Estimating alignment errors in sets of 2-D images

Baldwin, Philip R.; Penczek, Pawel A.

doi:10.1016/j.jsb.2005.02.006

Cited by 18 publications

(21 citation statements)

References 31 publications

(30 reference statements)

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“…Finally, we have the suppression of information due to the alignment process necessary to establishing spatial orientations of the collected projection images. For small errors, this loss can be expressed as an additional envelope function (Baldwin and Penczek, 2005; Jensen, 2001). …”

Section: Introductionmentioning

confidence: 99%

Image Restoration in Cryo-Electron Microscopy

Penczek¹

2010

Methods in Enzymology

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Image restoration techniques are used to obtain, given experimental measurements, the best possible approximation of the original object within the limits imposed by instrumental conditions and noise level in the data. In molecular electron microscopy, we are mainly interested in linear methods that preserve the respective relationships between mass densities within the restored map. Here, we describe the methodology of image restoration in structural electron microscopy, and more specifically, we will focus on the problem of the optimum recovery of Fourier amplitudes given electron microscope data collected under various defocus settings. We discuss in detail two classes of commonly used linear methods, the first of which consists of methods based on pseudoinverse restoration, and which is further subdivided into mean-square error, chi-square error, and constrained based restorations, where the methods in the latter two subclasses explicitly incorporates non-white distribution of noise in the data. The second class of methods is based on the Wiener filtration approach. We show that the Wiener filter-based methodology can be used to obtain a solution to the problem of amplitude correction (or “sharpening”) of the electron microscopy map that makes it visually comparable to maps determined by X-ray crystallography, and thus amenable to comparable interpretation. Finally, we present a semi-heuristic Wiener filter-based solution to the problem of image restoration given sets of heterogeneous solutions. We conclude the chapter with a discussion of image restoration protocols implemented in commonly used single particle software packages.

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Section: Introductionmentioning

confidence: 99%

Image Restoration in Cryo-Electron Microscopy

Penczek¹

2010

Methods in Enzymology

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“…At this point it is not clear whether the variance due to alignment errors can be distinguished from the variance due to structural heterogeneity. As we argued in our earlier paper (Baldwin and Penczek, 2005), there is ambiguity in the possible interpretation of the variance in the data, which can be thought of as caused by alignment errors or the presence of multiple classes of particles in the dataset. To reduce this variance, in the former case one would chose to correct the alignment, while in the latter one would try to classify the data into homogeneous classes.…”

Section: Discussionmentioning

confidence: 94%

“…(10), the former should not. Unfortunately it is not immediately apparent how one could design a method that would allow us to distinguish between the two components (Baldwin and Penczek, 2005).…”

Section: Application Of the Bootstrap Methods To The Variance Estimatimentioning

confidence: 99%

Estimation of variance in single-particle reconstruction using the bootstrap technique

Penczek

Yang

Frank

et al. 2006

Journal of Structural Biology

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114

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“…Re-projection error is a common measure of alignment accuracy, and gives a good indication of the quality of the subsequent reconstruction (Baldwin et al, 2005;Brandt et al, 2001a,b;Penzcek et al, 1995). To assess the effectiveness of our alignment models, we compared the mean square error produced by the projective, quadratic, and cubic models.…”

Section: Alignmentmentioning

confidence: 99%