Fluorescent molecule space and angle distribution reconstruction method based on high-dimension efficient deconvolution

Abstract

The invention discloses a fluorescence molecule space and angle distribution reconstruction method based on high-dimension efficient deconvolution, and the method can achieve the faster reconstruction of the space and angle distribution of fluorescence molecules through the data of a polarization fluorescence microscope through a newly designed space angle back projection operator and an iteration frame. Under the condition that the resolution and angle distribution accuracy of noise suppression and reconstruction results in space are kept, the number of iterations is reduced to one, and the reconstruction time and the memory occupation cost are remarkably reduced. Therefore, the high-dimensional efficient deconvolution algorithm for reconstructing molecular space angle distribution from polarized fluorescence microscopic data is effectively designed, the problems that an existing method is large in iteration frequency, long in calculation time and high in calculation cost are solved, and powerful algorithm support is provided for follow-up larger-scale and higher-dimensional fluorescent molecular structure research.

Description

Technical Field

[0001] The present invention belongs to the technical field of fluorescence microscopy imaging, and particularly relates to a method for reconstructing the spatial and angular distribution of fluorescent molecules based on high-dimensional efficient deconvolution. Background Art

[0002] Fluorescence microscopes are widely used in biological sciences to image fluorescent molecules that label specific proteins and biologically important molecules. Most fluorescent molecules absorb and emit light through an electric dipole moment, and the fluorescent dipoles of the labeled structures are trapped in an angular potential, with relatively stable directivity. Within any diffraction-limited observation region, fluorescent molecules with different orientations can be regarded as a fluorophore ensemble. Therefore, for the fluorophore ensemble, it has spatial position and orientation distribution characteristics, that is, spatial and angular distribution.

[0003] Due to the above characteristics, most fluorescent reporter molecules absorb and emit light through an electric dipole moment, that is, in a polarization anisotropy mode. Therefore, a polarization optical microscope can be used to examine the excitation and emission modes of fluorophores, thereby drawing conclusions about the direction of fluorescent reporter molecules. By performing multiple measurements on the same region under variable polarization illumination and / or detection, the fluorescence anisotropy of the sample can be obtained for indirect observation and research. However, in order to further explore the biological characteristics of the sample, it is necessary to recover the three-dimensional spatial and angular distribution of fluorescent molecules from these polarization measurements. In addition, generally, the frequency bandwidth of the optical system is limited, so blurring and noise will occur, causing the measured image to degrade. However, if the imaging model of the system can be mathematically described, then the sample information can be restored through an inverse problem solving algorithm, and the spatial and angular distribution of the sample can be reconstructed.

[0004] Currently, a method for reconstructing the spatial and angular distribution of fluorescent molecules based on the generalized Richardson-Lucy algorithm [Liu Huafeng, Guo Min, Liu Junyu. Method for reconstructing the spatial and angular distribution of fluorescent molecules based on the generalized Richardson-Lucy algorithm: CN115953319B] has modeled the imaging model of the system and derived an iterative solution algorithm.

[0005] The prior art has the following technical problems:

[0006] 1) Many iterations. The iterative solution algorithm generates a large computational burden, usually requiring 10 to 100 iterations for different systems or samples. If the number of iterations is too small, the final estimated result will not converge, that is, the most ideal spatial angle recovery cannot be obtained.

[0007] 2) High computational time and memory consumption costs. When the number of perspectives or polarization modulations of the system increases significantly, the computational time and memory consumption costs will increase proportionally, and it is extremely easy to exceed the hardware conditions of ordinary computing devices.

[0008] Therefore, how to minimize the number of iterations as much as possible, maintain an acceptable computational cost, while suppressing noise and maintaining the resolution and accuracy of the reconstructed results in terms of spatial and angular distributions, is a research hotspot in this field. Summary of the Invention

[0009] In view of the above, the present invention provides a method for reconstructing the spatial and angular distributions of fluorescent molecules based on high-dimensional efficient deconvolution. Through a newly designed spatial angular back-projection operator and iterative framework, it is possible to reduce the number of iterations to 1 while maintaining noise suppression and the resolution of the reconstructed results in space and the accuracy of angular distribution, significantly reducing the reconstruction time and memory occupancy cost. The present invention is achieved through the following technical solutions:

[0010] The present invention discloses a method for reconstructing the spatial and angular distributions of fluorescent molecules based on high-dimensional efficient deconvolution, comprising the following steps:

[0011] 1) In a fluorescence microscope device, a laser light source is used to illuminate a sample, and the fluorescence emitted by the sample is collected by an objective lens and an image is obtained on a camera; for single or multiple viewpoints, respectively, the fluorescently labeled biological sample is excited by several excitation lights with different polarization states, and data acquisition is performed through the objective lens to obtain the biological sample volume image data corresponding to each viewpoint and each polarization mode;

[0012] 2) Through simulation, the system function corresponding to each viewpoint and each polarization mode is obtained, and the system function is globally normalized to obtain a spatial angular transfer function;

[0013] 3) The biological sample volume image data collected is preprocessed to obtain the preprocessed biological sample volume image data;

[0014] 4) An unmatched spatial angular back-projection function is obtained through the spatial angular transfer function, a spatial angular mapping function is obtained through the spatial angular transfer function and the spatial angular back-projection function, and spatial angular measurement data is formed through the spatial angular back-projection function and the preprocessed biological sample volume image data;

[0015] 5) The spatial angular distribution of the fluorescent molecules of the biological sample is iteratively estimated through the spatial angular mapping function and the spatial angular measurement data.

[0016] As a further improvement, the imaging equation of the fluorescence microscope device of the present invention is as follows:

[0017]

[0018] Wherein: is the spectrum of the biological sample volume image data, representing the viewpoint , polarization Spatial frequency of the following biological sample volume image data component; is the spatial angular transfer function, representing the viewing angle , polarization mode under the microscope system for spatial frequency , angular frequency component response ability; is the spatial angular distribution of the fluorescent molecules in the biological sample, representing the spatial frequency in the biological sample , angular frequency component at.

[0019] As a further improvement, the number of viewing angles and the number of polarization states described in the present invention are single or multiple, and the polarization state is applied after the laser light source or in front of the camera in the fluorescence microscopy device; the biological sample volume image data is obtained by stacking two-dimensional slice images.

[0020] As a further improvement, the spatial angular transfer function in step 2) of the present invention has a five-dimensional matrix structure with three spatial dimensions plus one angular dimension and one polarization dimension.

[0021] As a further improvement, in step 2) of the present invention, the system function is globally normalized to obtain the following calculation expression for the spatial angular transfer function:

[0022]

[0023] Where: is the system function obtained by simulation, representing the viewing angle , polarization mode under the system for spatial frequency , angular frequency component response ability.

[0024] As a further improvement, in step 4) of the present invention, the formation of the non-matching spatial angular backprojection function according to the spatial angular transfer function is specifically:

[0025]

[0026] Where, is a given parameter; , and are the singular value, left singular vector, and right singular vector at the spatial frequency , angular frequency respectively, and are obtained by performing singular value decomposition on the spatial angular transfer function .

[0027] As a further improvement, in step 4) of the present invention, a spatial angle mapping function is formed according to the spatial angle transfer function and the spatial angle backprojection function:

[0028]

[0029] Wherein, is the spatial angle transfer function, is the spatial angle backprojection function At , The corresponding function.

[0030] As a further improvement, in step 4) of the present invention, spatial angle measurement data is formed according to the spatial angle backprojection function and the preprocessed volume image data of the biological sample:

[0031]

[0032] Wherein, is the spatial angle backprojection function; is the preprocessed volume image data of the biological sample, representing the gray value at the corresponding position in the biological sample image data collected under the polarization excitation mode ; And and represent the Fourier transform and its inverse transform in three-dimensional space.

[0033] As a further improvement, in step 5) of the present invention, the spatial angle distribution of the fluorescent molecules in the biological sample is iteratively estimated through the spatial angle mapping function and the spatial angle measurement data, specifically:

[0034]

[0035] Wherein: and represent the spatial angle distributions of the fluorescent molecules in the biological sample estimated at the and th times, the component at the angular frequency at the spatial position ; is a natural number; , and represent the spatial angle projection operation, the spatial angle division operation, and the spatial angle multiplication operation respectively;

[0036] Spatial angle projection operation The expression of

[0037]

[0038] Spatial angle division operation The expression is as follows:

[0039]

[0040] Spatial angle multiplication operation The expression is as follows:

[0041]

[0042] Where is the Gaunt coefficient.

[0043] As a further improvement, the represents the th estimated spatial angle distribution of the fluorescent molecules in the biological sample. Wherein, when the expression is as follows:

[0044] .

[0045] The beneficial effects of the present invention are as follows:

[0046] The present invention discloses a method for reconstructing the spatial angle distribution of fluorescent molecules based on high-dimensional efficient deconvolution, which can more quickly reconstruct the spatial and angular distributions of fluorescent molecules through fluorescence microscope data, significantly improving the reconstruction efficiency and the utilization rate of computing resources.

[0047] The present invention has the following innovative points:

[0048] 1) Greatly reduce the number of iterations. By designing a new spatial angle back-projection operator, compared with the existing methods that rely on multiple iterations and have a slow algorithm convergence speed, the number of iterations required for iterative reconstruction is significantly reduced. In most cases, only one iteration is required to obtain accurate results, and the reconstruction efficiency is greatly improved;

[0049] 2) Adapt to different levels of noise. The given parameters in the spatial angle back-projection operator are prior regularization terms beneficial to the reconstruction stability, which can adapt to different noise levels, achieve robust suppression of noise in experimental data, and maintain good noise suppression and reconstruction fidelity;

[0050] 3) Optimize the processing of large data. The present invention designs a new iterative framework. Aiming at the problem of high computational time and memory consumption cost in the prior art, by decoupling a large number of fixed structure terms involved in the calculation from the variables updated with iterations, the pre-computable part can be generated once before the iteration, and there is no need to repeat the calculation during the iteration process. This mechanism is particularly suitable for the case of a large number of polarization states, and can compress the reconstruction memory overhead and running time to a fraction of the original method.

[0051] Generally speaking, the present invention designs a high-dimensional spatial angular deconvolution algorithm for efficiently reconstructing the spatial and angular distributions of fluorescent molecules from fluorescence microscopic data. While suppressing noise and maintaining the spatial resolution and angular distribution accuracy of the reconstruction results, it reduces the time burden brought by multiple iterations and the computational memory burden brought by a large amount of observation data. The present invention solves the problems of computational bottlenecks and low iteration efficiency in the processing of multi-polarization state data in existing fluorescence imaging systems, and provides strong algorithm support for subsequent larger-scale and higher-dimensional research on the structure of fluorescent molecules. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a schematic flow chart of the method for reconstructing the spatial and angular distributions of fluorescent molecules based on high-dimensional efficient deconvolution of the present invention;

[0053] Figure 2 It is a single iteration time test chart for comparing the new iteration framework of the present invention with the method for reconstructing the spatial and angular distributions of fluorescent molecules based on the generalized Richardson-Lucy algorithm. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0054] In order to describe the present invention more specifically, the technical solutions of the present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0055] As Figure 1 shown, the method for reconstructing the spatial and angular distributions of fluorescent molecules based on high-dimensional efficient deconvolution of the present invention includes the following steps:

[0056] S1. In a fluorescence microscope device, a laser light source is used to illuminate a sample, and the fluorescence emitted by the sample is collected by an objective lens and an image is obtained on a camera. The excitation light path of the fluorescence microscopy device emits a laser of a certain polarization state, which irradiates a biological sample labeled with fluorescence or having fluorescence itself to emit fluorescence. Further polarization or non-polarization modulation is added in front of the camera of the fluorescence microscopy device for the acquisition of fluorescence data. The focal plane of the acquisition light path is continuously moved so that the signals of the entire biological sample are traversed, and the images collected each time are stacked to form three-dimensional biological sample volume image data. For data with multiple view angles and multiple polarizations, the polarization state of the excitation light path of the fluorescence microscopy device is adjusted to collect multiple sets of volume data, and the biological sample volume image data at each view angle and polarization state is obtained.

[0057] S2. The system function at each view angle and polarization mode is obtained by simulation, and the spatial angular transfer function is obtained through overall normalization:

[0058]

[0059] Where: is the system function obtained through simulation, indicating the viewing angle , Polarization Mode The spatial frequency of the system , Angle frequency the responsiveness of the ingredients; is the spatial angle transfer function obtained by overall normalization, which represents the viewing angle , Polarization Mode The spatial frequency of the system , Angle frequency Responsiveness of ingredients.

[0060] Save them in the form of multidimensional matrices for subsequent data processing.

[0061] S3. Preprocess the collected biological sample volume image data. Since the reference coordinate systems of the collected images are inconsistent, preprocessing is first performed. Select a viewing angle and polarization mode as a reference, perform linear interpolation on the data obtained from other viewing angles and polarization modes, and rotate them at a certain angle so that they have corresponding coordinate systems. At this time, a roughly registered image is obtained. For more accurate image fusion, an intensity-based registration method is used to generate a registration matrix. The data of each viewing angle and excitation mode is multiplied by the corresponding registration matrix to obtain the preprocessed biological sample volume image data. .in, Representation perspective Polarization excitation mode The corresponding position in the biological sample image data collected under The grayscale at .

[0062] S4: 1) Obtain the non-matching spatial angle back-projection function through the spatial angle transfer function. Perform singular value decomposition into spatial frequencies , Angle frequency The singular values, left singular vectors, and right singular vectors at , and , where they satisfy:

[0063]

[0064] Further forming the non-matching space angle back projection function :

[0065] ;

[0066] in, For the given parameters.

[0067] 2) Obtain the spatial angle mapping function through the spatial angle transfer function and the spatial angle back-projection function. According to the spatial angle transfer function and the non-matching spatial angle back-projection function at , the corresponding function , form the spatial angle mapping function :

[0068] ; 3) Form the spatial angle measurement data through the spatial angle back-projection function and the preprocessed volume image data of the biological sample. According to the spatial angle back-projection function and the preprocessed volume image data of the biological sample form the spatial angle measurement data :

[0069] ;

[0070] wherein, and represent the Fourier transform and its inverse transform in three-dimensional space.

[0071] 4) Save them in the form of a multi-dimensional matrix for subsequent data processing.

[0072] S5. Through the spatial angle mapping function and the spatial angle measurement data, iteratively estimate the spatial angle distribution of the fluorescent molecules in the biological sample. Use the following framework for iterative calculation to obtain the corresponding estimated results of the spatial angle distribution of the fluorescent molecules in the biological sample in each iteration:

[0073]

[0074] wherein, and represent the spatial angle distributions of the fluorescent molecules in the biological sample estimated at the and th estimations, the component at the angular frequency at the spatial position ; is a natural number. Additionally, represents the spatial angle projection operation, represents the spatial angle division operation, and represents the spatial angle multiplication operation, and the expressions are as follows respectively:

[0075]

[0076] ;

[0077]

[0078] wherein is the Gaunt coefficient.

[0079] Taking the reconstruction of data obtained in multiple perspectives and multiple polarization modes as an example, the iterative framework of the present invention is described in detail, including the content that can be pre-computed, the initial value of the iteration, the formula of the iterative process, and:

[0080] 1) The spatial angular back-projection operator in the prior art is directly transposed from the spatial angular transfer function, while here the method of singular value decomposition is used to generate a non-matching spatial angular back-projection operator:

[0081]

[0082] wherein is a given parameter; , and are the singular value, left singular vector, and right singular vector at the spatial frequency , angular frequency , respectively, which are obtained by performing singular value decomposition on the spatial angular transfer function . 2) The spatial angular mapping function and the spatial angular measurement data can be pre-computed, without occupying the time of the iterative process, and the computational cost is not affected by the number of polarization measurements:

[0083]

[0084]

[0085] wherein is the spatial angular transfer function; is the spatial angular back-projection function at , corresponding function; is the pre-processed volume image data of the biological sample; and represent the Fourier transform and its inverse transform in three-dimensional space.

[0086] 3) The initial value and the iterative process of the iteration:

[0087] The initial value and the process of the iteration are divided into two types. The first type, the additive iteration is:

[0088]

[0089] starting from ;

[0090]

[0091]

[0092]

[0093]

[0094] End.

[0095] Second, the multiplication iteration is as follows:

[0096]

[0097] From ;

[0098]

[0099]

[0100]

[0101] End.

[0102] Where: and represent the spatial angular distribution of the fluorescent molecules in the biological sample estimated at the and times, the component at the angular frequency at the spatial position ; is a natural number. , and represent spatial angular projection operation, spatial angular division operation and spatial angular multiplication operation respectively. The expressions are as follows:

[0103]

[0104]

[0105]

[0106] Where is the Gaunt coefficient.

[0107] For example Figure 2As shown below, simulated data is used to verify the effectiveness of the present invention. A phantom with a certain spatial and angular distribution is randomly generated, and the forward projection using the spatial angular transfer function is used to simulate the excitation and acquisition processes of a fluorescence microscope, obtaining multiple sets of simulation data, each having 6, 18, 42, and 60 polarization measurements. The present invention is used for reconstruction, and the time used for a single iteration during reconstruction is recorded, and all are compared with the iteration and the generalized Richardson-Lucy algorithm. Together, they illustrate that the reconstruction time of the present invention for a single iteration is much lower than the result using the generalized Richardson-Lucy algorithm, and this acceleration effect becomes more significant as the number of polarization measurements increases.

[0108] The above description of the embodiments is to enable those of ordinary skill in the art to understand and apply the present invention. It is obvious that those familiar with the technology in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative labor. Therefore, the present invention is not limited to the above embodiments, and all improvements and modifications made by those skilled in the art to the present invention according to the disclosure of the present invention should be within the protection scope of the present invention.

Claims

1. A method for reconstructing the spatial and angular distribution of fluorescent molecules based on high-dimensional efficient deconvolution, characterized in that It includes the following steps: 1) In a fluorescence microscope device, a laser light source is used to illuminate a sample, and the fluorescence emitted by the sample is collected by an objective lens and an image is obtained on a camera; for single or multiple perspectives, fluorescence excitation of the fluorescently labeled biological sample is performed using several excitation lights with different polarization states respectively, and data acquisition is carried out through the objective lens to obtain the biological sample volume image data corresponding to each perspective and each polarization mode; 2) Through simulation, the system function corresponding to each perspective and each polarization mode is obtained, and the system function is globally normalized to obtain the spatial angular transfer function; 3) The biological sample volume image data collected is preprocessed to obtain the preprocessed biological sample volume image data; 4) The non-matching spatial angular backprojection function is obtained through the spatial angular transfer function, the spatial angular mapping function is obtained through the spatial angular transfer function and the spatial angular backprojection function, and the spatial angular measurement data is formed through the spatial angular backprojection function and the preprocessed biological sample volume image data; 5) Through the spatial angular mapping function and the spatial angular measurement data, the spatial angular distribution of the fluorescent molecules in the biological sample is iteratively estimated.

2. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 1, wherein The imaging equation of the fluorescence microscope device is as follows: ； Wherein: is the spectrum of the volume image data of the biological sample, representing the viewing angle , polarization and the spatial frequency of the volume image data of the biological sample at components; is the spatial angular transfer function, representing the viewing angle , polarization mode and the response ability of the microscopic system to the spatial frequency , angular frequency components at; is the spatial angular distribution of the fluorescent molecules in the biological sample, representing the components at the spatial frequency , angular frequency in the biological sample.

3. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 1 or 2, characterized in that: The number of perspectives and the number of polarization states are single or multiple, and the polarization state is applied after the laser light source or in front of the camera in the fluorescence microscope device; the biological sample volume image data is obtained by stacking two-dimensional slice images.

4. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 3, characterized in that: The spatial angular transfer function in step 2) has a five-dimensional matrix structure with three spatial dimensions plus one angular dimension and one polarization dimension.

5. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 4, characterized in that: The calculation expression for obtaining the spatial angular transfer function by globally normalizing the system function in step 2) is as follows: ； Wherein: is the system function obtained by simulation, representing the viewing angle , polarization mode under which the system responds to the spatial frequency , angular frequency component response ability.

6. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 5, wherein: In step 4), the specific method for forming the non-matching spatial angular backprojection function according to the spatial angular transfer function is: ； Among them, is a given parameter; , and are the singular value, left singular vector, and right singular vector at the spatial frequency , angular frequency , respectively, and are obtained by performing singular value decomposition on the spatial angle transfer function .

7. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 1 or 2 or 4 or 5 or 6, characterized in that: In step 4), the spatial angular mapping function is formed according to the spatial angular transfer function and the spatial angular backprojection function: ； Among them, is the spatial angle transfer function, is the spatial angle back-projection function at , is the corresponding function.

8. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 7, wherein: In step 4), the spatial angular measurement data is formed according to the spatial angular backprojection function and the preprocessed biological sample volume image data: ； Among them, is the spatial angle back-projection function; is the volume image data of the biological sample after preprocessing, representing the perspective polarization excitation mode at the corresponding position in the biological sample image data collected under the gray value at the location; and represent the Fourier transform and its inverse transform in three-dimensional space.

9. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 8, wherein: In step 5), the specific method for iteratively estimating the spatial angular distribution of the fluorescent molecules in the biological sample through the spatial angular mapping function and the spatial angular measurement data is: ； Wherein: and represent the spatial angular distributions of the fluorescent molecules in the biological sample estimated for the and times, and the components at the angular frequencies at the spatial position ; is a natural number; , , and represent spatial angular projection operation, spatial angular division operation, and spatial angular multiplication operation, respectively; The above-mentioned spatial angle projection operation has the following expression: ； The above-mentioned spatial angle division operation has the following expression: ； The above-mentioned spatial angle multiplication operation has the following expression: ； Among them is the Gaunt coefficient.

10. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 1 or 2 or 4 or 5 or 6 or 8 or 9, characterized in that: The spatial angular distribution of the fluorescent molecules in the biological sample represented by the th estimated value, where the expression when is as follows: 。

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