An adaptation of the Wiener filter suitable for analyzing images of isolated single particles

The Wiener filter is a standard means of optimizing the signal in sums of aligned, noisy images obtained by electron cryo-microscopy (cryo-EM). However, estimation of the resolution-dependent (“spectral”) signal-to-noise ratio (SSNR) from the input data has remained problematic, and error reduction due to specific application of the SSNR term within a Wiener filter has not been reported. Here we describe an adjustment to the Wiener filter for optimal summation of images of isolated particles surrounded by large regions of featureless background, as is typically the case in single-particle cryo-EM applications. We show that the density within the particle area can be optimized, in the least-squares sense, by scaling the SSNR term found in the conventional Wiener filter by a factor that reflects the fraction of the image field occupied by the particle. We also give related expressions that allow the SSNR to be computed for application in this new filter, by incorporating a masking step into a Fourier Ring Correlation (FRC), a standard resolution measure. Furthermore, we show that this masked FRC estimation scheme substantially improves on the accuracy of conventional SSNR estimation methods. We demonstrate the validity of our new approach in numeric tests with simulated data corresponding to realistic cryo-EM imaging conditions. This variation of the Wiener filter and accompanying derivation should prove useful for a variety of single-particle cryo-EM applications, including 3D reconstruction.     

Bone SPECT image reconstruction using deconvolution and wavelet transformation: Development,performance assessment and comparison in phantom and patient study with standard OSEM and resolution recovery algorithm

PurposeThe aim of this work was to introduce a new algorithm for image reconstruction in bone SPECT and to compare its performances with a commercially available standard OSEM and resolution recovery (RR) reconstruction.Materials and methodsThe algorithm was built applying the Lucy-Richardson deconvolution adn logarithmic image processing to the projections. A modification of the coefficients of wavelet decomposition was used to suppress the noise. The comparison with vendor software was performed both in a phantom study, using Signal-to-Noise ratio (SNR), Signal-to-Background ratio (SBR), spatial resolution and in clinical studies, by visual assessment of changes in contrast, spatial resolution and lesion detectability.ResultsA change in the SNR (from −4 to 40%), an increase in the SBR (from 19 to 40%), a minor improvement in spatial resolution and a similar noise level were observed in the phantom study in comparison to the standard OSEM. A decrease in the SNR, a worse spatial resolution, but only a 3 to 13 % lower SBR were achieved in comparison with the vendor supplied RR algorithm. The proposed algorithm creates patient images with better contrast and lesion detectability compared to clinically used OSEM. Compared to RR, more than half of obtained images showed better contrast and nearly half of them have better lesion detectability.ConclusionThe proposed algorithm compares favorably with the standard OSEM. Although less favorable, the comparison with RR and noise suppression algorithms, suggests that it can be used with only a slight decrease in the SBR.     

Review: resolution issues in single-particle reconstruction

Specific factors that affect the resolution of single-particle reconstructions are discussed. We present reconstructions of six particles (DNA-dependent protein kinase catalytic subunit, alphaB-crystallin, the ribonucleoprotein vault, hepatitis A virus, adenovirus type 2, and the adenovirus type 12/alpha(v)beta5 integrin complex), which have a variety of symmetries (asymmetric to 60-fold) and a wide range of molecular masses (470 kDa to 150 MDa). In the case of icosahedral viruses, we have found that applying a "soft" mask to remove regions of disordered density improves the resolution given by the Fourier shell correlation 0.5 criterion. This masking procedure is also useful during refinement to improve the quality of the reference model and thus aid in precise alignment of the particle images. For asymmetric particles, we note that image classification, although often a necessary step to generate a first reconstruction, can limit the achievable resolution. The diameter of the particle and the available computational power can also affect the resolution, as can structural variability within the particle.     

Averaging tens to hundreds of icosahedral particle images to resolve protein secondary structure elements using a Multi-Path Simulated Annealing optimization algorithm

Accurately determining a cryoEM particle's alignment parameters is crucial to high resolution single particle 3-D reconstruction. We developed Multi-Path Simulated Annealing, a Monte-Carlo type of optimization algorithm, for globally aligning the center and orientation of a particle simultaneously. A consistency criterion was developed to ensure the alignment parameters are correct and to remove some bad particles from a large pool of images of icosahedral particles. Without using any a priori model, this procedure is able to reconstruct a structure from a random initial model. Combining the procedure above with a new empirical double threshold particle selection method, we are able to pick tens of best quality particles to reconstruct a subnanometer resolution map from scratch. Using the best 62 particles of rice dwarf virus, the reconstruction reached 9.6A resolution at which four helices of the P3A subunit of RDV are resolved. Furthermore, with the 284 best particles, the reconstruction is improved to 7.9A resolution, and 21 of 22 helices and six of seven beta sheets are resolved.     

NMR spectroscopy reveals unexpected structural variation at the protein–protein interface in MHC class I molecules

It is well established that non-uniform sampling (NUS) allows acquisition of multi-dimensional NMR spectra at a resolution that cannot be obtained with traditional uniform acquisition through the indirect dimensions. However, the impact of NUS on the signal-to-noise ratio (SNR) and sensitivity are less well documented. SNR and sensitivity are essential aspects of NMR experiments as they define the quality and extent of data that can be obtained. This is particularly important for spectroscopy with low concentration samples of biological macromolecules. There are different ways of defining the SNR depending on how to measure the noise, and the distinction between SNR and sensitivity is often not clear. While there are defined procedures for measuring sensitivity with high concentration NMR standards, such as sucrose, there is no clear or generally accepted definition of sensitivity when comparing different acquisition and processing methods for spectra of biological macromolecules with many weak signals close to the level of noise. Here we propose tools for estimating the SNR and sensitivity of NUS spectra with respect to sampling schedule and reconstruction method. We compare uniformly acquired spectra with NUS spectra obtained in the same total measuring time. The time saving obtained when only 1/k of the Nyquist grid points are sampled is used to measure k-fold more scans per increment. We show that judiciously chosen NUS schedules together with suitable reconstruction methods can yield a significant increase of the SNR within the same total measurement time. Furthermore, we propose to define the sensitivity as the probability to detect weak peaks and show that time-equivalent NUS can considerably increase this detection sensitivity. The sensitivity gain increases with the number of NUS indirect dimensions. Thus, well-chosen NUS schedules and reconstruction methods can significantly increase the information content of multidimensional NMR spectra of challenging biological macromolecules.     

Assessing the capabilities of a 4kx4k CCD camera for electron cryo-microscopy at 300kV

CCD cameras have numerous advantages over photographic film for detecting electrons; however the point spread function of these cameras has not been sufficient for single particle data collection to subnanometer resolution with 300kV microscopes. We have adopted spectral signal to noise ratio (SNR) as a parameter for assessing detector quality for single particle imaging. The robustness of this parameter is confirmed under a variety of experimental conditions. Using this parameter, we demonstrate that the SNR of images of either amorphous carbon film or ice embedded virus particles collected on a new commercially available 4kx4k CCD camera are slightly better than photographic film at low spatial frequency (<1/5 Nyquist frequency), and as good as photographic film out to half of the Nyquist frequency. In addition it is slightly easier to visualize ice embedded particles on this CCD camera than on photographic film. Based on this analysis it is realistic to collect images containing subnanometer resolution data (6-9A) using this CCD camera at an effective magnification of approximately 112000x on a 300kV electron microscope.     

A Highlights from MBoC Selection: Cega: a single particle segmentation algorithm to identify moving particles in a noisy system

Improvements to particle tracking algorithms are required to effectively analyze the motility of biological molecules in complex or noisy systems. A typical single particle tracking (SPT) algorithm detects particle coordinates for trajectory assembly. However, particle detection filters fail for data sets with low signal-to-noise levels. When tracking molecular motors in complex systems, standard techniques often fail to separate the fluorescent signatures of moving particles from background signal. We developed an approach to analyze the motility of kinesin motor proteins moving along the microtubule cytoskeleton of extracted neurons using the Kullback-Leibler divergence to identify regions where there are significant differences between models of moving particles and background signal. We tested our software on both simulated and experimental data and found a noticeable improvement in SPT capability and a higher identification rate of motors as compared with current methods. This algorithm, called Cega, for “find the object,” produces data amenable to conventional blob detection techniques that can then be used to obtain coordinates for downstream SPT processing. We anticipate that this algorithm will be useful for those interested in tracking moving particles in complex in vitro or in vivo environments.     

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

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.     

ResLog plots as an empirical metric of the quality of cryo-EM reconstructions

Compared to the field of X-ray crystallography, the field of single particle three-dimensional electron microscopy has few reliable metrics for assessing the quality of 3D reconstructions. New metrics are needed that can determine whether a given 3D reconstruction accurately reflects the structure of the particles from which it was derived or instead depicts a plausible though incorrect structure due to coarse misalignment of particles. Here an empirical procedure is presented for differentiating between a reconstruction with well-aligned particles and a reconstruction with grossly misclassified particles. For a given dataset, 3D reconstructions are computed from subsets of particles with decreasing numbers of particles contributing to the reconstruction. A plot of inverse resolution vs. the logarithm of the number of particles (a “ResLog” plot) provides metrics for the reliability of the reconstruction and the overall quality of the dataset and processing. Specifically, the y-intercept of a regression line provides a measure of the relative accuracy of the particle alignment and classification, and the slope is an indicator of the overall data quality including the imaging conditions and processing steps. ResLog plots can also be used to optimize conditions for data collection and reconstruction parameters. Although resolution estimates can vary by method of calculation, ResLog-derived parameters are consistent whether calculated by Fourier shell correlation or Fourier neighbor correlation, or a new coordinate-based metric that serves as a yardstick for structures where atomic coordinates are available. ResLog plots could become part of a standard set of parameters to be included in 3D reconstruction reports.     

A binary segmentation approach for boxing ribosome particles in cryo EM micrographs

Three-dimensional reconstruction of ribosome particles from electron micrographs requires selection of many single-particle images. Roughly 100,000 particles are required to achieve approximately 10 A resolution. Manual selection of particles, by visual observation of the micrographs on a computer screen, is recognized as a bottleneck in automated single-particle reconstruction. This paper describes an efficient approach for automated boxing of ribosome particles in micrographs. Use of a fast, anisotropic non-linear reaction-diffusion method to pre-process micrographs and rank-leveling to enhance the contrast between particles and the background, followed by binary and morphological segmentation constitute the core of this technique. Modifying the shape of the particles to facilitate segmentation of individual particles within clusters and boxing the isolated particles is successfully attempted. Tests on a limited number of micrographs have shown that over 80% success is achieved in automatic particle picking.     

Acoustic signal perception in a noisy habitat: lessons from synchronising insects

Acoustically communicating animals often have to cope with ambient noise that has the potential to interfere with the perception of conspecific signals. Here we use the synchronous display of mating signals in males of the tropical katydid Mecopoda elongata in order to assess the influence of nocturnal rainforest noise on signal perception. Loud background noise may disturb chorus synchrony either by masking the signals of males or by interaction of noisy events with the song oscillator. Phase-locked synchrony of males was studied under various signal-to-noise ratios (SNRs) using either native noise or the audio component of noise (<9 kHz). Synchronous entrainment was lost at a SNR of -3 dB when native noise was used, whereas with the audio component still 50% of chirp periods matched the pacer period at a SNR of -7 dB. Since the chirp period of solo singing males remained almost unaffected by noise, our results suggest that masking interference limits chorus synchrony by rendering conspecific signals ambiguous. Further, entrainment with periodic artificial signals indicates that synchrony is achieved by ignoring heterospecific signals and attending to a conspecific signal period. Additionally, the encoding of conspecific chirps was studied in an auditory neuron under the same background noise regimes.     

Seeing GroEL at 6 A resolution by single particle electron cryomicroscopy

We present a reconstruction of native GroEL by electron cryomicroscopy (cryo-EM) and single particle analysis at 6 A resolution. alpha helices are clearly visible and beta sheet density is also visible at this resolution. While the overall conformation of this structure is quite consistent with the published X-ray data, a measurable shift in the positions of three alpha helices in the intermediate domain is observed, not consistent with any of the 7 monomeric structures in the Protein Data Bank model (1OEL). In addition, there is evidence for slight rearrangement or flexibility in parts of the apical domain. The 6 A resolution cryo-EM GroEL structure clearly demonstrates the veracity and expanding scope of cryo-EM and the single particle reconstruction technique for macromolecular machines.     

An iterative deconvolution algorithm for image recovery in clinical CT: A phantom study

PurposeTo study the feasibility of using an iterative reconstruction algorithm to improve previously reconstructed CT images which are judged to be non-diagnostic on clinical review. A novel rapidly converging, iterative algorithm (RSEMD) to reduce noise as compared with standard filtered back-projection algorithm has been developed.Materials and methodsThe RSEMD method was tested on in-silico, Catphan^®500, and anthropomorphic 4D XCAT phantoms. The method was applied to noisy CT images previously reconstructed with FBP to determine improvements in SNR and CNR. To test the potential improvement in clinically relevant CT images, 4D XCAT phantom images were used to simulate a small, low contrast lesion placed in the liver.ResultsIn all of the phantom studies the images proved to have higher resolution and lower noise as compared with images reconstructed by conventional FBP. In general, the values of SNR and CNR reached a plateau at around 20 iterations with an improvement factor of about 1.5 for in noisy CT images. Improvements in lesion conspicuity after the application of RSEMD have also been demonstrated. The results obtained with the RSEMD method are in agreement with other iterative algorithms employed either in image space or with hybrid reconstruction algorithms.ConclusionsIn this proof of concept work, a rapidly converging, iterative deconvolution algorithm with a novel resolution subsets-based approach that operates on DICOM CT images has been demonstrated. The RSEMD method can be applied to sub-optimal routine-dose clinical CT images to improve image quality to potentially diagnostically acceptable levels.     

A statistical approach to computer processing of cryo-electron microscope images: virion classification and 3-D reconstruction

The scattering density of the virus is represented as a truncated weighted sum of orthonormal basis functions in spherical coordinates, where the angular dependence of each basis function has icosahedral symmetry. A statistical model of the image formation process is proposed and the maximum likelihood estimation method computed by an expectation-maximization algorithm is used to estimate the weights in the sum and thereby compute a 3-D reconstruction of the virus particle. If multiple types of virus particle are represented in the boxed images then multiple 3-D reconstructions are computed simultaneously without first requiring that the type of particle shown in each boxed image be determined. Examples of the procedure are described for viruses with known structure: (1). 3-D reconstruction of Flockhouse Virus from experimental images, (2). 3-D reconstruction of the capsid of Nudaurelia Omega Capensis Virus from synthetic images, and (3). 3-D reconstruction of both the capsid and the procapsid of Nudaurelia Omega Capensis Virus from a mixture of unclassified synthetic images.     

High-Performance Fluorescence Molecular Tomography through Shape-Based Reconstruction Using Spherical Harmonics Parameterization

Fluorescence molecular tomography in the near-infrared region is becoming a powerful modality for mapping the three-dimensional quantitative distributions of fluorochromes in live small animals. However, wider application of fluorescence molecular tomography still requires more accurate and stable reconstruction tools. We propose a shape-based reconstruction method that uses spherical harmonics parameterization, where fluorophores are assumed to be distributed as piecewise constants inside disjointed subdomains and the remaining background. The inverse problem is then formulated as a constrained nonlinear least-squares problem with respect to shape parameters, which decreases ill-posedness because of the significantly reduced number of unknowns. Since different shape parameters contribute differently to the boundary measurements, a two-step and modified block coordinate descent optimization algorithm is introduced to stabilize the reconstruction. We first evaluated our method using numerical simulations under various conditions for the noise level and fluorescent background; it showed significant superiority over conventional voxel-based methods in terms of the spatial resolution, reconstruction accuracy with regard to the morphology and intensity, and robustness against the initial estimated distribution. In our phantom experiment, our method again showed better spatial resolution and more accurate intensity reconstruction. Finally, the results of an in vivo experiment demonstrated its applicability to the imaging of mice.     

Few-sweep estimation of evoked potential based on a generalized subspace approach

A generalized subspace approach is proposed for single channel brain evoked potential (EP) extraction from background electroencephalogram (EEG) signal. The method realizes the optimum estimate of EP signal from the observable noisy signal. The underlying principle is to project the signal and noise into signal and noise coefficient subspace respectively by applying projection matrix at first. Secondly, coefficient weighting matrix is achieved based on the autocorrelation matrices of the noise and the noisy signal. With the coefficient weighting matrix, we can remove the noise projection coefficients and estimate the signal ones. EP signal is then obtained by averaging the signals estimated with the reconstruction matrix. Given different signal-to-noise ratio (SNR) conditions, the algorithm can estimate the EP signal with only two sweeps observable noisy signals. Our approach is shown to have excellent capability of estimating EP signal even in poor SNR conditions. The interference of spontaneous EEG has been eliminated with significantly improved SNR. The simulation results have demonstrated the effectiveness and superior performance of the proposed method.     

The resolution dependence of optimal exposures in liquid nitrogen temperature electron cryomicroscopy of catalase crystals

Electron beam damage is the fundamental limit to resolution in electron cryomicroscopy (cryo-EM) of frozen, hydrated specimens. Radiation damage increases with the number of electrons used to obtain an image and affects information at higher spatial frequencies before low-resolution information. For the experimentalist, a balance exists between electron exposures sufficient to obtain a useful signal-to-noise ratio (SNR) in images and exposures that limit the damage to structural features. In single particle cryo-EM this balance is particularly delicate: low-resolution features must be imaged with a sufficient SNR to allow image alignment so that high-resolution features recorded below the noise level can be recovered by averaging independent images. By measuring the fading of Fourier components from images obtained at 200 kV of thin crystals of catalase embedded in ice, we have determined the electron exposures that will maximize the SNR at resolutions between 86 and 2.9 Å. These data allow for a rational choice of exposure for single particle cryo-EM. For example, for 20 Å resolution, the SNR is maximized at ～20 e^?/Ų, whereas for 3 Å resolution, it is maximized at ～10 e^?/Ų. We illustrate the effects of exposure in single particle cryo-EM with data collected at ～12–15 and ～24–30 e^?/Ų.     

Toward standardized quantitative image quality (IQ) assessment in computed tomography (CT): A comprehensive framework for automated and comparative IQ analysis based on ICRU Report 87

PurposeBased on the guidelines from “Report 87: Radiation Dose and Image-quality Assessment in Computed Tomography” of the International Commission on Radiation Units and Measurements (ICRU), a software framework for automated quantitative image quality analysis was developed and its usability for a variety of scientific questions demonstrated.MethodsThe extendable framework currently implements the calculation of the recommended Fourier image quality (IQ) metrics modulation transfer function (MTF) and noise-power spectrum (NPS), and additional IQ quantities such as noise magnitude, CT number accuracy, uniformity across the field-of-view, contrast-to-noise ratio (CNR) and signal-to-noise ratio (SNR) of simulated lesions for a commercially available cone-beam phantom. Sample image data were acquired with different scan and reconstruction settings on CT systems from different manufacturers.ResultsSpatial resolution is analyzed in terms of edge-spread function, line-spread-function, and MTF. 3D NPS is calculated according to ICRU Report 87, and condensed to 2D and radially averaged 1D representations. Noise magnitude, CT numbers, and uniformity of these quantities are assessed on large samples of ROIs. Low-contrast resolution (CNR, SNR) is quantitatively evaluated as a function of lesion contrast and diameter. Simultaneous automated processing of several image datasets allows for straightforward comparative assessment.ConclusionsThe presented framework enables systematic, reproducible, automated and time-efficient quantitative IQ analysis. Consistent application of the ICRU guidelines facilitates standardization of quantitative assessment not only for routine quality assurance, but for a number of research questions, e.g. the comparison of different scanner models or acquisition protocols, and the evaluation of new technology or reconstruction methods.     

Fast automatic particle picking from cryo-electron micrographs using a locally normalized cross-correlation function: a case study

Recent progress in single-particle reconstruction methods and cryo-EM techniques has led to the determination of macromolecular structures with unprecedented resolution. The number of particles that goes into the reconstruction is a key determinant in achieving high resolution. Interactive manual picking of particles from an electron micrograph is a very time-consuming, tedious, and inefficient process. We have implemented a fast automatic particle picking procedure in the SPIDER environment. The procedure makes use of template matching schemes and employs a recently developed locally normalized correlation algorithm based on Fourier techniques. As a test, we have used this procedure to pick 70S Escherichia coli ribosomes from a cryo-electron micrograph. Different search strategies including use of a circular mask and asymmetric masks for different orientations of the particle have been explored, and their relative efficiencies are discussed. The results indicate that the procedure can be optimally used to pick ribosomes in a fully automatic way within the limit of selecting less than 10% false positives while missing about 15% of true positives.