Denoising of Electron Tomograms
The crucial problem inherent to electron tomography is radiation damage or, related to this, the choice of the correct electron dose: an excessive dose destroys the specimen, especially biological ones, while an insufficient dose results in images that are noisy and lack information. Sophisticated and highly automated techniques have been developed both for data acquisition with the aim of keeping the electron dose as low as possible, and for image processing, in order to extract reliable information from the recorded data. However, the tolerable dose is very small, especially for unstained, frozen-hydrated specimens. As a rule of thumb, 5000e/nm2 are tolerable for such specimens. According to the dose fractionation theorem (Hegerl and Hoppe, 1978), the total tolerable dose has to be divided by the number of projection views in order to find the dose allowed for each image of a tilt series. In addition, the low scattering power of biological material results in low-contrast images. For instance, assuming a tilt series of 50 images, a pixel size of 1nm2, phase contrast imaging with a contrast of 10%, and considering only the shot noise of the electrons, the signal-to-noise ratio (SNR defined as energy of signal over energy of noice) in the projection images is in the order of 1. An increase in the number of projection images, a decrease of the pixel size and additional noise arising from the image recording system push the SNR below 1.
KeywordsDiscrete Wavelet Transformation Noise Reduction Root Mean Square Deviation Wavelet Transformation Projection Image
Barth, M., Bryan, R. K., Hegerl, R. and Baumeister, W. (1988). Estimation of missing cone data in three-dimensional electron microscopy. Scanning Microsc. Suppl.
Daubechies, I. (1992). Ten Lectures on Wavelets
. SIAM Publications, Philadelphia.Google Scholar
Donoho, D.L. (1995). De-noising by soft thresholding. IEEE Trans. Inform. Theory
Fernández, J. J. and Li, S. (2003). An improved algorithm for anisotropic nonlinear diffusion for denoising cryo-tomograms. J. Struct. Biol.
Frangakis, A. and Hegerl, R. (2001). Noise reduction in electron tomographic reconstructions using nonlinear anisotropic diffusion. J. Struct. Biol.
Frank, J. (2002). Single-particle imaging of macromolecules by cryo-electron microscopy. Annu. Rev. Biophys. Biomol. Struct.
Fujiyoshi, Y. (1998). The structural study of membrane proteins by electron crystallography. Adv. Biophys.
Hegerl, R. and Hoppe, W. (1976). Influence of electron noise on three-dimensional image reconstruction. Z. Naturforsch.
Jiang, W., Baker, M. L., Wu, Q., Bajaj, C. and Chiu, W. (2003). Applications of a bilateral denoising filter in biological electron microscopy. J. Struct. Biol.
Mallat, S. G. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Machine Intell.
Moss, W. C., Haase, S., Lyle, J. M., Agard, D. A. and Sedat, J.W. (2005). A novel 3D wavelet-based filter for visualizing features in noisy biological data. J. Microsc.
Mrazek, P. and Navara, M. (2003). Selection of optimal stopping time for nonlinear diffusion filtering. Int. J. Comput. Vis.
Perona, P. and Malik, J. (1990). Scale-space and edge detection using anistropic diffusion. IEEE Trans. Pattern Anal. Machine Intell.
Russ, J. C. (1995). The Image Processing Handbook
. CRC Press, Boca Raton, Florida.Google Scholar
Skoglund, U., Öfverstedt, L. G., Burnett, R. M. and Bricogne, G. (1996). Maximum-entropy three-dimensional reconstruction with deconvolution of the contrast transfer function: a test with application with adenovirus. J. Struct. Biol.
Stoschek, A. and Hegerl, R. (1997). Denoising of electron tomographic reconstructions using multiscale transformations. J. Struct. Biol.
Stoschek, A., Yu, T. P. Y., and Hegerl, R. (1997) Denoising of electron tomographic reconstructions biological specimens using multidimensional multiscale transforms. Proc. Of ICA SSP97, Munich, IEEE Computer Society Press, Vol. 4, pp. 2793–2796.Google Scholar
Tomasi, C. and Manduchi, R. (1998). Bilateral filtering for gray and color images. In Proceedings of the IEEE International Conference on Computer Vision
. Bombay, pp. 59–66.Google Scholar
Weickert, J. (1998). Anisotropic Diffusion in Image Processing
. Teubner, Stuttgart.Google Scholar
Weickert, J. (1999). Coherence-enhancing diffusion of color images. Image Vis. Comput.
Yu, T. P.Y., Stoschek, A. and Donoho, D. L. (1996). Translation-and direction-invariant denoising of 2D and 3D images: experience and algorithms. Proc. SPIE
© Springer Science+Business Media, LLC 2007