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• Computed Tomography (CT) is an important medical imaging technique – Puts to use two important image transforms (Radon and Fourier transforms) that were mathematically formulated many years before its invention

- Sjors H W Scheres, Haixiao Gao, Mikel Valle, Gabor T Herman, Paul P B Eggermont, Joachim Frank +1 other
- Nature methods
- 2007

Although three-dimensional electron microscopy (3D-EM) permits structural characterization of macromolecular assemblies in distinct functional states, the inability to classify projections from structurally heterogeneous samples has severely limited its application. We present a maximum likelihood-based classification method that does not depend on prior… (More)

A maximum-likelihood approach to multi-reference image refinement is presented. In contrast to conventional cross-correlation refinement, the new approach includes a formal description of the noise, implying that it is especially suited to cases with low signal-to-noise ratios. Application of this approach to a cryo-electron microscopy dataset revealed two… (More)

- Dan Butnariu, Ran Davidi, Gabor T Herman, Ivan G Kazantsev
- 2007

We study the convergence behavior of a class of projection methods for solving convex feasibility and optimization problems. We prove that the algorithms in this class converge to solutions of the consistent convex feasibility problem, and that their convergence is stable under summable perturbations. The class of projection methods we study contains, among… (More)

A prospective sample of 69 healthy adults, age range 18-80 years, was studied with magnetic resonance imaging scans (T2 weighted, 5 mm thick) of the entire cranium. Volumes were obtained by a segmentation algorithm that uses proton density and T2 pixel values to correct field inhomogeneities ("shading"). Average (+/- SD) brain volume, excluding cerebellum,… (More)

Algebraic reconstruction techniques (ART) are iterative procedures for recovering objects from their projections. It is claimed that by a careful adjustment of the order in which the collected data are accessed during the reconstruction procedure and of the so-called relaxation parameters that are to be chosen in an algebraic reconstruction technique, ART… (More)

Fuzzy segmentation is an effective way of segmenting out objects in pictures containing both random noise and shading. This is illustrated both on mathematically created pictures and on some obtained from medical imaging. A theory of fuzzy segmentation is presented. To perform fuzzy segmentation, a 'connectedness map' needs to be produced. It is… (More)

In many three-dimensional imaging applications the three-dimensional scene is represented by a three-dimensional array of volume elements, or voxels for short. A subset Q of the voxels is specified by some property. The objects in the scene are then defined as subsets of Q formed by voxels which are “connected” in some appropriate sense. It is… (More)