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. 2005 Mar;149(3):243-55.
doi: 10.1016/j.jsb.2004.10.011.

Spectral signal-to-noise ratio and resolution assessment of 3D reconstructions

M Unser  1 , C O S Sorzano, P Thévenaz, S Jonić, C El-Bez, S De Carlo, J F Conway, B L Trus
Affiliations

Spectral signal-to-noise ratio and resolution assessment of 3D reconstructions

M Unser et al. J Struct Biol. 2005 Mar.

Abstract

Measuring the quality of three-dimensional (3D) reconstructed biological macromolecules by transmission electron microscopy is still an open problem. In this article, we extend the applicability of the spectral signal-to-noise ratio (SSNR) to the evaluation of 3D volumes reconstructed with any reconstruction algorithm. The basis of the method is to measure the consistency between the data and a corresponding set of reprojections computed for the reconstructed 3D map. The idiosyncrasies of the reconstruction algorithm are taken explicitly into account by performing a noise-only reconstruction. This results in the definition of a 3D SSNR which provides an objective indicator of the quality of the 3D reconstruction. Furthermore, the information to build the SSNR can be used to produce a volumetric SSNR (VSSNR). Our method overcomes the need to divide the data set in two. It also provides a direct measure of the performance of the reconstruction algorithm itself; this latter information is typically not available with the standard resolution methods which are primarily focused on reproducibility alone.

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Figures

Fig. 1
Fig. 1
Nearly even angular distribution. A small triangle is placed at the tip of the unit vectors representing each projection direction. The in-plane rotation angle is represented by the relative rotation of each triangle. The separation between projections for this distribution is approximately 6°.
Fig. 2
Fig. 2
SSNR (top), FSC, and FSCref (bottom) of the reconstruction of the bacteriorhodopsin from simulated data with an even angular distribution. The SSNR is also shown in logarithmic scale (dB) according to the formula SSNR(dB) = 10log10 (SSNR).
Fig. 3
Fig. 3
Different realizations of the attenuation factor for the angular distribution of Fig. 1.
Fig. 4
Fig. 4
Even angular distribution perturbed by angular noise. A random number (normally distributed with zero mean and standard deviation 5°) is added to each of the three Euler angles describing the projection directions in Fig. 1.
Fig. 5
Fig. 5
SSNR (top), FSC, and FSCref (bottom) of the reconstruction of the bacteriorhodopsin from simulated data with a perturbed angular distribution. The SSNR is also shown in logarithmic scale (dB) according to the formula SSNR(dB) = 10log10 (SSNR).
Fig. 6
Fig. 6
Radial profile of the contrast transfer function used for computer simulations.
Fig. 7
Fig. 7
SSNR (top), FSC, and FSCref (bottom) of the reconstruction of the bacteriorhodopsin from simulated data with an even angular distribution when the microscope aberrations are simulated. The SSNR is also shown in logarithmic scale (dB) according to the formula SSNR(dB) = 10log10 (SSNR).
Fig. 8
Fig. 8
Uneven angular distribution. Projections are randomly distributed on the projection space although top views are more frequent than lateral ones.
Fig. 9
Fig. 9
Uneven distribution with a missing cone. Projections are distributed randomly on the projection space. Top views are more frequent and no projection is taken with a tilt angle greater than 45°.
Fig. 10
Fig. 10
Top and side view of the volumetric SSNR for the reconstruction of bacteriorhodopsin from simulated data using an even (top), an uneven (middle), and an uneven distribution with a missing cone (bottom). The mesh corresponds to the isosurface of SSNR = 1. The solid isosurface corresponds to a SSNR = 4.
Fig. 11
Fig. 11
(Top) Isosurface of a phantom simulating a cross-section of an organelle with a set of proteins at random orientations. (Bottom) Tomographic reconstruction of the phantom at two different orientations. On the right image it can be seen that the organelle wall is very well defined along the tilt axis (vertical axis of this image) while there is a huge uncertainty along the perpendicular direction (horizontal axis of this image).
Fig. 12
Fig. 12
Top and side view of the volumetric SSNR for the tomographic reconstructions. The isosurface correspond to a SSNR = 1.
Fig. 13
Fig. 13
SSNR (top), FSC, and FSCref (bottom) of the reconstruction of GroEL using experimental cryo-microscopy data when compared with the X-ray model of GroEL. The SSNR is also shown in logarithmic scale (dB) according to the formula SSNR(dB) = 10log10 (SSNR).
Fig. 14
Fig. 14
Top and side view of the volumetric SSNR for the reconstruction of GroEL using experimental cryo-microscopy data. The mesh corresponds to the isosurface of SSNR = 1. The solid isosurface corresponds to a SSNR = 4.
Fig. 15
Fig. 15
Histogram of the tilt angle of the 2160 GroEL experimental images.
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