then minimize the asymmetric L(2) pseudo-distance between the surface of the deformable atlas and the surface topography range data. Once this registration is accomplished, the internal anatomy of the atlas is transformed to the coordinate system of the range data using elastic energy minimization. We evaluated our method by using it to register a digital mouse atlas to a surface model produced from a manually labeled CT mouse data set. Dice coefficents indicated excellent agreement in the brain and heart, with fair agreement in the kidneys and bladder. We also present example results produced using our method to align the digital mouse atlas to surface range data.

• A Parameterization-Based Numerical Method for Isotropic and Anisotropic Diffusion Smoothing on Non-Flat Surfaces

  Authors: A.A. Joshi, D.W. Shattuck, P.M. Thompson, R.M. Leahy

  Image Processing, IEEE Transactions on. 07/2009;

  Neuroimaging data, such as 3D maps of cortical thickness or neural activation, can often be analyzed more informatively with respect to the cortical surface rather than the entire volume of theNeuroimaging data, such as 3D maps of cortical thickness or neural activation, can often be analyzed more informatively with respect to the cortical surface rather than the entire volume of the brain. Any cortical surface-based analysis should be carried out using computations in the intrinsic geometry of the surface rather than using the metric of the ambient 3D space. We present parameterization-based numerical methods for performing isotropic and anisotropic filtering on triangulated surface geometries. In contrast to existing FEM-based methods for triangulated geometries, our approach accounts for the metric of the surface. In order to discretize and numerically compute the isotropic and anisotropic geometric operators, we first parameterize the surface using a p-harmonic mapping. We then use this parameterization as our computational domain and account for the surface metric while carrying out isotropic and anisotropic filtering. To validate our method, we compare our numerical results to the analytical expression for isotropic diffusion on a spherical surface. We apply these methods to smoothing of mean curvature maps on the cortical surface, a step commonly required for analysis of gyrification or for registering surface-based maps across subjects.

• Spatial Distortion Correction and Crystal Identification for MRI-Compatible Position-Sensitive Avalanche Photodiode-Based PET Scanners

  Authors: A.J. Chaudhari, A.A. Joshi, Yibao Wu, R.M. Leahy, S.R. Cherry, R.D. Badawi

  Nuclear Science, IEEE Transactions on. 07/2009;

  Position-sensitive avalanche photodiodes (PSAPDs) are gaining widespread acceptance in modern PET scanner designs, and owing to their relative insensitivity to magnetic fields, especially in thosePosition-sensitive avalanche photodiodes (PSAPDs) are gaining widespread acceptance in modern PET scanner designs, and owing to their relative insensitivity to magnetic fields, especially in those that are MRI-compatible. Flood histograms in PET scanners are used to determine the crystal of annihilation photon interaction and hence, for detector characterization and routine quality control. For PET detectors that use PSAPDs, flood histograms show a characteristic pincushion distortion when Anger logic is used for event positioning. A small rotation in the flood histogram is also observed when the detectors are placed in a magnetic field. We first present a general purpose automatic method for spatial distortion correction for flood histograms of PSAPD-based PET detectors when placed both inside and outside a MRI scanner. Analytical formulas derived for this scheme are based on a hybrid approach that combines desirable properties from two existing event positioning schemes. The rotation of the flood histogram due to the magnetic field is determined iteratively and is accounted for in the scheme. We then provide implementation details of a method for crystal identification we have previously proposed and evaluate it for cases when the PET detectors are both outside and in a magnetic field. In this scheme, Fourier analysis is used to generate a lower-order spatial approximation of the distortion-corrected PSAPD flood histogram, which we call the ldquotemplaterdquo. The template is then registered to the flood histogram using a diffeomorphic iterative intensity-based warping scheme. The calculated deformation field is then applied to the segmentation of the template to obtain a segmentation of the flood histogram. A manual correction tool is also developed for exceptional cases. We present a quantitative assessment of the proposed distortion correction scheme and crystal identification method against conventional methods. Our results indicate that our proposed methods l- ead to a large reduction in manual labor and indeed can routinely be used for calibration and characterization studies in MRI-compatible PET scanners based on PSAPDs.

• Lesion Detection in Dynamic FDG-PET Using Matched Subspace Detection

  Authors: Zheng Li, Quanzheng Li, Xiaoli Yu, P.S. Conti, R.M. Leahy

  Medical Imaging, IEEE Transactions on. 03/2009;

  We describe a matched subspace detection algorithm to assist in the detection of small tumors in dynamic positron emission tomography (PET) images. The algorithm is designed to differentiate tumorsWe describe a matched subspace detection algorithm to assist in the detection of small tumors in dynamic positron emission tomography (PET) images. The algorithm is designed to differentiate tumors from background using the time activity curves (TACs) that characterize the uptake of PET tracers. TACs are modeled using linear subspaces with additive Gaussian noise. Using TACs from a primary tumor region of interest (ROI) and one or more background ROIs, each identified by a human observer, two linear subspaces are identified. Applying a matched subspace detector to these identified subspaces on a voxel-by-voxel basis throughout the dynamic image produces a test statistic at each voxel which on thresholding indicates potential locations of secondary or metastatic tumors. The detector is derived for three cases: using a single TAC with white noise of unknown variance, using a single TAC with known noise covariance, and detection using multiple TACs within a small ROI with known noise covariance. The noise covariance is estimated for the reconstructed image from the observed sinogram data. To evaluate the proposed method, a simulation-based receiver operating characteristic (ROC) study for dynamic PET tumor detection is designed. The detector uses a dynamic sequence of frame-by-frame 2-D reconstructions as input. We compare the performance of the subspace detectors with that of a Hotelling observer applied to a single frame image and of the Patlak method applied to the dynamic data. We also show examples of the application of each detection approach to clinical PET data from a breast cancer patient with metastatic disease.

• A two-step imaging procedure for MEG characterization of cortical currents: Location and spatial extent

  Authors: S. Khan, B. Cottereau, R.M. Leahy, J.C. Mosher, H. Amman, S. Baillet

  Biomedical Imaging: From Nano to Macro, 2008. ISBI 2008. 5th IEEE International Symposium on; 06/2008

  There is theoretical and experimental evidence that the spatial extent of mass neural activity is an important factor of brain response in neuroimaging studies. Direct estimation of the surface areaThere is theoretical and experimental evidence that the spatial extent of mass neural activity is an important factor of brain response in neuroimaging studies. Direct estimation of the surface area of activated regions would importantly complement the quantitative analysis of amplitude variations of cortical currents. These latter are accessible at the regional scale through source modeling of magnetoencephalographic signals. Here we present a joint approach to the estimation of both the local spatial extent and amplitude variations of neural current sources. The technique operates in two consecutive steps: 1) the compact modeling of regional cortical currents using equivalent current multipoles and 2) the remapping of these latter back onto the cortical surface using a sparse-focal imaging model. This Multipole Cortical Remapping technique operates in a Bayesian framework. Performances are evaluated using extensive Monte-Carlo simulations and are complemented with real data from a somatosensory mapping MEG experiment.

• Mutual information based non-rigidmouse registration using a scale-space approach

  Authors: S. Somayajula, A.A. Joshi, R.M. Leahy

  Biomedical Imaging: From Nano to Macro, 2008. ISBI 2008. 5th IEEE International Symposium on; 06/2008

  We propose a scale-space based approach to non-rigid small animal image registration. Scale-space theory is based on generating a family of images by blurring an image with Gaussian kernels ofWe propose a scale-space based approach to non-rigid small animal image registration. Scale-space theory is based on generating a family of images by blurring an image with Gaussian kernels of increasing width. This approach can be used to extract features at varying levels of detail from an image. We define the scale-space feature vector at each voxel of an image as a vector of intensities of the scale- space images at that voxel. We generate scale-space images of the target and template images, and extract their corresponding scale- space feature vectors at each voxel. The extracted feature vectors are aligned using mutual information based non-rigid registration to simultaneously align global structure as well as detail in the images. We represent the displacement field in terms of the discrete cosine transform (DCT) basis, and use the Laplacian of the displacement field as a regularizing term. The DCT representation of the displacement field simplifies the Laplacian regularization term to a diagonal, thus reducing computational cost. We apply the scale-space registration algorithm on mouse images obtained from two time points of a longitudinal study, and compare its performance with that of a hierarchical multi-scale approach. The results indicate that scale- space based registration gives better skeletal as well as soft tissue alignment compared to the hierarchical multi-scale approach.

• Analysis of Resolution and Noise Properties of Nonquadratically Regularized Image Reconstruction Methods for PET

  Authors: Sangtae Ahn, R.M. Leahy

  Medical Imaging, IEEE Transactions on. 04/2008;

  We present accurate and efficient methods for estimating the spatial resolution and noise properties of nonquadratically regularized image reconstruction for positron emission tomography (PET). It isWe present accurate and efficient methods for estimating the spatial resolution and noise properties of nonquadratically regularized image reconstruction for positron emission tomography (PET). It is well known that quadratic regularization tends to over-smooth sharp edges. Many types of edge-preserving nonquadratic penalties have been proposed to overcome this problem. However, there has been little research on the quantitative analysis of nonquadratic regularization due to its nonlinearity. In contrast, quadratically regularized estimators are approximately linear and are well understood in terms of resolution and variance properties. We derive new approximate expressions for the linearized local perturbation response (LLPR) and variance using the Taylor expansion with the remainder term. Although the expressions are implicit, we can use them to accurately predict resolution and variance for nonquadratic regularization where the conventional expressions based on the first-order Taylor truncation fail. They also motivate us to extend the use of a certainty-based modified penalty to nonquadratic regularization cases in order to achieve spatially uniform perturbation responses, analogous to uniform spatial resolution in quadratic regularization. Finally, we develop computationally efficient methods for predicting resolution and variance of nonquadratically regularized reconstruction and present simulations that illustrate the validity of these methods.

• Surface-Constrained Volumetric Brain Registration Using Harmonic Mappings

  Authors: A.A. Joshi, D.W. Shattuck, P.M. Thompson, R.M. Leahy

  Medical Imaging, IEEE Transactions on. 01/2008;

  In order to compare anatomical and functional brain imaging data across subjects, the images must first be registered to a common coordinate system in which anatomical features are aligned.In order to compare anatomical and functional brain imaging data across subjects, the images must first be registered to a common coordinate system in which anatomical features are aligned. Intensity-based volume registration methods can align subcortical structures well, but the variability in sulcal folding patterns typically results in misalignment of the cortical surface. Conversely, surface-based registration using sulcal features can produce excellent cortical alignment but the mapping between brains is restricted to the cortical surface. Here we describe a method for volumetric registration that also produces an accurate one-to-one point correspondence between cortical surfaces. This is achieved by first parameterizing and aligning the cortical surfaces using sulcal landmarks. We then use a constrained harmonic mapping to extend this surface correspondence to the entire cortical volume. Finally, this mapping is refined using an intensity-based warp. We demonstrate the utility of the method by applying it to T1-weighted magnetic resonance images (MRIs). We evaluate the performance of our proposed method relative to existing methods that use only intensity information; for this comparison we compute the intersubject alignment of expert-labeled subcortical structures after registration.