A method of noise estimation for cryo-electron tomography images

Abstract

The application discloses a noise estimation method for frozen electronic tomography images. The method is based on image space correlation, extracts smooth image blocks as noise estimation samples, uses principal component analysis method to separate real signals and noise, selects redundant dimension number to estimate noise level, greatly guarantees the accuracy and robustness of noise estimation result. The noise estimation for a single image comprises the following steps: selecting a sufficient number of smooth image blocks as noise estimation samples; separating noise and real signals by using the principal component analysis method; and selecting a suitable redundant dimension number to estimate the noise level.

Description

Technical Field

[0001] This invention belongs to the fields of cryo-electron tomography image processing and computer vision, and particularly relates to a noise estimation method for cryo-electron tomography images. Background Technology

[0002] Cryo-electron tomography (cryo-electron computed tomography) has become an important tool for reconstructing the three-dimensional structures of biomolecules at nanoscale resolution through electron microscopic projection images, attracting increasing attention. However, due to the low electron dose and limited sampling angle, electron tomography images typically have a low signal-to-noise ratio, affecting subsequent image analysis and understanding, thus burying useful structural information in noise.

[0003] Electron tomography 3D reconstruction, in the imaging stage, involves placing the biological sample in a transmission electron microscope and rotating it along a direction perpendicular to the electron beam. A two-dimensional projection image is captured at each rotation angle, and this image is recorded using a high-sensitivity device. The collected image data is then analyzed and processed, and finally, a 3D image of the biological sample's structure is obtained through a reconstruction algorithm. The reconstructed 3D image has an extremely low signal-to-noise ratio, requiring a series of post-processing techniques, including denoising, to improve its interpretability.

[0004] Noise level is a crucial parameter in many denoising methods; only accurate estimation of the noise level can achieve good denoising results. Too low a noise estimate will fail to effectively remove noise, while too high a noise estimate will lead to blurred results and loss of image detail. However, in the real world, the noise intensity of cryo-electron tomography images is unknown and needs to be estimated. Accurately estimating the noise intensity of 3D images remains a challenge. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a noise estimation method for cryo-electron tomography images, specifically addressing the issue of unknown noise models and levels in electron tomography images. The core idea of ​​this invention is to extract a sufficient number of smooth image patches based on image spatial correlation, serving as an effective set of image patches for noise level estimation, thus effectively reducing the amount of data required for noise estimation in three-dimensional electron tomography images. Furthermore, the noise level is estimated based on the distribution of eigenvalues ​​of the image patch covariance matrix, effectively improving the accuracy and robustness of noise level estimation.

[0006] A noise estimation method for cryo-electron tomography images, comprising the following steps:

[0007] (1) Calculate image patch texture intensity based on spatial correlation: For a three-dimensional electron tomography image, n×n×n image patches are extracted by sliding with step size p; when calculating the image patch texture intensity, image patches with small differences between adjacent voxels are taken as smooth image patches with small texture intensity, and several image patches with the smallest texture intensity are selected as noise estimation samples; p is 3; n is the image patch size and is 8.

[0008] (2) Eigenvalue decomposition: The covariance matrix eigenvalue decomposition is performed on the selected smooth image blocks. The eigenvalues ​​of the image block covariance matrix are composed of several principal dimension eigenvalues ​​and redundant dimension eigenvalues.

[0009] (3) Determine the number of redundant dimensions: Remove the largest eigenvalue from the eigenvalue set. When the mean and median of the remaining eigenvalue set are the same, the number of redundant dimension eigenvalues ​​is obtained. Thus, the mean of the redundant dimension eigenvalues ​​is the noise level estimation result, and the principal component analysis method is used to complete the noise estimation of the electron tomography image.

[0010] Specifically, in step (1), the texture intensity is calculated based on the spatial correlation of image patches; the inter-voxel correlation degree dist is used to calculate the following:

[0011]

[0012] Where j represents the voxel index adjacent to voxel i, k represents the number of voxels adjacent to voxel i, and x, y, and z represent the spatial coordinates of the voxel in the 3D image. Each voxel has 26 adjacent voxels. Then, the voxel dist within the image patch is calculated. i The mean value is used to determine the smoothness of image patches.

[0013] Specifically, the voxel dist within the image block i The expression for calculating the mean is:

[0014]

[0015] Where r represents the number of voxels within the image patch, μ dist The smaller the value, the smaller the difference between voxels within the image patch, and the smoother the image patch.

[0016] The beneficial effects of this invention are as follows:

[0017] The method of this invention targets noise estimation in cryo-electron tomography images. It measures the texture intensity of image patches based on spatial correlation and extracts a sufficient number of smooth image patches as noise estimation data samples, reducing the spatial requirements of the noise estimation process. Furthermore, it improves the accuracy and robustness of the noise estimation method by performing covariance matrix eigenvalue decomposition and selecting the number of redundant dimensions for the smooth image patches. Attached Figure Description

[0018] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0019] Figure 1 This is a schematic diagram of the principle of three-dimensional reconstruction of electron tomography in this invention;

[0020] Figure 2 This is a flowchart illustrating the noise estimation method based on spatial correlation and principal component analysis of the present invention.

[0021] Figure 3 This is a histogram of the squared eigenvalues ​​of the redundancy dimension of the covariance matrix of the smoothed image block at a noise level of 15 according to the present invention.

[0022] Figure 4 This is a schematic diagram of the noise level estimation results of the present invention. Detailed Implementation

[0023] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application.

[0024] A noise estimation method for cryo-electron tomography images includes the following steps:

[0025] (1) Calculate image patch texture intensity based on spatial correlation:

[0026] For three-dimensional electron tomography images, n×n×n image blocks are extracted by sliding with a step size p; when calculating the texture intensity of the image blocks, image blocks with small differences between adjacent voxels are used as smooth image blocks with low texture intensity, and several image blocks with the lowest texture intensity are selected as noise estimation samples.

[0027] (2) Perform covariance matrix eigenvalue decomposition on the selected smooth image patches:

[0028] The eigenvalues ​​of the image patch covariance matrix are composed of several principal dimension eigenvalues ​​and redundant dimension eigenvalues;

[0029] (3) Determine the number of redundant dimensions:

[0030] By continuously removing the largest eigenvalue from the eigenvalue set, the number of redundant dimension eigenvalues ​​is obtained when the mean and median of the remaining eigenvalue set are the same. At this point, the mean of the redundant dimension eigenvalues ​​is the noise level estimate, and the noise estimation of the electron tomography image is completed using the principal component analysis method.

[0031] The redundant dimension feature value in step (2) is related to the noise level.

[0032] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described below in conjunction with the embodiments and accompanying drawings.

[0033] Example

[0034] This set of experiments uses a three-dimensional electron density map of biological macromolecules for simulation experiments, with a size of 450×450×450.

[0035] Figure 1 This is a schematic diagram illustrating the principle of three-dimensional reconstruction of electron tomography according to the present invention. The noise estimation method based on smooth image patch extraction and principal component analysis described in this invention is applied to this set of data. Figure 2 The flowchart for estimating noise based on spatial correlation and principal component analysis of the present invention includes the following steps:

[0036] First, image patch texture intensity is calculated based on spatial correlation. For a 3D electron tomography image, n×n×n, n=8 image patches are extracted using a step size p=3. When calculating the texture intensity of image patches, patches with small differences between adjacent voxels are considered to have low texture intensity. The 5000 image patches with the lowest texture intensity are selected as noise estimation samples. Texture intensity is calculated based on the spatial correlation of image patches; the correlation degree between voxels (dist) is used for the following calculation:

[0037]

[0038] Where j represents the voxel index adjacent to voxel i, k represents the number of voxels adjacent to voxel i, and x, y, and z represent the spatial coordinates of the voxel in the 3D image. Each voxel has 26 adjacent voxels. Then, the voxel dist within the image patch is calculated. i The mean value is used to determine the smoothness of image patches.

[0039] The image block contains voxels dist i The expression for calculating the mean is:

[0040]

[0041] Where r represents the number of voxels within the image patch, μ dist The smaller the value, the smaller the difference between voxels within the image patch, and the smoother the image patch.

[0042] Secondly, the selected smooth image patches are subjected to covariance matrix eigenvalue decomposition. The eigenvalues ​​of the image patch covariance matrix consist of a few large principal dimension eigenvalues ​​and a majority of redundant dimension eigenvalues. Among them, the redundant dimension eigenvalues ​​are only related to the noise level. Figure 3 This is a histogram of the squared eigenvalues ​​of the redundant dimension of the covariance matrix of the smoothed image block when the noise level is 15 according to the present invention.

[0043] Finally, the number of redundant dimensions is determined. The eigenvalues ​​of the covariance matrix of a noisy image patch consist of a few large principal dimension eigenvalues ​​and a majority of redundant dimension eigenvalues. By continuously removing the largest eigenvalues, the number of redundant dimensions is obtained when the mean of the remaining eigenvalue set is the same as the median. The mean of the redundant dimension eigenvalues ​​is the noise level estimate. Thus, the noise estimation of electron tomography images based on smoothed image patch extraction and principal component analysis is complete. The noise estimation results for different intensities are shown below. Figure 4 As shown in the figure, the noise estimation results have high accuracy and robustness.

[0044] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein.

Claims

1. A noise estimation method for cryo-electron tomography images, characterized in that, Includes the following steps: (1) Calculate image patch texture intensity based on spatial correlation: For three-dimensional electron tomography images, with a step size of Slide Extraction Image patches of varying sizes; when calculating the texture intensity of image patches, image patches with small differences between adjacent voxels are considered smooth image patches with low texture intensity, and several image patches with the lowest texture intensity are selected as noise estimation samples; the step size The value is 3; The image patch size is set to 8; the texture intensity is calculated based on the spatial correlation of the image patches; the correlation between voxels is used. The calculation is as follows: ； in, Indicates voxel Adjacent voxel subscripts, Representation and voxels The number of adjacent voxels, x, y, and z represent the spatial coordinates of the voxel in the 3D image, and each voxel has 26 adjacent voxels; then the voxels within the image patch are calculated. The mean value is used to determine the smoothness of image patches; (2) Eigenvalue decomposition: The covariance matrix eigenvalues ​​of the selected smooth image blocks are decomposed. The eigenvalues ​​of the image block covariance matrix are composed of several principal dimension eigenvalues ​​and redundant dimension eigenvalues. (3) Determine the number of redundant dimensions: Remove the largest eigenvalue from the eigenvalue set. When the mean and median of the remaining eigenvalue set are the same, the number of redundant dimension eigenvalues ​​is obtained. Thus, the mean of the redundant dimension eigenvalues ​​is the noise level estimation result, and the principal component analysis method is used to complete the noise estimation of the electron tomography image.

2. The noise estimation method for cryo-electron tomography images according to claim 1, characterized in that, The voxels within the image block The expression for calculating the mean is: ； in, This indicates the number of voxels within an image patch. The smaller the value, the smaller the difference between voxels within the image patch, and the smoother the image patch.

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