Parmeshwar Khurd

An accelerated convergent ordered subsets algorithm for emission tomography

We propose an algorithm, E-COSEM (enhanced complete-data ordered subsets expectation-maximization), for fast maximum likelihood (ML) reconstruction in emission tomography. E-COSEM is founded on an incremental EM approach. Unlike the familiar OSEM (ordered subsets EM) algorithm which is not convergent, we show that E-COSEM converges to the ML solution. Alternatives to the OSEM include RAMLA, and for the related maximum a posteriori (MAP) problem, the BSREM and OS-SPS algorithms. These are fast and convergent, but require ajudicious choice of a user-specified relaxation schedule. E-COSEM itself uses a sequence of iteration-dependent parameters (very roughly akin to relaxation parameters) to control a tradeoff between a greedy, fast but non-convergent update and a slower but convergent update. These parameters are computed automatically at each iteration and require no user specification. For the ML case, our simulations show that E-COSEM is nearly as fast as RAMLA.

Quantification of Brain Maturation and Growth Patterns in C57BL/6J Mice via Computational Neuroanatomy of Diffusion Tensor Images

Diffusion Tensor magnetic resonance imaging and computational neuroanatomy are used to quantify postnatal developmental patterns of C57BL/6J mouse brain. Changes in neuronal organization and myelination occurring as the brain matures into adulthood are examined, and a normative baseline is developed, against which transgenic mice may be compared in genotype-phenotype studies. In early postnatal days, gray matter-based cortical and hippocampal structures exhibit high water diffusion anisotropy, presumably reflecting the radial neuronal organization. Anisotropy drops rapidly within a week, indicating that the underlying brain tissue becomes more isotropic in orientation, possibly due to formation of a complex randomly intertwined web of dendrites. Gradual white matter anisotropy increase implies progressively more organized axonal pathways, likely reflecting the myelination of axons forming tightly packed fiber bundles. In contrast to the spatially complex pattern of tissue maturation, volumetric growth is somewhat uniform, with the cortex and the cerebellum exhibiting slightly more pronounced growth. Temporally, structural growth rates demonstrate an initial rapid volumetric increase in most structures, gradually tapering off to a steady state by about 20 days. Fiber maturation reaches steady state in about 10 days for the cortex, to 30-40 days for the corpus callosum, the hippocampus, and the internal and external capsules.

Channelized hotelling and human observer study of optimal smoothing in SPECT MAP reconstruction

We compared the performance of a channelized Hotelling observer (CHO) to that of human observers to determine an optimal smoothing parameter /spl beta/ for an SKE/BKE detection task in a SPECT MAP (maximum a posteriori) reconstruction. The study is motivated in part by the recent development of theoretical methods that can rapidly predict CHO signal-to-noise ratios (SNRs) for MAP reconstructions. We found that a CHO not adjusted for internal noise effects was less predictive of the optimal smoothing parameters than one that used human observer data to tune the CHO for internal noise. We used a three-channel, square profile, radially symmetric channel structure, and, for internal noise, a method that altered the diagonal elements of the channel covariance matrix. The human observer study for two different signals A and B showed that /spl beta/ in the range 0.5-10.0 produced high detectability as measured by high d/sub A//sup 2/, while the CHO without internal noise showed high SNR/sup 2/ for /spl beta/ in the wider range 0.01-10.0. The CHO at location A was modified by internal noise utilizing human data at A, so that the d/sub A//sup 2/ and SNR/sup 2/ overlapped well, but when these internal noise parameters from A were applied at B, the curves did not overlap well. Nevertheless, both modified CHOs predicted a /spl beta/ range in accord with human data. We conclude that CHOs may need some way of incorporating internal noise without having to conduct a human study in the first place to determine internal noise parameters.

Decision strategies that maximize the area under the LROC curve

For the 2-class detection problem (signal absent/present), the likelihood ratio is an ideal observer in that it minimizes Bayes risk for arbitrary costs and it maximizes the area under the receiver operating characteristic (ROC) curve [AUC]. The AUC-optimizing property makes it a valuable tool in imaging system optimization. If one considered a different task, namely, joint detection and localization of the signal, then it would be similarly valuable to have a decision strategy that optimized a relevant scalar figure of merit. We are interested in quantifying performance on decision tasks involving location uncertainty using the localization ROC (LROC) methodology. Therefore, we derive decision strategies that maximize the area under the LROC curve, A/sub LROC/. We show that these decision strategies minimize Bayes risk under certain reasonable cost constraints. The detection-localization task is modeled as a decision problem in three increasingly realistic ways. In the first two models, we treat location as a discrete parameter having finitely many values resulting in an (L+1) class classification problem. In our first simple model, we do not include search tolerance effects and in the second, more general, model, we do. In the third and most general model, we treat location as a continuous parameter and also include search tolerance effects. In all cases, the essential proof that the observer maximizes A/sub LROC/ is obtained with a modified version of the Neyman-Pearson lemma. A separate form of proof is used to show that in all three cases, the decision strategy minimizes the Bayes risk under certain reasonable cost constraints.

Computer-aided gleason grading of prostate cancer histopathological images using texton forests

The Gleason score is the single most important prognostic indicator for prostate cancer candidates and plays a significant role in treatment planning. Histopathological imaging of prostate tissue samples provides the gold standard for obtaining the Gleason score, but the manual assignment of Gleason grades is a labor-intensive and error-prone process. We have developed a texture classification system for automatic and reproducible Gleason grading. Our system characterizes the texture in images belonging to a tumor grade by clustering extracted filter responses at each pixel into textons (basic texture elements). We have used random forests to cluster the filter responses into textons followed by the spatial pyramid match kernel in conjunction with an SVM classifier. We have demonstrated the efficacy of our system in distinguishing between Gleason grades 3 and 4.

Fast LROC analysis of Bayesian reconstructed emission tomographic images using model observers

Lesion detection and localization is an important task in emission computed tomography. Detection and localization performance with signal location uncertainty may be summarized by a scalar figure of merit, the area under the localization receiver operating characteristic (LROC) curve, A(LROC). We consider model observers to compute A(LROC) for two-dimensional maximum a posteriori (MAP) reconstructions. Model observers may be used to rapidly prototype studies that use human observers. We address the case background-known-exactly (BKE) and signal known except for location. Our A(LROC) calculation makes use of theoretical expressions for the mean and covariance of the reconstruction and, unlike conventional methods that also use model observers, does not require computation of a large number of sample reconstructions. We validate the results of the procedure by comparison to A(LROC) obtained using a gold-standard Monte Carlo method employing a large set of reconstructed noise samples. Under reasonable simulation conditions, our theoretical calculation is about one to two orders of magnitude faster than the conventional Monte Carlo method.

Automated malignancy detection in breast histopathological images

Detection of malignancy from histopathological images of breast cancer is a labor-intensive and error-prone process. To streamline this process, we present an efficient Computer Aided Diagnostic system that can differentiate between cancerous and non-cancerous H&E (hemotoxylin&eosin) biopsy samples. Our system uses novel textural, topological and morphometric features taking advantage of the special patterns of the nuclei cells in breast cancer histopathological images. We use a Support Vector Machine classifier on these features to diagnose malignancy. In conjunction with the maximum relevance - minimum redundancy feature selection technique, we obtain high sensitivity and specificity. We have also investigated the effect of image compression on classification performance.

A globally convergent regularized ordered-subset EM algorithm for list-mode reconstruction

List-mode (LM) acquisition allows collection of data attributes at higher levels of precision than is possible with binned (i.e., histogram-mode) data. Hence, it is particularly attractive for low-count data in emission tomography. An LM likelihood and convergent EM algorithm for LM reconstruction was presented in Parra and Barrett, TMI, v17, 1998. Faster ordered subset (OS) reconstruction algorithms for LM 3-D PET were presented in Reader et al., Phys. Med. Bio., v43, 1998. However, these OS algorithms are not globally convergent and they also do not include regularization using convex priors which can be beneficial in emission tomographic reconstruction. LM-OSEM algorithms incorporating regularization via inter-iteration filtering were presented in Levkovitz et al., TMI, v20, 2001, but these are again not globally convergent. Convergent preconditioned conjugate gradient algorithms for spatio-temporal LM reconstruction incorporating regularization were presented in Nichols, et al., TMI, v21, 2002, but these do not use OS for speedup. In this work, we present a globally convergent and regularized ordered-subset algorithm for LM reconstruction. Our algorithm is derived using an incremental EM approach. We investigated the speedup of our LM OS algorithm (versus a non-OS version) for a SPECT simulation, and found that the speedup was somewhat less than that enjoyed by other OS-type algorithms.

A channelized Hotelling observer study of lesion detection in SPECT MAP reconstruction using anatomical priors

In emission tomography, anatomical side information, in the form of organ and lesion boundaries, derived from intra-patient coregistered CT or MR scans can be incorporated into the reconstruction. Our interest is in exploring the efficacy of such side information for lesion detectability. To assess detectability we used the SNR of a channelized Hotelling observer and a signal-known exactly/background-known exactly detection task. In simulation studies, we incorporated anatomical side information into a SPECT MAP (maximum a posteriori) reconstruction by smoothing within but not across organ or lesion boundaries. A non-anatomical prior was applied by uniform smoothing across the entire image. We investigated whether the use of anatomical priors with organ boundaries alone or with perfect lesion boundaries alone would change lesion detectability relative to the case of a prior with no anatomical information. Furthermore, we investigated whether any such detectability changes for the organ-boundary case would be a function of the distance of the lesion to the organ boundary. We also investigated whether any detectability changes for the lesion-boundary case would be a function of the degree of proximity, i.e. a difference in the radius of the true functional lesion and the radius of the anatomical lesion boundary. Our results showed almost no detectability difference with versus without organ boundaries at any lesion-to-organ boundary distance. Our results also showed no difference in lesion detectability with and without lesion boundaries, and no variation of lesion detectability with degree of proximity.

On Analyzing Diffusion Tensor Images by Identifying Manifold Structure Using Isomaps

This paper addresses the problem of statistical analysis of diffusion tensor magnetic resonance images (DT-MRI). DT-MRI cannot be analyzed by commonly used linear methods, due to the inherent nonlinearity of tensors, which are restricted to lie on a nonlinear submanifold of the space in which they are defined, namely R6. We estimate this submanifold using the isomap manifold learning technique and perform tensor calculations using geodesic distances along this manifold. Multivariate statistics used in group analyses also use geodesic distances between tensors, thereby warranting that proper estimates of means and covariances are obtained via calculations restricted to the proper subspace of R6. Experimental results on data with known ground truth show that the proposed statistical analysis method properly captures statistical relationships among tensor image data, and it identifies group differences. Comparisons with standard statistical analyses that rely on Euclidean, rather than geodesic distances, are also discussed