Gene Gindi

Computerized three-dimensional segmented human anatomy.

Manual segmentation of 129 x-ray CT transverse slices of a living male human has been done and a computerized 3-dimensional volume array modeling all major internal structures of the body has been created. Each voxel of the volume contains a index number designating it as belonging to a given organ or internal structure. The original x-ray CT images were reconstructed in a 512 x 512 matrix with a resolution of 1 mm in the x,y plane. The z-axis resolution is 1 cm from neck to midthigh and 0.5 cm from neck to crown of the head. This volume array represents a high resolution model of the human anatomy and can serve as a voxel-based anthropomorphic phantom suitable for many computer-based modeling and simulation calculations.

Noise analysis of MAP - EM algorithms for emission tomography

The ability to theoretically model the propagation of photon noise through PET and SPECT tomographic reconstruction algorithms is crucial in evaluating the reconstructed image quality as a function of parameters of the algorithm. In a previous approach for the important case of the iterative ML-EM (maximum-likelihood-expectation-maximization) algorithm, judicious linearizations were used to model theoretically the propagation of a mean image and a covariance matrix from one iteration to the next. Our analysis extends this approach to the case of MAP (maximum a posteriori)-EM algorithms, where the EM approach incorporates prior terms. We analyse in detail two cases: a MAP-EM algorithm incorporating an independent gamma prior, and a one-step-late (OSL) version of a MAP-EM algorithm incorporating a multivariate Gaussian prior, for which familiar smoothing priors are special cases. To validate our theoretical analyses, we use a Monte Carlo methodology to compare, at each iteration, theoretical estimates of mean and covariance with sample estimates, and show that the theory works well in practical situations where the noise and bias in the reconstructed images do not assume extreme values.

A Bayesian Joint Mixture Framework for the Integration ofAnatomical Information in Functional Image Reconstruction

We present a Bayesian joint mixture framework for integrating anatomical image intensity and region segmentation information into emission tomographic reconstruction in medical imaging. The joint mixture framework is particularly well suited for this problem and allows us to integrate additional available information such as anatomical region segmentation information into the Bayesian model. Since this information is independently available as opposed to being estimated, it acts as a good constraint on the joint mixture model. After specifying the joint mixture model, we combine it with the standard emission tomographic likelihood. The Bayesian posterior is a combination of this likelihood and the joint mixture prior. Since well known EM algorithms separately exist for both the emission tomography (ET) likelihood and the joint mixture prior, we have designed a novel EM2 algorithm that comprises two EM algorithms—one for the likelihood and one for the prior. Despite being dove-tailed in this manner, the resulting EM2 algorithm is an alternating descent algorithm that is guaranteed to converge to a local minimum of the negative log Bayesian posterior. Results are shown on synthetic images with bias/variance plots used to gauge performance. The EM2 algorithm resulting from the joint mixture framework has the best bias/variance performance when compared with six other closely related algorithms that incorporate anatomical information to varying degrees.

Three-dimensional radiographic imaging with a restricted view angle

The properties of many three-dimensional radiographic imaging systems are examined within a common analytic framework. It is found, by performing an important coordinate transformation, that the projection data of these systems can be transformed to a form amenable to analysis by the central-slice theorem. Therefore, a clear relationship between the measured data set and the three-dimensional Fourier transform of the object can be established. For the Fourier aperture system, each measurement in the detector plane gives directly one point in the three-dimensional Fourier transform of the object. The limited view angle of these systems manifests itself in the incomplete collection of the Fourier transform of the object. This “missing cones” region in the Fourier space produces a point-spread function that has long-range conical ridges radiating from the central core. It is shown that degradations in linear reconstructions of extended objects are not as disastrous as might have been expected.

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.

Optimization in model matching and perceptual organization

We introduce an optimization approach for solving problems in computer vision that involve multiple levels of abstraction. Our objective functions include compositional and specialization hierarchies. We cast vision problems as inexact graph matching problems, formulate graph matching in terms of constrained optimization, and use analog neural networks to perform the optimization. The method is applicable to perceptual grouping and model matching. Preliminary experimental results are shown.

A new convex edge-preserving median prior with applications to tomography

In a Bayesian tomographic maximum a posteriori (MAP) reconstruction, an estimate of the object f is computed by iteratively minimizing an objective function that typically comprises the sum of a log-likelihood (data consistency) term and prior (or penalty) term. The prior can be used to stabilize the solution and to also impose spatial properties on the solution. One such property, preservation of edges and locally monotonic regions, is captured by the well-known median root prior (MRP), an empirical method that has been applied to emission and transmission tomography. We propose an entirely new class of convex priors that depends on f and also on m, an auxiliary field in register with f. We specialize this class to our median prior (MP). The approximate action of the median prior is to draw, at each iteration, an object voxel toward its own local median. This action is similar to that of MRP and results in solutions that impose the same sorts of object properties as does MRP. Our MAP method is not empirical, since the problem is stated completely as the minimization of a joint (on f and m) objective. We propose an alternating algorithm to compute the joint MAP solution and apply this to emission tomography, showing that the reconstructions are qualitatively similar to those obtained using MRP.

Development and evaluation of spectral classification algorithms for fluorescence guided laser angioplasty

The feasibility of utilizing spectral information to discriminate arterial tissue type is considered. Arterial fluorescence spectra from 350 to 700 nm were obtained from 100 human aortic specimens. Seven spectral classification algorithms were developed with the following techniques: multivariate linear regression, stepwise multivariate linear regression, principal components analysis, decision plane analysis, Bayes decision theory, principal peak ratio, and spectral width. The classification ability of each algorithm was evaluated by its application to the training set and to a validation set containing 82 additional spectra. All seven spectral classification algorithms prospectively classified atherosclerotic and normal aortas with an accuracy greater than 80% (range: 82-96%). Laser angioplasty systems incorporating spectral classification algorithms may therefore be capable of detection and selective ablation of atherosclerotic plaque.<<ETX>>

Hopfield model associative memory with nonzero-diagonal terms in memory matrix.

The discrete-valued neural network proposed by Hopfield requires zero-diagonal terms in the memory matrix so that the net evolves toward a local minimum of an energy function. For a version of this model with bipolar nodes and positive terms along the diagonal, the net evolves so that only updates that lower the energy by a sufficient amount are accepted. For a net programmed as an outer-product associative content-addressable memory, the version with nonzero-diagonal elements performs nearly identically to one with zero-diagonal terms, and the dropping of the zero-diagonal requirement is advantageous for optical implementation.

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.