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- Sjors H. W. Scheres, Haixiao Gao, +4 authors José María 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)

- 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.

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)

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)

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

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 kernel. Under mild smoothness and moment conditions we show that the entropy of the kernel density estimator equals a sum of independent and identically distributed (i.i.d.) random variables… (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 error… (More)

- Martin D. Altschuler, Y. Censor, +7 authors Monica 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)

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

A well studied procedure for estimating a parameter from observed data is to maximize the likelihood function. When a maximizer cannot be obtained in closed form, iterative maximization algorithms, such as the expectation maximization (EM) maximum likelihood algorithms, are needed. The standard formulation of the EM algorithms postulates that finding a… (More)

- By P. P. B. Eggermont, Paul P. B. Eggermont
- 2010

We consider Galerkin methods for monotone Abel-Volterra integral equations of the second kind on the half-line. The L2 theory follows from Kolodner's theory of monotone Hammerstein, equations. We derive the L°° theory from the L2 theory by relating the L2and L°°-spectra of operators of the form x —► 6 * (ax) to one another. Here * denotes convolution, and b… (More)

- By P. P. B. Eggermont, Paul P. B. Eggermont
- 2010

We present a unifying analysis of quadrature methods for Volterra integral equations of the first kind that are zero-stable and have an asymptotic repetition factor. We show that such methods are essentially collocation-projection methods with underlying subspaces that have nice approximation properties, and which are stable as projection methods. This is… (More)