Cryo-electron microscope image denoising based on the geodesic distance

BackgroundTo perform a three-dimensional (3-D) reconstruction of electron cryomicroscopy (cryo-EM) images of viruses, it is necessary to determine the similarity of image blocks of the two-dimensional (2-D) projections of the virus. The projections containing high resolution information are typically very noisy. Instead of the traditional Euler metric, this paper proposes a new method, based on the geodesic metric, to measure the similarity of blocks.ResultsOur method is a 2-D image denoising approach. A data set of 2243 cytoplasmic polyhedrosis virus (CPV) capsid particle images in different orientations was used to test the proposed method. Relative to Block-matching and three-dimensional filtering (BM3D), Stein’s unbiased risk estimator (SURE), Bayes shrink and K-means singular value decomposition (K-SVD), the experimental results show that the proposed method can achieve a peak signal-to-noise ratio (PSNR) of 45.65. The method can remove the noise from the cryo-EM image and improve the accuracy of particle picking.ConclusionsThe main contribution of the proposed model is to apply the geodesic distance to measure the similarity of image blocks. We conclude that manifold learning methods can effectively eliminate the noise of the cryo-EM image and improve the accuracy of particle picking.

[1]  M. Omair Ahmad,et al.  Spatially Adaptive Wavelet-Based Method Using the Cauchy Prior for Denoising the SAR Images , 2007, IEEE Transactions on Circuits and Systems for Video Technology.

[2]  D. DeRosier,et al.  The reconstruction of a three-dimensional structure from projections and its application to electron microscopy , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[3]  Alessandro Foi,et al.  Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering , 2007, IEEE Transactions on Image Processing.

[4]  Taneli Mielikäinen,et al.  Sinogram Denoising of Cryo-Electron Microscopy Images , 2005, ICCSA.

[5]  D. J. De Rosier,et al.  Reconstruction of Three Dimensional Structures from Electron Micrographs , 1968, Nature.

[6]  W Chiu,et al.  EMAN: semiautomated software for high-resolution single-particle reconstructions. , 1999, Journal of structural biology.

[7]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.

[8]  Vanishing geodesic distance for right-invariant Sobolev metrics on diffeomorphism groups , 2018, Annals of Global Analysis and Geometry.

[9]  Tian Xia,et al.  DeepPicker: a Deep Learning Approach for Fully Automated Particle Picking in Cryo-EM , 2016, Journal of structural biology.

[10]  Yao Xu,et al.  Clustering-Based Image Sparse Denoising in Wireless Multimedia Sensor Networks , 2015, Circuits Syst. Signal Process..

[11]  S. Scheres,et al.  How cryo-EM is revolutionizing structural biology. , 2015, Trends in biochemical sciences.

[12]  David Zhang,et al.  Patch Group Based Nonlocal Self-Similarity Prior Learning for Image Denoising , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[13]  Mineichi Kudo,et al.  Simple termination conditions for k-nearest neighbor method , 2003, Pattern Recognit. Lett..

[14]  Bin Li,et al.  A Method of Raster Data Mining Based on Multi Dimension Data Set , 2009, 2009 Sixth International Conference on Fuzzy Systems and Knowledge Discovery.

[15]  David J. Field,et al.  Emergence of simple-cell receptive field properties by learning a sparse code for natural images , 1996, Nature.

[16]  Zoubeida Messali,et al.  Nonparametric Denoising Methods Based on Contourlet Transform with Sharp Frequency Localization: Application to Low Exposure Time Electron Microscopy Images , 2015, Entropy.

[17]  Jia Wang,et al.  A Zernike-moment-based non-local denoising filter for cryo-EM images , 2013, Science China Life Sciences.

[18]  Yair Weiss,et al.  From learning models of natural image patches to whole image restoration , 2011, 2011 International Conference on Computer Vision.

[19]  Michael Elad,et al.  Dictionaries for Sparse Representation Modeling , 2010, Proceedings of the IEEE.

[20]  Lei Zhang,et al.  Weighted Nuclear Norm Minimization with Application to Image Denoising , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[21]  J. Sharpe Application of Optical Instrumentation in Medicine , 1977 .

[22]  Bernhard Schölkopf,et al.  Automatic particle picking using diffusion filtering and random forest classification , 2011 .

[23]  Anoop Cherian,et al.  Riemannian Dictionary Learning and Sparse Coding for Positive Definite Matrices , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[24]  Q. Ye The signed Euclidean distance transform and its applications , 1988, [1988 Proceedings] 9th International Conference on Pattern Recognition.

[25]  Roberto Cipolla,et al.  SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation , 2015, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[26]  Christian Jutten,et al.  A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed $\ell ^{0}$ Norm , 2008, IEEE Transactions on Signal Processing.