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- Sjors H W Scheres, Haixiao Gao, +4 authors Jose-Maria Carazo
- 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)

The coexistence of multiple distinct structural states often obstructs the application of three-dimensional cryo-electron microscopy to large macromolecular complexes. Maximum likelihood approaches are emerging as robust tools for solving the image classification problems that are posed by such samples. Here, we propose a statistical data model that allows… (More)

- Paul P. B. Eggermont, Vincent N. LaRiccia
- IEEE Trans. Information Theory
- 1999

General formulation of Shannon's main theorem in information theory, " Usp. van der Meulen, " Density-free convergence properties of various estimators of entropy, " Comput. Statist. Abstract— In the random sampling setting we estimate the entropy of a probability density distribution by the entropy of a kernel density estimator using the double exponential… (More)

We study minimum distance estimation problems related to maximum likelihood estimation in positron emission tomography (pet), which admit algorithms similar to the standard em algorithm for pet with the same type of monotonicity properties as does the em algorithm, see Vardi, Shepp, and Kaufman [25]. We derive the algorithms via the majorizing function… (More)

Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation of the spline smoother by an " equivalent " reproducing kernel regression estimator, as well as for proving uniform… (More)

- M. D. Altschuler, Y. Censor, +7 authors M. M. Yau
- Journal of Medical Systems
- 1980

The Dynamic Spatial Reconstructor (DSR) is a device constructed at the Biodynamics Research Unit of the Mayo Clinic for (among other things) the visualization of the beating heart inside the intact thorax. The device consists of 28 rotating X-ray sources arranged on a circular arc at 6° intervals (total span 162°) and a matching set of 28 imaging systems.… (More)

- Yu Cao, Paul P. B. Eggermont, Susan Terebey
- IEEE Trans. Image Processing
- 1999

We present a multiplicative algorithm for image reconstruction, together with a partial convergence proof. The iterative scheme aims to maximize cross Burg entropy between modeled and measured data. Its application to infrared astronomical satellite (IRAS) data shows reduced ringing around point sources, compared to the EM (Richardson-Lucy) algorithm.

- Charles Byrne, Paul P. B. Eggermont
- Handbook of Mathematical Methods in Imaging
- 2015

The EM algorithm is not a single algorithm, but a framework for the design of iterative likelihood maximization methods for parameter estimation. Any algorithm based on the EM framework we refer to as an " EM algorithm ". Because there is no inclusive theory that applies to all EM algorithms, the subject is a work in progress, and we find it appropriate to… (More)

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