scholarly journals A Fast Image Alignment Approach for 2D Classification of Cryo-EM Images Using Spectral Clustering

2021 ◽  
Vol 43 (3) ◽  
pp. 1652-1668
Author(s):  
Xiangwen Wang ◽  
Yonggang Lu ◽  
Jiaxuan Liu
Keyword(s):  
3D Reconstruction ◽  
Single Particle ◽  
Spectral Clustering ◽  
Correlation Matrix ◽  
Cross Correlation ◽  
Image Alignment ◽  
Alignment Algorithm ◽  
High Quality ◽  
Maximum Value ◽  
Projection Images

Three-dimensional (3D) reconstruction in single-particle cryo-electron microscopy (cryo-EM) is a significant technique for recovering the 3D structure of proteins or other biological macromolecules from their two-dimensional (2D) noisy projection images taken from unknown random directions. Class averaging in single-particle cryo-EM is an important procedure for producing high-quality initial 3D structures, where image alignment is a fundamental step. In this paper, an efficient image alignment algorithm using 2D interpolation in the frequency domain of images is proposed to improve the estimation accuracy of alignment parameters of rotation angles and translational shifts between the two projection images, which can obtain subpixel and subangle accuracy. The proposed algorithm firstly uses the Fourier transform of two projection images to calculate a discrete cross-correlation matrix and then performs the 2D interpolation around the maximum value in the cross-correlation matrix. The alignment parameters are directly determined according to the position of the maximum value in the cross-correlation matrix after interpolation. Furthermore, the proposed image alignment algorithm and a spectral clustering algorithm are used to compute class averages for single-particle 3D reconstruction. The proposed image alignment algorithm is firstly tested on a Lena image and two cryo-EM datasets. Results show that the proposed image alignment algorithm can estimate the alignment parameters accurately and efficiently. The proposed method is also used to reconstruct preliminary 3D structures from a simulated cryo-EM dataset and a real cryo-EM dataset and to compare them with RELION. Experimental results show that the proposed method can obtain more high-quality class averages than RELION and can obtain higher reconstruction resolution than RELION even without iteration.

scholarly journals Image Alignment Using 2D Interpolation in the Frequency Domain for Class Averaging in Single-particle Cryo-EM

2021 ◽  
Author(s):  
Xiangwen Wang ◽  
Yonggang Lu ◽  
Jiaxuan Liu
Keyword(s):  
Electron Microscopy ◽  
3D Reconstruction ◽  
Single Particle ◽  
Correlation Matrix ◽  
Cross Correlation ◽  
Image Alignment ◽  
Estimation Accuracy ◽  
Cryo Electron Microscopy ◽  
Maximum Value ◽  
Projection Images

Abstract Background: Three-dimensional (3D) reconstruction in single-particle cryo-electron microscopy is a significant technique for recovering the 3D structure of proteins or other biological macromolecules from their two-dimensional (2D) noisy projection images taken from unknown random directions. Class averaging in single-particle cryo-electron microscopy is an important procedure for producing high-quality initial 3D models due to the existence of a high level of noise in the projection images. Image alignment is a fundamental step in the class averaging. Results: In this paper, an efficient image alignment algorithm using 2D interpolation in the frequency domain of images is proposed to improve the estimation accuracy of alignment parameters. The proposed algorithm firstly uses the Fourier transform of two projection images to calculate a discrete cross-correlation matrix and then performs the 2D interpolation around the maximum value in the cross-correlation matrix. The alignment parameters of rotation angles and translational shifts in the x-axis and y-axis directions between the two projection images are directly determined according to the position of the maximum value in the cross-correlation matrix after interpolation. Furthermore, the proposed algorithm and the K-medoids clustering algorithm are used to compute class averages for single-particle 3D reconstruction. Conclusions: Results on simulated data set show that the proposed algorithm can be used to compute the alignment parameters efficiently, and using the 2D interpolation can improve the estimation accuracy of the alignment parameters, which usually leads to a better 3D reconstruction result.

Structural Studies on the Eukaryotic Ribosome

1990 ◽  
Vol 48 (1) ◽  
pp. 256-257
Author(s):  
Adriana Verschoor ◽  
Ronald Milligan ◽  
Suman Srivastava ◽  
Joachim Frank
Keyword(s):  
Chick Embryo ◽  
3D Reconstruction ◽  
Single Particle ◽  
Mass Density ◽  
Particle Surface ◽  
Uranyl Acetate ◽  
Electron Microscopic ◽  
Eukaryotic Ribosome ◽  
Negative Stain ◽  
Reconstruction Methods

We have studied the eukaryotic ribosome from two vertebrate species (rabbit reticulocyte and chick embryo ribosomes) in several different electron microscopic preparations (Fig. 1a-d), and we have applied image processing methods to two of the types of images. Reticulocyte ribosomes were examined in both negative stain (0.5% uranyl acetate, in a double-carbon preparation) and frozen hydrated preparation as single-particle specimens. In addition, chick embryo ribosomes in tetrameric and crystalline assemblies in frozen hydrated preparation have been examined. 2D averaging, multivariate statistical analysis, and classification methods have been applied to the negatively stained single-particle micrographs and the frozen hydrated tetramer micrographs to obtain statistically well defined projection images of the ribosome (Fig. 2a,c). 3D reconstruction methods, the random conical reconstruction scheme and weighted back projection, were applied to the negative-stain data, and several closely related reconstructions were obtained. The principal 3D reconstruction (Fig. 2b), which has a resolution of 3.7 nm according to the differential phase residual criterion, can be compared to the images of individual ribosomes in a 2D tetramer average (Fig. 2c) at a similar resolution, and a good agreement of the general morphology and of many of the characteristic features is seen.Both data sets show the ribosome in roughly the same ’view’ or orientation, with respect to the adsorptive surface in the electron microscopic preparation, as judged by the agreement in both the projected form and the distribution of characteristic density features. The negative-stain reconstruction reveals details of the ribosome morphology; the 2D frozen-hydrated average provides projection information on the native mass-density distribution within the structure. The 40S subunit appears to have an elongate core of higher density, while the 60S subunit shows a more complex pattern of dense features, comprising a rather globular core, locally extending close to the particle surface.

Multi-channel interference source detector

2021 ◽  
Author(s):  
V.N. Antipov ◽  
S.L. Ivanov ◽  
E.Е. Koltyshev ◽  
V.V. Mukhin ◽  
A.Yu. Frolov ◽  
...  
Keyword(s):  
Radio Emission ◽  
Radiation Pattern ◽  
Correlation Matrix ◽  
Cross Correlation ◽  
Emission Sources ◽  
Energy Correlation ◽  
Antenna Radiation Pattern ◽  
Channel Interference ◽  
Main Disadvantage ◽  
The Cross

Modern radars, along with the detection and measurement of target coordinates against the background of interference, must solve the problem of detecting radio emission sources and measuring their coordinates. Detection of interference, as well as targets, in the radar is provided in the main (total) channel based on the analysis of the rangefinder-Doppler portrait of the received signal. The main disadvantage of such a detector is that the interference coming along the side lobes of the sum antenna and falling into the dip of the antenna radiation pattern may not be detected. Therefore, the problem arises of developing and analyzing algorithms for detecting interference in a radar with several receiving channels. The article discusses the logical, energy, correlation and eigenvalues of the cross-correlation matrix of the received signals interference detectors for two receiving channels. Their characteristics are given. It is shown that two-channel interference detectors based on the analysis of the eigenvalues of the cross-correlation matrix have the highest efficiency. Energy and logical algorithms are quite a bit inferior to them. The developed algorithms make it possible to effectively detect radio emission sources even when they are in the dip of one of the antenna patterns.

Properties of Correlated Neural Activity Clusters in Cat Auditory Cortex Resemble Those of Neural Assemblies

2006 ◽  
Vol 96 (2) ◽  
pp. 746-764 ◽  
Author(s):  
Jos J. Eggermont
Keyword(s):  
Auditory Cortex ◽  
Spike Activity ◽  
Correlation Matrix ◽  
Cross Correlation ◽  
Receptive Fields ◽  
Primary Auditory Cortex ◽  
Simultaneous Recording ◽  
Electrode Arrays ◽  
Tone Stimulus ◽  
Neural Assemblies

Spiking activity was recorded from cat auditory cortex using multi-electrode arrays. Cross-correlograms were calculated for spikes recorded on separate microelectrodes. The pair-wise cross-correlation matrix was constructed for the peak values of the correlograms. Hierarchical clustering was performed on the cross-correlation matrix for six stimulus conditions. These were silence, three multi-tone stimulus ensembles with different spectral densities, low-pass amplitude-modulated noise, and Poisson-distributed click trains that each lasted 15 min. The resulting neuron clusters reflect patches in cortex of up to several mm2 in size that expand and contract in response to different stimuli. Cluster positions and size were very similar for spontaneous activity and multi-tone stimulus-evoked activity but differed between those conditions and the noise and click stimuli. Cluster size was significantly larger in posterior auditory field (PAF) compared with primary auditory cortex (AI), whereas the fraction of common spikes (within a 10-ms window) across all electrode activity participating in a cluster was significantly higher in AI compared with PAF. Clusters crossed area boundaries in <5% of the cases were simultaneous recording were made in AI and PAF. Clusters are therefore similar to but not synonymous with the traditional view of neural assemblies. Common-spike spectrotemporal receptive fields (STRFs) were obtained for common-spike activity and all-spike activity within a cluster. Common-spike STRFs had higher signal-to-noise ratio than all-spike STRFs and showed generally spectral and temporal sharpening. The coincident and noncoincident output of the clusters could potentially act in parallel and may serve different modes of stimulus coding.

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