Exploring an optimal wavelet-based filter for cryo-ET imaging

Cryo-electron tomography (cryo-ET) is one of the most advanced technologies for the in situ visualization of molecular machines by producing three-dimensional (3D) biological structures. However, cryo-ET imaging has two serious disadvantages—low dose and low image contrast—which result in high-resolution information being obscured by noise and image quality being degraded, and this causes errors in biological interpretation. The purpose of this research is to explore an optimal wavelet denoising technique to reduce noise in cryo-ET images. We perform tests using simulation data and design a filter using the optimum selected wavelet parameters (three-level decomposition, level-1 zeroed out, subband-dependent threshold, a soft-thresholding and spline-based discrete dyadic wavelet transform (DDWT)), which we call a modified wavelet shrinkage filter; this filter is suitable for noisy cryo-ET data. When testing using real cryo-ET experiment data, higher quality images and more accurate measures of a biological structure can be obtained with the modified wavelet shrinkage filter processing compared with conventional processing. Because the proposed method provides an inherent advantage when dealing with cryo-ET images, it can therefore extend the current state-of-the-art technology in assisting all aspects of cryo-ET studies: visualization, reconstruction, structural analysis, and interpretation.

[1]  C. Burrus,et al.  Introduction to Wavelets and Wavelet Transforms: A Primer , 1997 .

[2]  D. Vasishtan,et al.  Cellular electron cryo tomography and in situ sub-volume averaging reveal the context of microtubule-based processes , 2017, Journal of structural biology.

[3]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Eduardo A. B. da Silva,et al.  Multiscale Image Fusion Using the Undecimated Wavelet Transform With Spectral Factorization and Nonorthogonal Filter Banks , 2013, IEEE Transactions on Image Processing.

[5]  Mark Horowitz,et al.  Removing high contrast artifacts via digital inpainting in cryo-electron tomography: an application of compressed sensing. , 2012, Journal of structural biology.

[6]  Hideo Onishi,et al.  [Fundamental evaluation of wavelet transform based noise reduction using soft threshold method in single photon emission computed tomography image]. , 2013, Nihon Hoshasen Gijutsu Gakkai zasshi.

[7]  Wolfgang Baumeister,et al.  Expanding the boundaries of cryo-EM with phase plates. , 2017, Current opinion in structural biology.

[8]  A. de Marco,et al.  Cryo-electron tomography: an ideal method to study membrane-associated proteins , 2017, Philosophical Transactions of the Royal Society B: Biological Sciences.

[9]  Olgierd Unold,et al.  The development of the spatially correlated adjustment wavelet filter for atomic force microscopy data. , 2016, Ultramicroscopy.

[10]  Zhi Liu,et al.  WaVPeak: picking NMR peaks through wavelet-based smoothing and volume-based filtering , 2012, Bioinform..

[11]  Metin Akay,et al.  A Discrete Dyadic Wavelet Transform for Multidimensional Feature Analysis , 1998 .

[12]  Tim W. Nattkemper,et al.  A machine vision system for automated non-invasive assessment of cell viability via dark field microscopy, wavelet feature selection and classification , 2008, BMC Bioinformatics.

[13]  Song Li,et al.  WaveletQuant, an improved quantification software based on wavelet signal threshold de-noising for labeled quantitative proteomic analysis , 2010, BMC Bioinformatics.

[14]  J. Briggs,et al.  Implementation of a cryo-electron tomography tilt-scheme optimized for high resolution subtomogram averaging , 2017, Journal of structural biology.

[15]  S. Mallat VI – Wavelet zoom , 1999 .

[16]  Lei Hu,et al.  The Application of Wavelet-Domain Hidden Markov Tree Model in Diabetic Retinal Image Denoising , 2015, The open biomedical engineering journal.

[17]  Zhuan Qin,et al.  In Situ Structural Analysis of the Spirochetal Flagellar Motor by Cryo-Electron Tomography. , 2017, Methods in molecular biology.

[18]  O. Medalia,et al.  The structure of lamin filaments in somatic cells as revealed by cryo-electron tomography , 2017, Nucleus.

[19]  Carlos Oscar Sánchez Sorzano,et al.  TomoJ: tomography software for three-dimensional reconstruction in transmission electron microscopy , 2007, BMC Bioinformatics.

[20]  S. Mallat A wavelet tour of signal processing , 1998 .

[21]  Tessamma Thomas,et al.  Discrete wavelet transform de-noising in eukaryotic gene splicing , 2010, BMC Bioinformatics.

[22]  Rubén Fernández-Busnadiego,et al.  Cryo‐electron tomography—the cell biology that came in from the cold , 2017, FEBS letters.

[23]  Miguel A. Luengo-Oroz,et al.  Wavelet-based image fusion in multi-view three-dimensional microscopy , 2012, Bioinform..

[24]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

[25]  Min Xu,et al.  High precision alignment of cryo-electron subtomograms through gradient-based parallel optimization , 2012, BMC Systems Biology.

[26]  W. Baumeister,et al.  Cryo-Electron Tomography: Can it Reveal the Molecular Sociology of Cells in Atomic Detail? , 2016, Trends in cell biology.

[27]  Raghunath S. Holambe,et al.  Design of Low-Complexity High-Performance Wavelet Filters for Image Analysis , 2013, IEEE Transactions on Image Processing.

[28]  Andrew F. Laine,et al.  A Discrete Dyadic Wavelet Transform for Multidimensional Feature Analysis , 1997 .

[29]  Conrad C. Huang,et al.  Visualizing density maps with UCSF Chimera. , 2007, Journal of structural biology.

[30]  Huixin Zhou,et al.  Infrared and visible image fusion with spectral graph wavelet transform. , 2015, Journal of the Optical Society of America. A, Optics, image science, and vision.

[31]  O. Medalia,et al.  Cellular structural biology as revealed by cryo-electron tomography , 2016, Journal of Cell Science.

[32]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[33]  A V Bronnikov,et al.  Wavelet-based image enhancement in x-ray imaging and tomography. , 1998, Applied optics.

[34]  Zbigniew Starosolski,et al.  Developing a denoising filter for electron microscopy and tomography data in the cloud , 2012, Biophysical Reviews.

[35]  M. Baker,et al.  Applications of a bilateral denoising filter in biological electron microscopy. , 2003, Journal of structural biology.

[36]  Alexey N. Pavlov,et al.  Application of wavelet-based tools to study the dynamics of biological processes , 2006, Briefings Bioinform..

[37]  W Wan,et al.  Cryo-Electron Tomography and Subtomogram Averaging. , 2016, Methods in enzymology.

[38]  J. Briggs,et al.  Determination of protein structure at 8.5Å resolution using cryo-electron tomography and sub-tomogram averaging. , 2013, Journal of structural biology.