Showing papers by "Richard M. Leahy published in 1994"

Fast gradient-based methods for Bayesian reconstruction of transmission and emission PET images

Abstract: The authors describe conjugate gradient algorithms for reconstruction of transmission and emission PET images. The reconstructions are based on a Bayesian formulation, where the data are modeled as a collection of independent Poisson random variables and the image is modeled using a Markov random field. A conjugate gradient algorithm is used to compute a maximum a posteriori (MAP) estimate of the image by maximizing over the posterior density. To ensure nonnegativity of the solution, a penalty function is used to convert the problem to one of unconstrained optimization. Preconditioners are used to enhance convergence rates. These methods generally achieve effective convergence in 15-25 iterations. Reconstructions are presented of an /sup 18/FDG whole body scan from data collected using a Siemens/CTI ECAT931 whole body system. These results indicate significant improvements in emission image quality using the Bayesian approach, in comparison to filtered backprojection, particularly when reprojections of the MAP transmission image are used in place of the standard attenuation correction factors. >

Determining cardiac velocity fields and intraventricular pressure distribution from a sequence of ultrafast CT cardiac images

Abstract: A method of computing the velocity field and pressure distribution from a sequence of ultrafast CT (UFCT) cardiac images is demonstrated. UFCT multi-slice cine imaging gives a series of tomographic slices covering the volume of the heart at a rate of 17 frames per second. The complete volume data set can be modeled using equations of continuum theory and through regularization, velocity vectors of both blood and tissue can be determined at each voxel in the volume. The authors present a technique to determine the pressure distribution throughout the volume of the left ventricle using the computed velocity field. A numerical algorithm is developed by discretizing the pressure Poisson equation (PPE), which Is based on the Navier-Stokes equation. The algorithm is evaluated using a mathematical phantom of known velocity and pressure-Couette flow. It is shown that the algorithm based on the PPE can reconstruct the pressure distribution using only the velocity data. Furthermore, the PPE is shown to be robust in the presence of noise. The velocity field and pressure distribution derived from a UFCT study of a patient are also presented. >

Matching deformable atlas models to preprocessed magnetic resonance brain images

Abstract: We describe a method for automatically labelling regions of three-dimensional (3-D) Magnetic Resonance (MR) scans of human brains. Labelling consists of attaching anatomic names to particular regions of the cortical surface that appear in these images. The approach we take is to automatically match a deformable anatomical atlas model to preprocessed brain images, where preprocessing consists of 3-D Marr-Hildreth edge detection and morphological operations. These filtering operations automatically extract the brain and sulci from an MR image and provide a smoothed representation of the brain surface to which the deformable model can rapidly converge. The model itself is a 3-D B-spline surface whose control vertices are chosen to minimize a cost function that reflects the distance of the model from boundary-like features in the image. Minimization takes place using a conjugate gradient technique. >

A gradient projection conjugate gradient algorithm for Bayesian PET reconstruction

Abstract: In the Bayesian PET reconstruction problem, conjugate gradient (CG) algorithms were previously shown to have more favorable convergence rates than expectation maximization (EM) type algorithms. CG algorithms, however, are not easily applicable because of the non-negativity constraint. Earlier, the authors tackled this problem by augmenting the log-posterior density function with a penalty function, and using an appropriate preconditioner. Here, an active set approach is used which avoids some inherent problems of the penalty function method. This method simultaneously tries to estimate the "zero" variables (active set), and maximizes the cost function in the other variables (free) variables by using the following stages consecutively: (i) an unconstrained CG algorithm in the free variables followed by a bent line search, (ii) a gradient projection step to select a new active set. Using this gradient projection conjugate gradient algorithm, the authors retain fast convergence while avoiding the problem of selecting parameters inherent in their previous penalty function approach. >

A 3-D Morphological Algorithm for Automated Labelling of the Cortex in Magnetic Resonance Brain Images

Abstract: In this paper we describe a new method for auto~atic eztraction and anatomic labelling of the cortical urface in Magnetic Resonance (MR) images of the uman brain. Our algorithm consists of a series of morphological operations which automatically find the ortical surface and detect sulci in an MR volume imge. The extracted surface points are labelled as Usulusn or "not sulcus".

Simultaneous hyperparameter estimation and Bayesian image reconstruction for PET

Abstract: The authors present a new iterative algorithm for Bayesian PET image reconstruction that simultaneously estimates the PET image and the global hyperparameter /spl beta/ of a Gibbs prior. True maximum likelihood (ML) estimation of /spl beta/ is intractable for the PET reconstruction problem due to the complexity and high dimensionality of the probability densities involved. The new algorithm replaces the true likelihood function for the hyperparameter with an approximation in which the marginalization with respect to the image sample space is reduced to the product of a set of one dimensional integrals; one per image pixel. The approximation is closely related to the mean field theory of statistical mechanics. In essence, this reduction in complexity is achieved by approximating the influence of the neighbors of each pixel over their entire sample space with their estimated posterior modes. A preconditioned conjugate gradient algorithm is used to iteratively compute a MAP estimate of the image. At periodic intervals, the most recent image generated by this iterative procedure is used as an estimate of the posterior mode in the approximate marginalized log likelihood for the data given /spl beta/, which in turn is used to update the ML estimate of /spl beta/. The procedure is repeated until convergence of both the MAP image estimate and the ML estimate of /spl beta/. Results of a validation study using Monte Carlo simulations are presented. >

Automatic anatomical labelling of magnetic resonance brain images

Abstract: The authors describe their method for automatic anatomic labelling of cortical regions in magnetic resonance (MR) brain images. Their procedure consists of preprocessing head images with a three dimensional (3-D) Marr-Hildreth edge detector and a series of morphological filtering operations. The authors then label brain regions by matching a deformable atlas model to the processed images. They demonstrate an application of this technique to automatically labelling the lobes of the brain from a volume MR image. >