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. 2016 Jul;195(1):72-81.
doi: 10.1016/j.jsb.2016.04.013. Epub 2016 Apr 27.

Denoising and covariance estimation of single particle cryo-EM images

Tejal Bhamre  1 , Teng Zhang  2 , Amit Singer  3
Affiliations

Denoising and covariance estimation of single particle cryo-EM images

Tejal Bhamre et al. J Struct Biol. 2016 Jul.

Abstract

The problem of image restoration in cryo-EM entails correcting for the effects of the Contrast Transfer Function (CTF) and noise. Popular methods for image restoration include 'phase flipping', which corrects only for the Fourier phases but not amplitudes, and Wiener filtering, which requires the spectral signal to noise ratio. We propose a new image restoration method which we call 'Covariance Wiener Filtering' (CWF). In CWF, the covariance matrix of the projection images is used within the classical Wiener filtering framework for solving the image restoration deconvolution problem. Our estimation procedure for the covariance matrix is new and successfully corrects for the CTF. We demonstrate the efficacy of CWF by applying it to restore both simulated and experimental cryo-EM images. Results with experimental datasets demonstrate that CWF provides a good way to evaluate the particle images and to see what the dataset contains even without 2D classification and averaging.

Keywords: CTF correction; Steerable PCA; Wiener filtering.

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Figures

Fig. 1.
Fig. 1.
Synthetic white noise: A comparison of the denoising results of traditional Wiener filtering (TWF) and CWF for the synthetic dataset prepared from EMDB-6454, the P. falciparum 80S ribosome bound to E-tRNA. The dataset consists of 10,000 images of size 105 × 105, which are divided into 10 defocus groups, with the defocus value ranging from 1μm to 4μm. The two rows in each subfigure correspond to two clean images belonging to different defocus groups; the first one belongs to the group with the smallest defocus value of 1μm, while the second image belongs to the group with the largest defocus value of 4μm.
Fig. 2.
Fig. 2.
(a) Relative MSE versus the SNR, for a fixed number of images: The relative MSE of the denoised images as a function of the SNR, for synthetic data generated using EMDB-6454. The MSE reported here is averaged over all images. n denotes the number of images used in the experiment. (b) Relative MSE versus the number of images, for a fixed SNR: The relative MSE of the denoised images as a function of the number of images, for synthetic data generated using EMDB-6454. The MSE reported here is averaged over all images.
Fig. 3.
Fig. 3.
Relative MSE of the estimated covariance versus the number of images: The relative MSE of the estimated covariance Σˆ, with and without using eigenvalue shrinkage, as a function of number of images, for synthetic data generated using EMDB-6454.
Fig. 4.
Fig. 4.
Synthetic colored noise: Denoising results of CWF for the synthetic dataset with additive colored Gaussian noise, prepared from EMDB-6454, the P. falciparum 80S ribosome bound to E-tRNA, as detailed in the caption of Fig. 1.
Fig. 5.
Fig. 5.
Denoising an experimental dataset of TRPV1 (Liao et al., 2013): Here we show, for three images in the dataset, the raw image, the closest true projection image generated from the 3D reconstruction of the molecule (EMDB 5778), the denoised image obtained using TWF, and the denoised image obtained using CWF. In this experiment, 35,645 images of size 256 × 256 belonging to 935 defocus groups were used. The amplitude contrast is 10%, the spherical aberration is 2 mm, and the voltage is 300 kV.
Fig. 6.
Fig. 6.
Denoising an experimental dataset of the 80S ribosome (Wong et al., 2014): Here we show, for three images in the dataset, the raw image, the closest true projection image generated from the 3D reconstruction of the molecule (EMDB 2660), the denoised image obtained using TWF, and the denoised image obtained using CWF. In this experiment, the first 30000 images out of the 105,247 images in the dataset were used for covariance estimation. The images are of size 360 × 360 and belong to 290 defocus groups. The amplitude contrast is 10%, the spherical aberration is 2mm, and the voltage is 300 kV.
Fig. 7.
Fig. 7.
Denoising an experimental dataset of IP3R1 (Ludtke et al., 2011): Here we show, for three images in the dataset, the raw image, the closest true projection image generated from the 3D reconstruction of the molecule (EMDB 5278), the denoised image obtained using TWF, and the denoised image obtained using CWF. In this experiment, 37,382 images of size 256 × 256 belonging to 851 defocus groups were used. The amplitude contrast is 15%, the spherical aberration is 2 mm, and the voltage is 200 kV.
Fig. 8.
Fig. 8.
Denoising an experimental dataset of 70S (Agirrezabala et al., 2012): Here we show, for three images in the dataset, the raw image, the closest true projection image generated from the 3D reconstruction of the molecule (EMDB 5360), the denoised image obtained using TWF, and the denoised image obtained using CWF. In this experiment, the first 99,979 images out of the 216,517 images in the dataset were used for covariance estimation. The images are of size 250 × 250 and belong to 38 defocus groups. The amplitude contrast is 10%, the spherical aberration is 2.26 mm, and the voltage is 300 kV.
Fig. 9.
Fig. 9.
(a) Raw images: A sample of synthetic data generated using EMDB-6454 with additive colored Gaussian noise at SNR = 1/20.10% of the projection images are replaced by pure noise. The contrast parameter α ranges from 0.75 to 1.5. The outliers are shown in the last column. Inset in a yellow box is the contrast of each image. (b) Denoised images: The denoised images using CWF. Notice the low contrast outliers in the last column. (c) Estimated mean image. (d) Top 6 eigenimages: Inset in a yellow box is the corresponding eigenvalue.
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