A method for reconstructing the spatial and angular distribution of fluorescent molecules based on high-dimensional and efficient deconvolution

Abstract

The present invention discloses a method for reconstructing the spatial and angular distribution of fluorescent molecules based on high-dimensional and efficient deconvolution. Through a newly designed spatial angular back-projection operator and iterative framework, the spatial and angular distribution of fluorescent molecules can be reconstructed more quickly using polarized fluorescence microscopy data. While maintaining noise suppression and the spatial resolution and angular distribution accuracy of the reconstruction results, the number of iterations can be reduced to 1, significantly reducing reconstruction time and memory usage costs. Therefore, the present invention effectively designs a high-dimensional and efficient deconvolution algorithm for reconstructing the spatial angular distribution of molecules from polarized fluorescence microscopy data, solving the problems of the existing methods with a large number of iterations, long calculation time, and high computational cost, and providing powerful algorithmic support for subsequent larger-scale and higher-dimensional fluorescent molecular structure research.

Description

Technical Field

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

[0002] Fluorescence microscopy is widely used in the biological sciences to image fluorescent molecules that label specific proteins and biologically important molecules. Most fluorescent molecules absorb and emit light through their electronic dipole moments, and the fluorescence dipole of the labeled structure is trapped in an angular potential, resulting in relatively stable directionality. Within any diffraction-limited observation area, fluorescent molecules with different orientations can be considered as a fluorophore collection. Therefore, a fluorophore collection has spatial position and orientation distribution characteristics, namely, spatial and angular distribution.

[0003] Due to these properties, most fluorescent reporters absorb and emit light via their electron dipole moment, i.e., in polarization-anisotropic patterns. Therefore, polarized optical microscopy can be used to examine the excitation and emission patterns of fluorophores, allowing conclusions to be drawn about the orientation of the fluorescent reporter molecules. By performing multiple measurements of the same area under variable polarization illumination and / or detection, the fluorescence anisotropy of the sample can be indirectly observed and studied. However, to further explore the biological properties of the sample, it is necessary to recover the three-dimensional spatial and angular distribution of the fluorescent molecules from these polarization measurements. Furthermore, the frequency bandwidth of optical systems is generally limited, resulting in blurring and noise that degrade the measured image. However, if the imaging model of the system can be mathematically described, the sample information can be recovered using inverse problem-solving algorithms to reconstruct the spatial and angular distribution of the sample.

[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 established an imaging model for the system and derived an iterative solution algorithm.

[0005] The existing technology has the following technical problems:

[0006] 1) High number of iterations. Iterative solution algorithms generate a high computational burden, typically requiring 10 to 100 iterations for different systems or samples. If the number of iterations is too small, the final estimation result will not converge, meaning that the optimal spatial angle cannot be recovered.

[0007] 2) High computational time and memory consumption. When the viewing angle or the number of polarization modulations of the system increases significantly, the computational time and memory consumption will increase proportionally, easily exceeding the hardware requirements of ordinary computing devices.

[0008] Therefore, how to reduce the number of iterations as much as possible, maintain an acceptable computational cost, while suppressing noise and maintaining the resolution and accuracy of the reconstruction results in spatial and angular distribution is a hot topic of research 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 distribution of fluorescent molecules based on high-dimensional and efficient deconvolution. Through a newly designed spatial angular backprojection operator and iterative framework, the number of iterations can be reduced to 1 while maintaining noise suppression and the spatial resolution and angular distribution accuracy of the reconstruction results, significantly reducing reconstruction time and memory usage costs. The present invention is achieved through the following technical solutions:

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

[0011] 1) In a fluorescence microscope, a laser light source is used to illuminate the sample. The fluorescence emitted by the sample is collected by the objective lens and an image is obtained on the camera. For single or multiple viewing angles, the fluorescently labeled biological sample is excited by excitation light of several different polarization states, and data is collected through the objective lens to obtain volumetric image data of the biological sample corresponding to each polarization mode at each viewing angle.

[0012] 2) Through simulation, the system function corresponding to each viewing angle and each polarization mode is obtained, and the system function is normalized as a whole to obtain the spatial angle transfer function;

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

[0014] 4) obtaining a non-matching spatial angle back-projection function through the spatial angle transfer function, obtaining a spatial angle mapping function through the spatial angle transfer function and the spatial angle back-projection function, and forming spatial angle measurement data through the spatial angle back-projection function and the pre-processed biological sample volume image data;

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

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

[0017]

[0018] in: is the spectrum of the biological sample volume image data, indicating the viewing angle ,polarization The spatial frequency of the biological sample volume image data Quantity; is the space angle transfer function, which represents the viewing angle , polarization mode The spatial frequency of the microscope system , angular frequency responsiveness of the ingredients; is the spatial angular distribution of fluorescent molecules in biological samples, indicating the spatial frequency in biological samples , angular frequency The weight of the place.

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

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

[0021] As a further improvement, in step 2) of the present invention, the system function is normalized as a whole to obtain the calculation expression of the space angle transfer function as follows:

[0022]

[0023] in: is the system function obtained through simulation, indicating the viewing angle , polarization mode The system's spatial frequency , angular frequency Responsiveness of ingredients.

[0024] As a further improvement, the step 4) of the present invention is to form a non-matching space angle back projection function according to the space angle transfer function as follows:

[0025]

[0026] in, For the given parameters; 、 and The spatial frequencies , angular frequency The singular values, left singular vectors, and right singular vectors at are given by the space angle transfer function It is derived by performing singular value decomposition.

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

[0028]

[0029] in, is the space angle transfer function, is the spatial angle back-projection function exist 、 The corresponding function.

[0030] As a further improvement, step 4) of the present invention forms spatial angle measurement data according to the spatial angle back-projection function and the pre-processed biological sample volume image data:

[0031]

[0032] in, is the space angle back-projection function; is the preprocessed biological sample volume image data, indicating the viewing angle Polarization excitation mode The corresponding position in the biological sample image data collected Grayscale at and Represents 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 fluorescent molecules in the biological sample is iteratively estimated by using the spatial angle mapping function and the spatial angle measurement data as follows:

[0034]

[0035] in: and Indicates the and The estimated spatial angular distribution and spatial position of fluorescent molecules in biological samples Angle frequency The weight of the place; is a natural number; 、 and Respectively represent the space angle projection operation, space angle division operation and space angle multiplication operation;

[0036] Space angle projection operation The expression is as follows:

[0037]

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

[0039]

[0040] Space angle multiplication The expression is as follows:

[0041]

[0042] in is the Gaunt coefficient.

[0043] As a further improvement, the present invention Indicates the The estimated spatial angular distribution of fluorescent molecules in biological samples is 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 angular distribution of fluorescent molecules based on high-dimensional and efficient deconvolution. The method can more quickly reconstruct the spatial and angular distribution of fluorescent molecules through fluorescence microscope data, significantly improving the reconstruction efficiency and computing resource utilization.

[0047] The present invention has the following innovations:

[0048] 1) Significantly reduce the number of iterations. By designing a new spatial angle back-projection operator, the number of iterative reconstructions required is significantly reduced compared to existing methods that rely on multiple iterations and have slow algorithm convergence. In most cases, accurate results can be obtained with only one iteration, significantly improving reconstruction efficiency.

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

[0050] 3) Optimized large-scale data processing. This paper designs a new iterative framework to address the high computational time and memory consumption issues of existing techniques. By decoupling the numerous fixed structural terms involved in the computation from the variable terms that are updated with each iteration, the pre-calculated components are generated once before the iteration, eliminating the need for repeated calculations during the iterations. This mechanism is particularly suitable for processing a large number of polarization states, significantly reducing the reconstruction memory overhead and runtime to a fraction of those of existing methods.

[0051] In summary, this paper designs a high-dimensional spatial angular deconvolution algorithm for efficiently reconstructing the spatial and angular distributions of fluorescent molecules from fluorescence microscopy data. This algorithm suppresses noise, maintains the spatial resolution and angular distribution accuracy of the reconstructed results, and reduces the time burden associated with multiple iterations and the computational memory burden associated with large amounts of observation data. This approach addresses the computational bottlenecks and low iteration efficiency associated with processing multi-polarization state data in existing fluorescence imaging systems, providing powerful algorithmic support for subsequent larger-scale, higher-dimensional studies of fluorescent molecular structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 Schematic diagram of the process of the method for reconstructing the spatial and angular distribution of fluorescent molecules based on high-dimensional efficient deconvolution of the present invention;

[0053] Figure 2 A single iteration time test diagram for comparing the new iterative framework of the present invention with the fluorescence molecule spatial and angular distribution reconstruction method based on the generalized Richardson-Lucy algorithm. DETAILED DESCRIPTION

[0054] In order to describe the present invention more specifically, the technical solution of the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0055] like Figure 1 As shown, the present invention is based on a method for reconstructing the spatial and angular distribution of fluorescent molecules using high-dimensional and efficient deconvolution, comprising the following steps:

[0056] S1. In a fluorescence microscope, a laser light source is used to illuminate the sample. The fluorescence emitted by the sample is collected by the objective lens and an image is obtained on the camera. The excitation light path of the fluorescence microscope emits laser light of a certain polarization state, which illuminates a fluorescently labeled or inherently fluorescent biological sample to cause it to fluoresce. Polarization or non-polarization modulation is further added before the camera of the fluorescence microscope to collect fluorescence data. The focal plane of the collection light path is continuously moved to traverse the signal of the entire biological sample. The images collected each time are stacked to form three-dimensional volumetric image data of the biological sample. For data with multiple viewing angles and multiple polarizations, the polarization state of the excitation light path of the fluorescence microscope is adjusted, and multiple sets of volumetric data are collected to obtain volumetric image data of the biological sample at each viewing angle and polarization state.

[0057] S2. Get each perspective through simulation , polarization mode System functions under , and the space angle transfer function is obtained by overall normalization :

[0058]

[0059] in: is the system function obtained through simulation, indicating the viewing angle , polarization mode The system's spatial frequency , angular frequency responsiveness of the ingredients; is the space angle transfer function obtained by overall normalization, which represents the viewing angle , polarization mode The system's spatial frequency , angular 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, and perform linear interpolation and rotation of the data obtained from other viewing angles and polarization modes to make them have corresponding coordinate systems. At this time, the image obtained is a coarse registration. 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 are 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 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 , angular frequency The singular values, left singular vectors, and right singular vectors at 、 and , where they satisfy:

[0063]

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

[0065] ;

[0066] in, For the given parameters.

[0067] 2) The spatial angle mapping function is obtained through the spatial angle transfer function and the spatial angle back projection function. and non-matching spatial angle back-projection function exist 、 The corresponding function , forming a spatial angle mapping function :

[0068] ;

[0069] 3) The spatial angle measurement data is formed by the spatial angle back-projection function and the pre-processed biological sample volume image data. and preprocessed biological sample volume image data Generating spatial angle measurement data :

[0070] ;

[0071] in, and Represents the Fourier transform and its inverse transform in three-dimensional space.

[0072] 4) Save them in the form of multidimensional matrices for subsequent data processing.

[0073] S5. Iteratively estimate the spatial angular distribution of fluorescent molecules in the biological sample using the spatial angle mapping function and the spatial angle measurement data. Use the following framework for iterative calculations, obtaining the corresponding spatial angular distribution estimate of fluorescent molecules in the biological sample in each iteration:

[0074]

[0075] in, and Indicates the and The estimated spatial angular distribution and spatial position of fluorescent molecules in biological samples Angle frequency The weight of the place; is a natural number. In addition, Represents the spatial angle projection operation, Represents the space angle division operation and Represents the space angle multiplication operation, and the expressions are as follows:

[0076]

[0077] ;

[0078]

[0079] in is the Gaunt coefficient.

[0080] Taking the reconstruction of data obtained under multiple viewing angles and multiple polarization modes as an example, the iterative framework of the present invention is fully described, including the content that can be pre-calculated, the initial value of the iteration, the formula of the iterative process, and:

[0081] 1) The existing space angle back projection operator is directly derived from the transposition of the space angle transfer function, while here we use the singular value decomposition method to generate a non-matching space angle back projection operator:

[0082]

[0083] in, For the given parameters; 、 and The spatial frequencies , angular frequency The singular values, left singular vectors, and right singular vectors at are given by the space angle transfer function 2) The spatial angle mapping function and spatial angle measurement data can be pre-calculated, which does not take up the time of the iterative process, and the computational cost is not affected by the number of polarization measurements:

[0084]

[0085]

[0086] in, is the space angle transfer function; is the spatial angle back-projection function exist 、 The corresponding function when is the pre-processed biological sample volume image data; and Represents the Fourier transform and its inverse transform in three-dimensional space.

[0087] 3) Iteration initial value and iteration process:

[0088] There are two types of initial values ​​and processes for iteration. The first type, additive iteration, is:

[0089]

[0090] from ;

[0091]

[0092]

[0093]

[0094]

[0095] Finish.

[0096] The second, multiplication iteration is:

[0097]

[0098] from ;

[0099]

[0100]

[0101]

[0102] Finish.

[0103] in: and Indicates the and The estimated spatial angular distribution and spatial position of fluorescent molecules in biological samples Angle frequency The weight of the place; is a natural number. 、 and They represent the spatial angle projection operation, spatial angle division operation, and spatial angle multiplication operation respectively, and the expressions are as follows:

[0104]

[0105]

[0106]

[0107] in is the Gaunt coefficient.

[0108] like 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. The spatial angle transfer function is used for forward projection to simulate the excitation and acquisition process of a fluorescence microscope. Multiple sets of simulation data are obtained, with 6, 18, 42, and 60 polarization measurements, respectively. Reconstruction is performed using the present invention, and the time taken for a single iteration is recorded. The time is compared with that of the iterative method and the generalized Richardson-Lucy algorithm. Together, they show that the reconstruction time of the present invention in a single iteration is much lower than that of the method based on the generalized Richardson-Lucy algorithm, and this acceleration effect becomes more significant as the number of polarization measurements increases.

[0109] The above description of the embodiments is intended to facilitate understanding and application of the present invention by those skilled in the art. It will be apparent that those skilled in the art can readily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without requiring inventive effort. Therefore, the present invention is not limited to the above embodiments, and improvements and modifications made by those skilled in the art based on the disclosure of the present invention should fall within the scope of protection 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: The steps include: 1) In a fluorescence microscope, a laser light source is used to illuminate the sample. The fluorescence emitted by the sample is collected by the objective lens and an image is obtained on the camera. For single or multiple viewing angles, the fluorescently labeled biological sample is excited by excitation light of several different polarization states, and data is collected through the objective lens to obtain volumetric image data of the biological sample corresponding to each polarization mode at each viewing angle. 2) Through simulation, the system function corresponding to each viewing angle and each polarization mode is obtained, and the system function is normalized as a whole to obtain the spatial angle transfer function; 3) preprocessing the collected biological sample volume image data to obtain preprocessed biological sample volume image data; 4) obtaining a non-matching spatial angle back-projection function through the spatial angle transfer function, obtaining a spatial angle mapping function through the spatial angle transfer function and the spatial angle back-projection function, and forming spatial angle measurement data through the spatial angle back-projection function and the pre-processed biological sample volume image data; 5) The spatial angle distribution of fluorescent molecules in biological samples is iteratively estimated through the spatial angle mapping function and spatial angle measurement data.

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: ； in: is the spectrum of the biological sample volume image data, indicating the viewing angle ,polarization The spatial frequency of the biological sample volume image data Quantity; is the space angle transfer function, which represents the viewing angle , polarization mode The spatial frequency of the microscope system , angular frequency responsiveness of the ingredients; is the spatial angular distribution of fluorescent molecules in biological samples, indicating the spatial frequency in biological samples , angular frequency The weight of the place.

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 viewing angles and polarization states is single or multiple, and the polarization state is applied behind the laser light source or in front of the camera in the fluorescence microscope; the volume image data of the biological sample 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, wherein: The space angle transfer function in step 2) has three spatial dimensions plus one angle dimension and one polarization dimension, a five-dimensional matrix structure.

5. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 4, wherein: In step 2), the system function is normalized as a whole to obtain the calculation expression of the space angle transfer function as follows: ； in: is the system function obtained through simulation, indicating the viewing angle , polarization mode The system's spatial frequency , angular frequency Responsiveness of ingredients.

6. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 5, characterized in that: The non-matching space angle back projection function formed according to the space angle transfer function in step 4) is specifically: ； in, For the given parameters; 、 and The spatial frequencies , angular frequency The singular values, left singular vectors, and right singular vectors at are given by the space angle transfer function It is derived by performing singular value decomposition.

7. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 1, 2, 4, 5 or 6, wherein: In step 4), a space angle mapping function is formed based on the space angle transfer function and the space angle back projection function: ； in, is the space angle transfer function, is the spatial angle back-projection function exist 、 The corresponding function.

8. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 7, wherein: Step 4) Generate spatial angle measurement data based on the spatial angle back-projection function and the pre-processed biological sample volume image data: ； in, is the space angle back-projection function; is the preprocessed biological sample volume image data, indicating the viewing angle Polarization excitation mode The corresponding position in the biological sample image data collected Grayscale at and Represents 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, characterized in that: In step 5), the spatial angle distribution of fluorescent molecules in the biological sample is iteratively estimated using the spatial angle mapping function and the spatial angle measurement data as follows: ； in: and Indicates the and The estimated spatial angular distribution and spatial position of fluorescent molecules in biological samples Angle frequency The weight of the place; is a natural number; 、 and Respectively represent the space angle projection operation, space angle division operation and space angle multiplication operation; The spatial angle projection operation The expression is as follows: ； The space angle division operation The expression is as follows: ； The space angle multiplication operation The expression is as follows: ； in 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: described Indicates the The estimated spatial angular distribution of fluorescent molecules in biological samples is The expression is as follows: 。

Images