CN112215942B - Method and system for reconstructing partial tomographic three-dimensional image of refrigeration electron microscope - Google Patents
Method and system for reconstructing partial tomographic three-dimensional image of refrigeration electron microscope Download PDFInfo
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Abstract
The invention provides a reconstruction method of a partial tomographic three-dimensional image of a refrigeration electron microscope, which comprises the following steps: selecting and averaging a plurality of local tomographic three-dimensional image particles in a homogeneous manner to obtain an initial reference structure for registration of the local tomographic three-dimensional images; obtaining a plurality of pairs of optimal coarse rotation parameters and translation parameters by using a rapid rotation/translation matching algorithm; continuously updating the rotation parameter and the translation parameter by utilizing a local tomographic three-dimensional image registration algorithm to register the local tomographic three-dimensional image particles; and (3) aligning and averaging the local tomographic three-dimensional images by using the rotation parameters and the translation parameters obtained by registration to obtain a reconstructed local tomographic three-dimensional image.
Description
Technical Field
The invention relates to the technical field of structural biology, in particular to a method and a system for reconstructing a partial tomographic three-dimensional image of a refrigeration electron microscope.
Background
Cryo-electron tomography (cryo-electron tomography, cryo-ET) is an imaging technique that reconstructs the three-dimensional structure of cellular macromolecular complexes under natural conditions. With the improvement of the frozen electronic tomography image acquisition technology, more and more images are acquired and processed to obtain a large number of two-dimensional images, and a three-dimensional image is reconstructed by using the two-dimensional images. In recent years, low-temperature electron microscopy has been developed, and the quality of three-dimensional reconstructed images has been improved greatly. However, the frozen electron tomographic images still have low resolution, partial data loss, and low signal-to-noise ratio (SNR). The three-dimensional image obtained by utilizing the frozen electron tomography reconstruction has low resolution, and the three-dimensional structure and function of the biomacromolecule are difficult to study.
To solve these problems and to increase the resolution of local tomographic three-dimensional reconstruction in tomographic three-dimensional images, similar to single particle reconstruction techniques, iterative registration and averaging of a large number of local tomographic three-dimensional image particles containing the same structure is required. The specific process comprises the following steps: and selecting isomorphic three-dimensional particles from the three-dimensional image reconstructed by the fault, registering the three-dimensional image, then averaging the three-dimensional image, and continuously iterating the registering and averaging processes to obtain a high-resolution local fault three-dimensional structure.
The current local fault three-dimensional reconstruction technology is mainly divided into a cross-correlation method, an empirical Bayesian method and a coarse-granularity multi-resolution method. However, the existing local fault three-dimensional reconstruction technology needs to register the local fault three-dimensional images, the calculated amount of the related three-dimensional images is large, and the local fault three-dimensional reconstruction process needs to iterate for a plurality of times, so that the time cost of an algorithm is large. It is a significant challenge to compute resources, generally based on how much local tomographic three-dimensional image data is, requiring continuous computation for days, even weeks.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for reconstructing a partial tomographic three-dimensional image of a refrigeration electron microscope, which comprises the following steps:
step 1, selecting a plurality of local tomographic three-dimensional images with isomorphic constitution by using a local tomographic three-dimensional classification method, and averaging the plurality of local tomographic three-dimensional images to obtain an initial reference structure;
step 2, comparing each of the plurality of partial tomographic three-dimensional images with the initial reference structure by using a fast rotation matching algorithm (FRM) and a fast translation matching algorithm (FTM), wherein each of the plurality of partial tomographic three-dimensional images correspondingly obtains a plurality of pairs of optimal coarse rotation parameters and translation parameters;
step 3, initializing each of the plurality of pairs of optimal coarse rotation parameters and translation parameters to obtain corresponding initial rotation parameters and translation parameters, and setting parameters of the local tomographic three-dimensional image registration, including an update frequency m, a learning rate eta, a minimum distance min_d, an original distance old_d, a minimum distance difference eps, an inner iteration number maxIter_in and an outer iteration number maxIter_out;
step 4, obtaining the average derivative of the initial rotation parameter and the translation parameter through calculation;
the calculation formula of the average derivative is as follows:
wherein H is i (R，T)＝(V 1 (x i ) ★ -Λ R Λ T V 2 (x i ) ★ ) 2 I is a subscript of the partial tomographic three-dimensional image along the x-axis.
Step 5, performing m iterative computations on the initialized rotation parameters and the translation parameters to obtain corresponding suboptimal rotation parameters and translation parameters;
the iterative calculation formula is as follows:
wherein i is t For random selection among 1 to n, n is the side length of the partial tomographic three-dimensional image, and t is the current iteration.
Step 6, calculating and judging whether the Euclidean distance d of the current partial tomographic three-dimensional image is smaller than the minimum distance min_d, if so, assigning the Euclidean distance d to the minimum distance min_d, otherwise, keeping the minimum distance min_d to be the original value;
step 7, judging whether the absolute value of the difference between the minimum distance min_d and the original distance old_d is smaller than the minimum distance difference eps, if so, outputting the suboptimal rotation parameter and the translation parameter, otherwise, assigning the minimum distance min_d to the original distance old_d, initializing the suboptimal rotation parameter and the translation parameter as new initialized rotation parameter and translation parameter, and repeatedly and circularly executing the steps 3-7 maxIter times to output the suboptimal rotation parameter and the translation parameter obtained by the maxIter times;
step 8, aligning the corresponding local tomographic three-dimensional images in real space according to the suboptimal rotation parameters and the translation parameters, and averaging the aligned local tomographic three-dimensional images to obtain a reconstructed local tomographic three-dimensional image;
wherein V is 1 Representing one of the plurality of partial tomographic three-dimensional images currently being operated, V 2 Representing the initial reference structure, the rotation parameters r= (phi, theta, phi) T Can be regarded as the euler angle using the ZYZ convention, the translation parameter t= (τ) 1 ，τ 2 ，τ 3 ) T ，Λ R Defined as a rotation operation of the local tomographic three-dimensional image particles.
The invention also provides a system for reconstructing the partial tomographic three-dimensional image of the refrigeration electron microscope, which comprises:
the module 1 is used for selecting a plurality of local tomographic three-dimensional images with isomorphic constitution by utilizing a local tomographic three-dimensional classification method, and averaging the plurality of local tomographic three-dimensional images to obtain an initial reference structure;
a module 2, configured to compare each of the plurality of local tomographic three-dimensional images with the initial reference structure using a fast rotation matching algorithm (FRM) and a fast translation matching algorithm (FTM), where each of the plurality of local tomographic three-dimensional images correspondingly obtains a plurality of pairs of optimal coarse rotation parameters and translation parameters;
the module 3 is configured to initialize each of the plurality of pairs of optimal coarse rotation parameters and translation parameters to obtain corresponding initial rotation parameters and translation parameters, and set parameters of the local tomographic three-dimensional image registration, including an update frequency m, a learning rate η, a minimum distance min_d, an original distance old_d, a minimum distance difference eps, an inner iteration number maxIter, and an outer iteration number maxIter_out;
a module 4 for obtaining the average derivative of the initial rotation parameter and the translation parameter by calculation;
the calculation formula of the average derivative is as follows:
wherein H is i (R，T)＝(V 1 (x i ) ★ -Λ R Λ T V 2 (x i ) ★ ) 2 I is a subscript of the partial tomographic three-dimensional image along the x-axis.
The module 5 is used for carrying out m times of iterative computation on the initialized rotation parameters and the translation parameters to obtain corresponding suboptimal rotation parameters and translation parameters;
the iterative calculation formula is as follows:
wherein i is t For random selection among 1 to n, n is the side length of the partial tomographic three-dimensional image, and t is the current iteration.
A module 6, configured to calculate and determine whether a euclidean distance d of the current local tomographic three-dimensional image is smaller than a minimum distance min_d, if yes, assign the euclidean distance d to the minimum distance min_d, otherwise, the minimum distance min_d maintains an original value;
the module 7 is configured to determine whether the absolute value of the difference between the minimum distance min_d and the original distance old_d is smaller than the minimum distance difference eps, if yes, output the suboptimal rotation parameter and the translation parameter, otherwise, assign the minimum distance min_d to the original distance old_d, initialize the suboptimal rotation parameter and the translation parameter, as a new initialized rotation parameter and a new translation parameter, execute the above module 3-module 7maxIter repeatedly, and output the suboptimal rotation parameter and the translation parameter obtained by the maxIter repeatedly;
the module 8 is used for aligning the corresponding local tomographic three-dimensional images in a real space according to the suboptimal rotation parameters and the translation parameters, and averaging the aligned local tomographic three-dimensional images to obtain a reconstructed local tomographic three-dimensional image;
wherein V is 1 Representing one of the plurality of partial tomographic three-dimensional images currently being operated, V 2 Representing the initial reference structure, the rotation parameters r= (phi, theta, phi) T Can be regarded as the euler angle using the ZYZ convention, the translation parameter t= (τ) 1 ，τ 2 ，τ 3 ) T ，Λ R Defined as a rotation operation of the local tomographic three-dimensional image particles.
The advantages of the invention are as follows: based on the random variance reduction gradient, the invention provides a local tomographic three-dimensional image registration method and a local tomographic three-dimensional image registration system, which can effectively reduce the sampling range in the three-dimensional image registration process and reduce the time of the local tomographic three-dimensional image reconstruction process, so that the calculation time is less on the premise of obtaining the local tomographic three-dimensional reconstruction images with the same resolution precision, and the research efficiency based on the local tomographic three-dimensional reconstruction images is effectively improved.
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FIG. 1 is a flow chart of a method for reconstructing a partial tomographic image of a cryo-electron microscope according to an embodiment of the present invention.
Detailed Description
In order to make the above-mentioned features and effects of the present invention more clearly and more comprehensible, the following embodiments accompanied with figures are described in detail
FIG. 1 is a flow chart of a method for reconstructing a partial tomographic image of a cryo-electron microscope in accordance with an embodiment of the present invention.
Step 1: selection of homogeneous multiple local tomographic three-dimensional image particles and generation of an initial reference structure for local tomographic three-dimensional image registration. The method specifically comprises the following steps:
and 11, selecting and obtaining a plurality of local tomographic three-dimensional images with the same conformation by using a classification method of the local tomographic three-dimensional images. As is known in the art, the homogeneous local tomographic three-dimensional image may be selected from a database of existing local tomographic three-dimensional images.
Step 12, averaging the homogeneous local tomographic three-dimensional images to generate an initial reference structure for registering the local tomographic three-dimensional images, wherein the initial reference structure uses V 2 To represent.
Step 2: for each of the plurality of partial tomographic three-dimensional images of the homogeneous constitution in the first step, a fast rotation matching algorithm (FRM) and a fast translation matching algorithm (FTM) are respectively associated with the initial reference structure V 2 A comparison is made so that each of the plurality of partial tomographic three-dimensional images can correspondingly result in a plurality of pairs of optimal coarse rotation parameters and translation parameters. The method specifically comprises the following steps:
step 21, first, a plurality of partial tomographic three-dimensional images V 1 And an initial reference structure V 2 Converting from real space to fourier space; then, fourier coefficients corresponding to each of the plurality of partial tomographic three-dimensional images are converted into spherical coordinates, the spherical coordinates are utilized to be unfolded, constraint cross-correlation values CCC of regularized spherical functions under different frequencies are calculated, and a three-dimensional array of a plurality of corresponding CCC values is obtained; finally, searching the optimal coarse rotation parameters R corresponding to the maximum of the top N CCC values in the three-dimensional array of each CCC value max . The calculation formula of the CCC value is as follows:
in the above formulas (1) - (4), V 1 Representing one of the current local tomographic three-dimensional images, V 2 Representing the initial reference structure, the rotation parameters r= (phi, theta, phi) T Can be regarded as Euler angles, k using the ZYZ convention max Is the maximum frequency band involved, +.is the spherical harmonic dependent operation,and->Is V 1 And V 2 Fourier space transformation.
The CCC value is calculated by the formula, and the peak value of the CCC value represents the optimal coarse rotation parameter R max It is common practice to select N optimal peaks to obtain N corresponding optimal coarse rotation parameters R max The value of N is usually set to any integer from 2 to 10, and the invention is not limited thereto.
Step 22, first, the partial tomographic three-dimensional image V 1 And reference structure V 2 Constrained in fourier space; then, the partial tomographic three-dimensional image V is calculated using a Fast Fourier Transform (FFT) -based algorithm 1 And reference structure V 2 Is of local relevance of (a)Obtaining the corresponding optimal rough translation parameter T max . Optimal coarse rotation parameter T max The calculation formula of (2) is as follows:
wherein,is a local tomographic three-dimensional image normalized and registered +.>And initial reference Structure->Participation in the calculation includes three parts: first, normalized and registered local tomographic three-dimensional image +.>Second, normalized and registered local tomographic three-dimensional image or initial reference structure +.>And thirdly, a constraint cross-correlation value CCC.
Normalized and registered local tomographic three-dimensional imagesAnd initial reference Structure->The calculation formula of (2) is as follows:
mean value of local tomographic three-dimensional imageAnd->Restricted by M and Ω, expressed as:
local constraint cross-correlation functionCalculated by equation (10):
in the above formulas (5) - (10), V 1 Representing one of the current local tomographic three-dimensional images, V 2 Representing an initial reference structure, Λ R Defined as rotation operation of the partial tomographic three-dimensional image, rotation parameter r= (Φ, θ, ψ) T Can be regarded as the euler angle using the ZYZ convention, the translation parameter t= (τ) 1 ，τ 2 ，τ 3 ) T ，Defined as fourier transform, ">Defined as inverse fourier transform, three-dimensional template->A missing cone representing a partial tomographic three-dimensional image in fourier space, wherein the median value is 1 in the data region and 0 in the region without data coverage,/in the region without data coverage>Defined as a partial tomographic three-dimensional image V 1 And V 2 In the fourier space aligned overlap region, M is defined as a binarized template function in real space.
Thus, the operations of steps 21-22, namely comparing each of the plurality of partial tomographic three-dimensional images of the same conformation in step 1 with the initial reference structure by FRM and FTM, result in each of the plurality of partial tomographic three-dimensional images corresponding to a plurality of pairs of optimal coarse rotation and translation parameters, e.g., denoted as { (R) 1 ，T 1 )，(R 2 ，T 2 )，...，(R N ，T N )}。
Step 3: the registration operation is sequentially performed on the plurality of local tomographic three-dimensional images in the step 1, and is specifically performed in such a way that the embodiment of the present invention is continuously updated (R, T) by the local tomographic three-dimensional image registration algorithm given the initial rotation parameter R and the translation parameter T of the local tomographic three-dimensional image. The method specifically comprises the following steps:
step 31, setting parameters required for local tomographic three-dimensional image registration and initializing rotation parametersAnd translation parameter->Wherein the initial rotation parameter->And translation parameter->For the plurality of pairs of optima obtained in the second step of initializingThe coarse rotation and translation parameters are obtained and parameters in the local tomoregistration, including the update frequency m, the learning rate η, the inner iteration number maxIter_in, the outer iteration number maxIter_out, the minimum distance min_d, the original distance old_d, and the minimum distance difference eps are set, and in this embodiment, specific values of these parameters are currently set to m=10, η=1/(20×maxIter), maxIter_in_maxIter_out=20, min_d=old_d= -1, and eps=0.0001.
Step 32, rotational parameters for registration of local tomographic three-dimensional imagesAnd translation parameter->Assignment of value, whereinSetting an initial rotation parameter R 0 And translation parameter T 0 ，/>And calculating the mean derivative of the rotation parameter +.>And mean derivative of translation parameters +.>The calculation formula of the average derivative is:
wherein H is i (R，T)＝(V 1 (x i ) ★ -Λ R Λ T V 2 (x i ) ★ ) 2 I is the subscript of the partial tomographic three-dimensional image along the x-axis.
Step 33, setting m iterations, m being the update frequency, and calculating the rotation parameter R of the partial tomographic three-dimensional image in the current iteration t t And translation parameter T t . The method specifically comprises the following steps:
step 331, randomly selecting i among 1 to n t Where n is the side length of the currently operated partial tomographic three-dimensional image.
Step 332, calculating the rotation parameter R of the partial tomographic three-dimensional image in the current iteration t t And translation parameter T t . The calculation formula is as follows:
step 333, judging whether the current iteration times t reach the maximum value m times, if not, turning to step 331; otherwise, go to step 34 and obtain rotation parameter R obtained by the mth iteration m And translation parameter T m 。
Step 34, rotation parameters in the current iteration kAnd translation parameter->Assignment, wherein->
Step 35, calculating Euclidean distance d (R, T) of the local tomographic three-dimensional image of the current operation, wherein
And 36, judging whether the Euclidean distance d is smaller than the minimum distance min_d, and if so, assigning the value of the current Euclidean distance d to the minimum distance min_d.
Step 37, judging whether the absolute value of the difference between the minimum distance min_d and the original distance old_d is smaller than the minimum distance difference eps, if so, outputting a suboptimal rotation parameter and a translation parameter corresponding to the current iteration k, and turning to step 4; otherwise, the value of the minimum distance min_d is assigned to the original distance old_d.
Step 38, judging whether the current iteration number k reaches the inner iteration number maxIter_in, if not, turning to step 32; otherwise, outputting the suboptimal rotation parameter and the translation parameter corresponding to the current iteration k, and turning to the step 4.
Step 4: and (3) aligning and averaging the local tomographic three-dimensional image by using the suboptimal rotation parameters and the translation parameters obtained in the step (3), and obtaining a reconstructed local tomographic three-dimensional image. The method specifically comprises the following steps:
and step 41, carrying out space position transformation on the local tomographic three-dimensional image according to the suboptimal rotation parameter and the translation parameter obtained in the third step, and realizing alignment of the local tomographic three-dimensional image in a real space.
And 42, after the local tomographic three-dimensional images are aligned, splitting the local tomographic three-dimensional images according to the parity sequence numbers, so as to obtain 2 groups of aligned local tomographic three-dimensional images, and then, for each group, respectively averaging to form 2 reconstructed local tomographic three-dimensional images, wherein the 2 reconstructed local tomographic three-dimensional images are respectively represented by half_map1 and half_map2.
And 43, converting the half_map1 and half_map2 three-dimensional images into a Fourier space, and calculating the resolution corresponding to the 2 three-dimensional structures by using a Fourier spherical shell coefficient (FSC), wherein the FSC threshold is set to be 0.143, and designating the voxel value of the local tomographic three-dimensional image to obtain the corresponding resolution current_resolution. The calculation formula of FSC is:
wherein s is i Corresponds to a series of spherical shells s, F (s i ) Is the radial frequency s in Fourier space i Is used to determine the complex number of structural factors of (a),is all fourier space voxels s in the spherical shell s i Sum of F(s) i ) ★ Represents F(s) i ) Is a complex conjugate of (a) and (b).
And step 44, averaging all the aligned partial tomographic three-dimensional images to obtain a reconstructed partial tomographic three-dimensional image.
And 45, judging whether the resolution current_resolution value is smaller than a resolution preset threshold value, if so, outputting the reconstructed local tomographic three-dimensional image obtained in the step 44 and the resolution current_resolution obtained in the step 43, if not, taking the reconstructed local tomographic three-dimensional image obtained in the step 44 as an initial reference structure in the step 2, turning to the step 2, repeatedly executing the steps 2-4 until the maximum Iter_out time is reached, and outputting the reconstructed local tomographic three-dimensional image obtained in the maximum Iter_out time.
The following is an example of a system corresponding to the above method embodiment, and the system of this embodiment may be implemented in conjunction with the above embodiment. The related technical details mentioned in the above embodiments are still valid in the system of the present embodiment, and are not repeated here for reducing repetition.
The invention also provides a system for reconstructing the partial tomographic three-dimensional image of the refrigeration electron microscope, which comprises:
the module 1 is used for selecting a plurality of local tomographic three-dimensional images with isomorphic constitution by utilizing a local tomographic three-dimensional classification method, and averaging the plurality of local tomographic three-dimensional images to obtain an initial reference structure;
a module 2, configured to compare each of the plurality of local tomographic three-dimensional images with the initial reference structure using a fast rotation matching algorithm (FRM) and a fast translation matching algorithm (FTM), where each of the plurality of local tomographic three-dimensional images correspondingly obtains a plurality of pairs of optimal coarse rotation parameters and translation parameters;
the module 3 is configured to initialize each of the plurality of pairs of optimal coarse rotation parameters and translation parameters to obtain corresponding initial rotation parameters and translation parameters, and set parameters of the local tomographic three-dimensional image registration, including an update frequency m, a learning rate η, a minimum distance min_d, an original distance old_d, a minimum distance difference eps, an inner iteration number maxIter, and an outer iteration number maxIter_out;
a module 4 for obtaining the average derivative of the initial rotation parameter and the translation parameter by calculation;
the calculation formula of the average derivative is as follows:
wherein H is i (R，T)＝(V 1 (x i ) ★ -Λ R Λ T V 2 (x i ) ★ ) 2 I is a subscript of the partial tomographic three-dimensional image along the x-axis.
The module 5 is used for carrying out m times of iterative computation on the initialized rotation parameters and the translation parameters to obtain corresponding suboptimal rotation parameters and translation parameters;
the iterative calculation formula is as follows:
wherein i is t To randomly select from 1 to n, n is the local breakAnd the side length of the layer three-dimensional image, and t is the current iteration.
A module 6, configured to calculate and determine whether a euclidean distance d of the current local tomographic three-dimensional image is smaller than a minimum distance min_d, if yes, assign the euclidean distance d to the minimum distance min_d, otherwise, the minimum distance min_d maintains an original value;
the module 7 is configured to determine whether the absolute value of the difference between the minimum distance min_d and the original distance old_d is smaller than the minimum distance difference eps, if yes, output the suboptimal rotation parameter and the translation parameter, otherwise, assign the minimum distance min_d to the original distance old_d, initialize the suboptimal rotation parameter and the translation parameter, as new initialized rotation parameter and translation parameter, repeatedly execute the above-mentioned modules 3-7 to maxIter_in times, and output the suboptimal rotation parameter and the translation parameter obtained by the maxIter_in times;
the module 8 is used for aligning the corresponding local tomographic three-dimensional images in a real space according to the suboptimal rotation parameters and the translation parameters, and averaging the aligned local tomographic three-dimensional images to obtain a reconstructed local tomographic three-dimensional image;
wherein V is 1 Representing one of the plurality of partial tomographic three-dimensional images currently being operated, V 2 Representing the initial reference structure, the rotation parameters r= (phi, theta, phi) T Can be regarded as the euler angle using the ZYZ convention, the translation parameter t= (τ) 1 ，τ 2 ，τ 3 ) T ，Λ R Defined as a rotation operation of the local tomographic three-dimensional image particles.
In an embodiment of the present invention, the module 2 in the above-mentioned partial tomographic three-dimensional image reconstruction system for a cryo-electron microscope includes: a module 2.1 for converting the plurality of partial tomographic three-dimensional images and the initial reference structure from real space to fourier space; the module 2.2 is used for converting Fourier coefficients corresponding to the plurality of local fault three-dimensional images into spherical coordinates, expanding the spherical coordinates by utilizing spherical harmonics, calculating constraint cross-correlation values of regularized spherical functions under different frequencies, and obtaining a three-dimensional array of the constraint cross-correlation values; and a module 2.3 for retrieving the plurality of optimal rotation parameters in a three-dimensional array of the constraint cross-correlation values, wherein a maximum of the constraint cross-correlation values corresponds to the plurality of optimal coarse rotation parameters;
in an embodiment of the present invention, the module 2 in the above-mentioned partial tomographic three-dimensional image reconstruction system for a cryoelectron microscope further includes: a module 2.4 for constraining the plurality of partial tomographic three-dimensional images and the initial reference structure in fourier space; and a module 2.5 for calculating local correlation values of the plurality of local tomographic three-dimensional images and an initial reference structure, respectively, using a Fast Fourier Transform (FFT) based algorithm, and obtaining the plurality of optimal coarse translation parameters corresponding thereto;
in an embodiment of the present invention, the parameters in the module 3 in the above-mentioned partial tomographic image reconstruction system are set to an update frequency m=10, a learning rate η=1/(20×maxiter), a minimum distance min_d=an original distance old_d= -1, a minimum distance difference eps=0.0001, and an inner iteration number maxiter_in=an outer iteration number maxiter_out=20.
In an embodiment of the present invention, the module 8 in the above-mentioned partial tomographic three-dimensional image reconstruction system for a cryoelectron microscope includes: the module 8.1 is used for splitting the aligned local tomographic three-dimensional images according to the odd-even serial numbers to obtain two groups of aligned local tomographic three-dimensional images, and respectively averaging the two groups of aligned local tomographic three-dimensional images to obtain two reconstructed local tomographic three-dimensional images; a module 8.2 for converting the two reconstructed partial tomographic three-dimensional images into fourier space, and calculating the current resolution corresponding to the two reconstructed partial tomographic three-dimensional images by using fourier spherical shell coefficients (FSCs); and a module 8.3, configured to determine whether the current resolution is less than a preset resolution, if yes, output the reconstructed local tomographic three-dimensional image, otherwise, repeatedly execute the modules 3-8 to maxiter_out times with the reconstructed local tomographic three-dimensional image as a new initial reference structure, and output the reconstructed local tomographic three-dimensional image of the maxiter_out time.
In summary, based on the random variance reduction gradient, the invention provides a local tomographic three-dimensional image registration method and a local tomographic three-dimensional image registration system, which can effectively reduce the sampling range in the three-dimensional image registration process and reduce the time of the local tomographic three-dimensional image reconstruction process, so that the calculation time is less on the premise of obtaining the local tomographic three-dimensional reconstruction images with the same resolution precision, and the research efficiency based on the local tomographic three-dimensional reconstruction images is effectively improved.
Claims (10)
1. A method for reconstructing a partial tomographic three-dimensional image of a cryoelectron microscope is characterized by comprising the following steps:
step 1, selecting a plurality of local tomographic three-dimensional images with isomorphic constitution by using a local tomographic three-dimensional classification method, and averaging the plurality of local tomographic three-dimensional images to obtain an initial reference structure;
step 2, comparing each of the plurality of partial tomographic three-dimensional images with the initial reference structure by using a rapid rotation matching algorithm and a rapid translation matching algorithm, wherein each of the plurality of partial tomographic three-dimensional images correspondingly obtains a plurality of pairs of optimal coarse rotation parameters and optimal coarse translation parameters;
step 3, initializing each of the optimal coarse rotation parameters and the optimal coarse translation parameters to obtain corresponding initial rotation parameters and initial translation parameters, and setting parameters of the local tomographic three-dimensional image registration, including an update frequency m, a learning rate eta, a minimum distance min_d, an original distance old_d, a minimum distance difference eps, an inner iteration number maxIter_in and an outer iteration number maxIter_out;
step 4, obtaining the average derivative of the initial rotation parameter and the initial translation parameter through calculation;
the calculation formulas of the average derivatives of the initial rotation parameter and the initial translation parameter are respectively as follows:
wherein,representing the initial rotation parameters +.>Representing initial translation parameters, i is a subscript of the partial tomographic three-dimensional image along an x-axis, n is a side length of the partial tomographic three-dimensional image, +.>Defined as the average derivative of the initial rotation parameter, +.>Defined as the average derivative of the initial translation parameter, +.>Representing the input of the initial rotation parameter +.>And initial translation parameters->After that, V 1 And V 2 The i distance measurement along the x-axis direction of the partial tomographic three-dimensional image after spatial alignment is smaller than or equal to n, and i is larger than 0;
step 5, performing iterative computation for a plurality of times aiming at the initial rotation parameter and the initial translation parameter to obtain a corresponding suboptimal rotation parameter and suboptimal translation parameter;
the iterative calculation formulas of the initial rotation parameter and the initial translation parameter are respectively as follows:
wherein R is t-1 And R is t Respectively representing the rotation parameters obtained by calculation in the T-1 th iteration and the T-th iteration, T t-1 And T t Respectively representing the translation parameters obtained by calculation in the t-1 th iteration and the t-th iteration,representing the input rotation parameter R t-1 And translation parameter T t-1 After that, V 1 And V 2 Spatially aligned ith along x-axis direction of a partial tomographic three-dimensional image t Is a measure of the distance of (a),representing the input of the initial rotation parameter +.>And initial translation parameters->After that, V 1 And V 2 Spatially aligned ith along x-axis direction of a partial tomographic three-dimensional image t Distance measure i of (1) t Less than or equal to n and i t Greater than 0;
step 6, calculating and judging whether the Euclidean distance d of the current partial tomographic three-dimensional image is smaller than the minimum distance min_d, if so, assigning the Euclidean distance d to the minimum distance min_d, otherwise, keeping the minimum distance min_d to be the original value;
step 7, judging whether the absolute value of the difference between the minimum distance min_d and the original distance old_d is smaller than the minimum distance difference eps, if so, outputting the suboptimal rotation parameter and the suboptimal translation parameter, otherwise, assigning the minimum distance min_d to the original distance old_d, initializing the suboptimal rotation parameter and the suboptimal translation parameter as new initial rotation parameter and translation parameter, repeatedly executing the steps 3-7 to maxIter_in times, and outputting the suboptimal rotation parameter and the suboptimal translation parameter obtained by the maxIter_in times;
step 8, aligning the local tomographic three-dimensional images corresponding to the suboptimal rotation parameters and the suboptimal translation parameters obtained in the step 7 in a real space, and averaging the aligned local tomographic three-dimensional images to obtain a reconstructed local tomographic three-dimensional image;
wherein V is 1 Representing one of the plurality of partial tomographic three-dimensional images currently being operated, V 2 Representing the initial reference structure.
2. The method for reconstructing a partial tomographic image according to claim 1, wherein said step 2 comprises:
step 2.1, converting the plurality of local tomographic three-dimensional images and the initial reference structure from real space to fourier space;
2.2, converting Fourier coefficients corresponding to the partial tomographic three-dimensional images into spherical coordinates, expanding by utilizing spherical harmonics, and calculating constraint cross-correlation values of regularized spherical functions under different frequencies to obtain a three-dimensional array of the constraint cross-correlation values;
and 2.3, searching a plurality of optimal coarse rotation parameters in the three-dimensional array of the constraint cross-correlation values, wherein the maximum value of the constraint cross-correlation values corresponds to the plurality of optimal coarse rotation parameters.
3. The method for reconstructing a partial tomographic image according to claim 2, wherein said step 2 comprises:
step 2.4, constraining the plurality of local tomographic three-dimensional images and the initial reference structure in fourier space;
and 2.5, calculating local correlation values of the local tomographic three-dimensional images and the initial reference structure by using a fast Fourier transform algorithm, and obtaining a plurality of corresponding optimal coarse translation parameters.
4. The method for reconstructing a partial tomographic three-dimensional image according to claim 1, wherein the parameters in the step 3 are set to an update frequency m=10, a learning rate η=1/(20×maxiter), a minimum distance min_d=an original distance old_d= -1, a minimum distance difference eps=0.0001, and an inner iteration number maxiter_in=an outer iteration number maxiter_out=20; where maxIter represents the number of iterations.
5. The method for reconstructing a partial tomographic image according to claim 1, wherein said step 8 comprises:
step 8.1, splitting the aligned local tomographic three-dimensional images according to the odd-even serial numbers to obtain two groups of aligned local tomographic three-dimensional images, and respectively averaging the two groups of aligned local tomographic three-dimensional images to obtain two reconstructed local tomographic three-dimensional images;
step 8.2, converting the two reconstructed local tomographic three-dimensional images into a Fourier space, and calculating the current resolution corresponding to the two reconstructed local tomographic three-dimensional images by using a Fourier spherical shell coefficient;
and 8.3, judging whether the current resolution is smaller than a preset resolution, if so, outputting the reconstructed local tomographic three-dimensional image, otherwise, taking the reconstructed local tomographic three-dimensional image as a new initial reference structure, repeatedly executing the steps 3-8 to maxIter_out times, and outputting the reconstructed local tomographic three-dimensional image of the maxIter_out times.
6. A system for reconstructing a partial tomographic image of a cryoelectron microscope, comprising:
the module 1 is used for selecting a plurality of local tomographic three-dimensional images with isomorphic constitution by utilizing a local tomographic three-dimensional classification method, and averaging the plurality of local tomographic three-dimensional images to obtain an initial reference structure;
the module 2 is used for comparing each of the plurality of local tomographic three-dimensional images with the initial reference structure respectively by utilizing a fast rotation matching algorithm and a fast translation matching algorithm, and each of the plurality of local tomographic three-dimensional images correspondingly obtains a plurality of pairs of optimal coarse rotation parameters and optimal coarse translation parameters;
the module 3 is configured to initialize each of the plurality of pairs of the optimal coarse rotation parameter and the optimal coarse translation parameter to obtain a corresponding initial rotation parameter and an initial translation parameter, and set parameters of the local tomographic three-dimensional image registration, including an update frequency m, a learning rate η, a minimum distance min_d, an original distance old_d, a minimum distance difference eps, an inner iteration number maxiter_in, and an outer iteration number maxiter_out;
a module 4 for obtaining the average derivatives of the initial rotation parameter and the initial translation parameter by calculation;
the calculation formulas of the average derivatives of the initial rotation parameter and the initial translation parameter are respectively as follows:
wherein,representing the initial rotation parameters +.>Representing initial translation parameters, i is a subscript of the partial tomographic three-dimensional image along an x-axis, n is a side length of the partial tomographic three-dimensional image, +.>Defined as the average derivative of the initial rotation parameter, +.>Defined as the average derivative of the initial translation parameter, +.>Representing the input of the initial rotation parameter +.>And initial translation parameters->After that, V 1 And V 2 The i distance measurement along the x-axis direction of the partial tomographic three-dimensional image after spatial alignment is smaller than or equal to n, and i is larger than 0;
the module 5 is used for carrying out repeated iterative computation on the initial rotation parameter and the initial translation parameter to obtain a corresponding suboptimal rotation parameter and suboptimal translation parameter;
the iterative calculation formulas of the initial rotation parameter and the initial translation parameter are respectively as follows:
wherein R is t-1 And R is t Respectively representing the rotation parameters obtained by calculation in the T-1 th iteration and the T-th iteration, T t-1 And T t Respectively representing the translation parameters obtained by calculation in the t-1 th iteration and the t-th iteration,representing the input rotation parameter R t-1 And translation parameter T t-1 After that, V 1 And V 2 Spatially aligned ith along x-axis direction of a partial tomographic three-dimensional image t Is a measure of the distance of (a),representing the input of the initial rotation parameter +.>And initial translation parameters->After that, V 1 And V 2 Spatially aligned ith along x-axis direction of a partial tomographic three-dimensional image t Distance measure i of (1) t Less than or equal to n and i t Greater than 0;
a module 6, configured to calculate and determine whether a euclidean distance d of the current local tomographic three-dimensional image is smaller than a minimum distance min_d, if yes, assign the euclidean distance d to the minimum distance min_d, otherwise, the minimum distance min_d maintains an original value;
the module 7 is configured to determine whether an absolute value of a difference between a minimum distance min_d and an original distance old_d is smaller than a minimum distance difference epS, if yes, output the suboptimal rotation parameter and the suboptimal translation parameter, otherwise, assign the minimum distance min_d to the original distance old_d, initialize the suboptimal rotation parameter and the suboptimal translation parameter, as new initial rotation parameter and translation parameter, repeatedly execute the above module 3-module 7 to maxIter_in times, and output the suboptimal rotation parameter and the suboptimal translation parameter obtained by the maxIter_in times;
the module 8 is configured to align the local tomographic three-dimensional images corresponding to the suboptimal rotation parameter and the suboptimal translation parameter obtained in the module 7 in real space, and average the aligned local tomographic three-dimensional images to obtain a reconstructed local tomographic three-dimensional image;
wherein V is 1 Representing the current operationOne of the plurality of partial tomographic three-dimensional images is made, V2 representing the initial reference structure.
7. The system for reconstructing a partial tomographic image according to claim 6, wherein said module 2 comprises:
a module 2.1 for converting the plurality of partial tomographic three-dimensional images and the initial reference structure from real space to fourier space;
the module 2.2 is used for converting Fourier coefficients corresponding to the plurality of local fault three-dimensional images into spherical coordinates, expanding the spherical coordinates by utilizing spherical harmonics, calculating constraint cross-correlation values of regularized spherical functions under different frequencies, and obtaining a three-dimensional array of the constraint cross-correlation values;
and 2.3, retrieving a plurality of optimal coarse rotation parameters in the three-dimensional array of constraint cross-correlation values, wherein the maximum value of the constraint cross-correlation values corresponds to the plurality of optimal coarse rotation parameters.
8. The system for reconstructing a partial tomographic image according to claim 7, wherein said module 2 comprises:
a module 2.4 for constraining the plurality of partial tomographic three-dimensional images and the initial reference structure in fourier space;
and 2.5, calculating local correlation values of the local tomographic three-dimensional images and the initial reference structure respectively by using a fast Fourier transform algorithm, and obtaining a plurality of corresponding optimal coarse translation parameters.
9. The system for reconstructing a partial tomographic three-dimensional image according to claim 6, wherein the parameters in the module 3 are set to an update frequency m=10, a learning rate η=1/(20×maxiter), a minimum distance min_d=an original distance old_d= -1, a minimum distance difference eps=0.0001, and an inner iteration number maxiter_in=an outer iteration number maxiter_out=20; where maxIter represents the number of iterations.
10. The system for reconstructing a partial tomographic image according to claim 6 wherein said module 8 comprises:
the module 8.1 is used for splitting the aligned local tomographic three-dimensional images according to the odd-even serial numbers to obtain two groups of aligned local tomographic three-dimensional images, and respectively averaging the two groups of aligned local tomographic three-dimensional images to obtain two reconstructed local tomographic three-dimensional images;
the module 8.2 is used for converting the two reconstructed local tomographic three-dimensional images into a Fourier space, and calculating the current resolution corresponding to the two reconstructed local tomographic three-dimensional images by utilizing a Fourier spherical shell coefficient;
and a module 8.3, configured to determine whether the current resolution is less than a preset resolution, if yes, output the reconstructed local tomographic three-dimensional image, otherwise, repeatedly execute the modules 3-module 8 to maxiter_out times with the reconstructed local tomographic three-dimensional image as a new initial reference structure, and output the reconstructed local tomographic three-dimensional image of the maxiter_out times.
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