A fluorescence microscopic super-resolution reconstruction method based on inverse-diffraction dynamics

Abstract

The application discloses a fluorescence microscopic super-resolution reconstruction method based on inverse diffraction dynamics, and relates to the technical field of super-resolution reconstruction of fluorescence microscopic images, and can be used for super-resolution reconstruction of fluorescence microscopic images. The method comprises the following steps: super-resolution fluorescence microscopic image data is used as training data; an optical diffraction forward propagation model is established, and a propagation distance is discretized into multiple propagation levels; the forward propagation model is used for diffraction degradation modeling of the training data to generate a diffraction state sequence corresponding to each propagation level; a super-resolution reconstruction model containing a propagation conditioning residual operator is trained by using the level diffraction state sequence, a step-by-step inverse diffraction update along the propagation levels is learned, a super-resolution state of an object plane is gradually recovered from a strong degradation state, and a trained super-resolution reconstruction model is obtained; and a diffraction-limited fluorescence microscopic image to be processed is input into the super-resolution reconstruction model, a step-by-step inverse diffraction update along the propagation levels is performed, and a super-resolution reconstruction result is output. The application can realize stable recovery of high spatial frequency information attenuated in a diffraction process under the condition of only diffraction-limited fluorescence observation, and realizes transverse super-resolution reconstruction.

Description

Technical Field

[0001] This invention belongs to the field of super-resolution fluorescence microscopy imaging technology, and specifically relates to a fluorescence microscopy super-resolution reconstruction method based on inverse diffraction dynamics. Background Technology

[0002] In studies revealing life processes at the cellular and molecular scale, overcoming the optical diffraction limit and achieving super-resolution fluorescence microscopy under far-field conditions has long been one of the core technological challenges in the fields of bioimaging and optical engineering. Fluorescence microscopy is constrained by the physical law of the diffraction limit, and the lateral resolution of conventional far-field microscopy is usually around 200 nm. This is because: first, the numerical aperture (NA) of the objective lens of the microscopy system limits the angular range and spatial frequency bandwidth of the propagating waves that can be collected; second, evanescent waves carrying subwavelength information decay exponentially when propagating in free space, and high spatial frequency information is gradually suppressed as it propagates, ultimately leading to obvious diffraction blurring and loss of detail in the far-field image.

[0003] Existing super-resolution technologies are mainly divided into two paths: far-field super-resolution and near-field super-resolution. (1) Far-field super-resolution: Super-resolution information is obtained under far-field conditions by engineering modulation of the excitation or emission field (e.g., structured modulation of phase / intensity) or by utilizing the statistical properties of molecular emission to extend the observable spectrum. Typical examples include structured illumination microscopy (SIM), stimulated emission loss microscopy (STED), and single-molecule localization microscopy (SMLM). This type of technology has been widely used in life science research, but usually requires a trade-off between resolution and photon dose, imaging speed, and experimental setup complexity. For example, super-resolution is often accompanied by higher light dose (potential phototoxicity / photobleaching risk), longer imaging time, or more complex optical paths and labeling strategies.

[0004] (2) Near-field super-resolution: This method uses near-field probes or special optical structures to couple evanescent fields into detectable signals, thereby acquiring subwavelength information. Examples include near-field scanning optical microscopy (NSOM), superlenses, and superoscillations. Although such methods can achieve super-resolution imaging under specific conditions, they usually suffer from problems such as extremely short working distances, limited sample compatibility, and complex system implementation. In particular, their versatility and operability are significantly limited in applications such as live-cell nanoimaging.

[0005] These limitations have prompted researchers to further explore computational reconstruction strategies in order to recover more structural details from diffraction-limited observations without significantly increasing hardware complexity.

[0006] Existing methods for super-resolution computation mainly fall into two categories: deconvolution and deep learning reconstruction. (1) Deconvolution methods typically simplify the imaging degradation into a convolution model and use prior regularization to achieve inversion. These methods are simple to implement and highly interpretable, but the convolution approximation often fails to accurately reflect the real wave optical propagation process, and is prone to instability or detail artifacts when noise or system mismatch is present.

[0007] (2) Deep learning reconstruction methods learn the mapping from low-resolution observations to super-resolution results through a data-driven approach, which can improve image detail and usability under certain conditions. However, many deep learning schemes still tend to use empirical mapping or convolution approximation, and do not explicitly describe super-resolution as "an inverse diffraction process constrained by wave propagation". Therefore, the physical consistency constraint is weak and lacks interpretability. The reconstruction results may be sensitive to noise and training set bias, resulting in limited generalization ability across modes and optical configurations, and may produce high-frequency pseudo-structures that are inconsistent with the real propagation physics. Furthermore, existing deep learning super-resolution methods usually rely on strictly registered low-resolution observations and super-resolution references as supervision signals during the training phase. Such paired data are often difficult to obtain in fluorescence microscopy: on the one hand, super-resolution references often come from different imaging modes or different hardware systems (such as SIM / STED / SMLM), which are costly to acquire and have system differences with the mode to be processed; on the other hand, the field of view, distortion, drift and phototoxicity between different modes can lead to registration difficulties, and the registration error further introduces artifacts and affects training stability and generalization ability.

[0008] Therefore, there is an urgent need for an interpretable computational framework that can complete model learning and super-resolution reconstruction under physical forward propagation constraints without relying on strictly paired image pairs acquired from real sources.

[0009] Unlike the empirical mappings mentioned above, analytical inverse diffraction schemes start directly from the wave equation and achieve rigorous physical inversion through explicit inversion or extrapolation of propagation operators (e.g., backpropagation based on angular spectra), without requiring paired data. While theoretically physically rigorous, this type of method often exhibits significant instability under real-world experimental conditions: explicit inverse propagation strongly amplifies noise, especially components related to evanescent decay, leading to highly sensitive reconstructions to noise and model mismatches, making it difficult to operate stably under real-world measurement conditions.

[0010] In summary, existing super-resolution technologies have at least the following problems: (1) Problems of insufficient physical consistency and interpretability: Empirical mapping deep learning super-resolution lacks explicit propagation physical constraints, lacks interpretability, is prone to high-frequency pseudo-structures inconsistent with optical propagation, and has limited generalization across modalities / systems; (2) Many supervised deep learning super-resolution methods rely on strictly registered pairwise training data (relying on real-acquired and strictly registered low-resolution and super-resolution pairwise images), but such pairwise data is often difficult to obtain on a large scale in fluorescence microscopy applications; at the same time, cross-modal / cross-system registration errors can easily introduce structural mismatch and training bias, resulting in reconstruction results that are sensitive to the distribution of training data and have limited generalization. (3) Instability of inverse propagation: Although analytical inverse diffraction is a rigorous physical inversion calculation, it will significantly amplify noise in the real microscopic imaging environment, especially when it involves the evanescent decay related components, which is extremely unstable (leading to unstable reconstruction). (4) Simply performing image enhancement-type "sharpening / contrast enhancement" is insufficient to guarantee interpretable super-resolution reconstruction; (5) Problem of limited generalization across modal / system: Different imaging modes (such as wide field, confocal) and different system conditions will lead to changes in propagation model or imaging characteristics, making it difficult for existing methods to be stably transferred.

[0011] Therefore, there is an urgent need in this field for a new interpretable computational reconstruction framework that can both preserve the physical constraints of inverse diffraction / inverse propagation, making the reconstruction process interpretable and measurement consistent, and avoid the amplification and instability of noise caused by analytical inverse propagation, while maintaining robustness and generalization ability in real microscopic systems. Summary of the Invention

[0012] The purpose of this invention is to provide a fluorescence microscopy super-resolution reconstruction method based on inverse diffraction dynamics, which can stably recover high spatial frequency information attenuated during diffraction under diffraction-limited fluorescence observation conditions (such as single-frame wide-field or confocal), achieve lateral super-resolution reconstruction, and improve the generalization and interpretability across structures and modes.

[0013] To achieve the above-mentioned objectives, the present invention provides the following technical solution: A fluorescence microscopy super-resolution reconstruction method based on inverse diffraction dynamics, the method comprising: S1) Obtain super-resolution fluorescence microscopy image data as training data; S2) Establish an optical diffraction forward propagation model and discretize the propagation distance into multiple propagation levels; based on the forward propagation model, perform diffraction degradation modeling on the super-resolution training data to generate diffraction state sequences corresponding to each propagation level; S3) Train a super-resolution reconstruction model containing propagation conditional residual operators using a hierarchical diffraction state sequence, so that the super-resolution reconstruction model learns to perform stepwise inverse diffraction updates along the propagation hierarchy, gradually recovering from a strongly degenerate state to the super-resolution state of the object plane, and obtains a trained super-resolution reconstruction model. S4) Input the diffraction-limited fluorescence microscopy image to be processed into the trained super-resolution reconstruction model. The super-resolution reconstruction model performs stepwise inverse diffraction updates along the propagation level and outputs the super-resolution reconstruction result.

[0014] Wherein: the diffraction-limited fluorescence microscopy image in S4 refers to low-resolution observation; the method provided by this invention does not require real acquisition and strict registration of low-resolution (such as ordinary wide-field imaging or ordinary confocal imaging, etc.) / super-resolution (such as structured light illumination imaging SIM or stimulated emission loss microscopy STED, etc.) paired images during the training phase, and only requires input of diffraction-limited observations to output super-resolution results during the inference phase.

[0015] This invention provides a method for training a propagation-conditional inverse diffraction model by generating a degenerate hierarchical sequence based solely on super-resolution samples and a forward diffraction model. This invention describes fluorescence super-resolution reconstruction as "propagation-constrained inverse diffraction dynamics": learning / performing stepwise inverse propagation updates under explicit forward propagation model constraints, rather than empirical mapping enhancement or analytical inverse propagation direct inversion. This invention provides an inverse update mechanism for discrete propagation hierarchies: hierarchies are constructed according to discrete propagation distances and updated layer by layer by a propagation-conditional residual network, forming physically interpretable inverse propagation trajectories. This invention is applicable to multimodal and volumetric data implementations: the method can be applied to wide-field, confocal, etc., and can process confocal 3D layer-cut images to enhance lateral details without changing axial sampling / axial resolution.

[0016] In S1, the super-resolution fluorescence microscopy image data comes from Structured Illumination Microscopy (SIM), Stimulated Emission Depletion Microscopy (STED), or Single-Molecule Localization Microscopy (SMLM). It can also come from other super-resolution imaging / reference reconstruction results.

[0017] In S2, the method for establishing the forward propagation model of optical diffraction and discretizing the propagation distance into multiple propagation levels is as follows: S21) The angular spectrum propagation model is used to describe the propagation field distribution of the object's planar field at a distance z; S22) The complex amplitude field is converted into fluorescence microscopy recording intensity to establish a forward propagation model: S23) Divide the working distance of the microscope into K parts evenly, and discretize the propagation distance into K propagation levels.

[0018] The expression for the propagation field distribution in S21 is: ; in, This represents the complex amplitude field at a propagation distance of z in the plane; Represents the spectrum of the planar field of an object in the spatial frequency domain; For the transverse wave vector component in the spatial frequency domain; For wave number, The imaging wavelength; Longitudinal wave vector component satisfy: ; From equation (2), we can see that: when hour, It is a purely imaginary number, corresponding to the fleeting component; ; in Indicates the noise term; Furthermore, the K propagation levels are represented as follows: ; in, Represents the object plane or reference plane. This indicates the propagation level corresponding to the observation.

[0019] Larger propagation levels correspond to stronger diffraction degradation states, which can be used as training inputs or intermediate supervision targets, such as... The level with the strongest diffraction degradation.

[0020] In S2, the method for modeling diffraction degradation of the super-resolution training data based on the forward propagation model and generating diffraction state sequences corresponding to each propagation level is as follows: Given object plane super-resolution parameters Based on the forward propagation operator Generate the diffraction state sequence at the discrete propagation level: ; in Indicates the level of propagation The physical propagation state at the location (or its intensity domain equivalent representation); This yields the training sample pairs: and the supervision required for intermediate propagation levels .

[0021] The object plane super-resolution parameters are derived from the object field (or its equivalent representation) corresponding to the reference reconstruction of SIM, STED, or SMLM. Indicates the distance of transmission The physical propagation state at the location (or its intensity domain equivalent representation).

[0022] In S3, this specifically includes: propagating along predefined levels by... Gradually updated to The stepwise reconstruction sequence was obtained. ,in This is the output of the super-resolution reconstruction result.

[0023] The reconstruction process involves: the diffraction-limited map (the most blurred map) corresponding to... Location, and then reasoning to K -1, and then estimate backwards sequentially, from K -1 to K -2, K -2 to K -3, and so on, all the way up to k =0 represents the clearest reconstruction result.

[0024] Furthermore, taking the initial estimate corresponding to the diffraction-limited observation as a starting point, in the... At the propagation level, the current estimate is updated using propagation-conditionalized residual mapping to obtain the th propagation level. -1 level of propagation estimation; Inverse diffraction updates follow the following form: ; in: Indicates the level of propagation The current estimate below; This indicates the updated estimate, corresponding to a propagation level closer to the object plane (with weaker degradation); Representation and propagation hierarchy The corresponding forward propagation operator (or its discrete implementation / parameter representation); For parameters The propagation conditional residual operator is used to predict the propagation from the hierarchical level. arrive The residual correction amount.

[0025] Furthermore, during training, at the propagation level Predict based on the current state (or estimate) and compare it with the corresponding real state. Alignment.

[0026] Furthermore, during training, the parameters are optimized using the following stepwise loss function: ; Among them, expectations The average can be taken from the training data distribution and the sampling distribution of the propagation hierarchy.

[0027] Furthermore, a weighted summation of the losses at different propagation levels is performed: ; in, This is a weighting coefficient used to balance the learning difficulty of each level.

[0028] Compared with the prior art, the present invention has the following superior effects: (1) No real paired training data is required, reducing the cost of data acquisition and registration. Many supervised deep learning super-resolution methods rely on real-collected and strictly registered low-resolution / high-resolution paired images, which has high data acquisition costs and is prone to introducing cross-modal registration errors. In the training stage, this invention only requires super-resolution training data and generates multi-level diffraction degradation states as training signals based on the optical forward diffraction / propagation model, thereby avoiding dependence on real paired images, reducing the difficulty of data preparation and reducing the training bias introduced by registration errors.

[0029] (2) Strong physical consistency and interpretability Under the constraints of a clear forward propagation / diffraction model, this invention describes the reconstruction as a stepwise inverse diffraction dynamic update process at the propagation level, making the reconstruction path consistent with the wave propagation mechanism and more interpretable. Compared with empirical mapping network enhancement methods, it is less likely to generate high-frequency pseudo-structures that are inconsistent with propagation physics.

[0030] (3) High stability and strong noise resistance Analytical inverse diffraction / explicit backpropagation is prone to amplifying noise and causing instability under real noise and system mismatch conditions. This invention replaces the explicit analytical inverse operator with a stepwise residual update of propagation parameterization, decomposing the inverse problem into multiple sub-steps with better conditions, thereby reducing the risk of noise amplification and improving the reconstruction stability and robustness under actual measurement conditions.

[0031] (4) Better generalization ability across structures / modalities This invention organizes inverse updates based on the physical propagation hierarchy and uses diffraction degradation sequences generated by the forward model for training, enabling the model to learn inverse diffraction rules related to the imaging mechanism and reducing dependence on specific training data distributions. Therefore, it is easier to maintain stable super-resolution reconstruction performance under different sample structures, densities and imaging modes (such as wide field, confocal, etc.).

[0032] (5) The inference deployment is simple, requiring only diffraction-limited observations to output super-resolution results. This invention does not require an additional super-resolution reference, multi-frame acquisition, or complex excitation modulation during the inference stage. It only requires inputting a single frame or a few frames of diffraction-limited fluorescence images into the trained model to output super-resolution reconstruction results, which facilitates integration with existing microscopic imaging workflows and improves efficiency.

[0033] (6) It has strong scalability and is easy to adapt to different propagation parameters and system configurations. Because this invention organizes the reconstruction process with propagation hierarchy and propagation conditionation mechanism, the hierarchy settings and condition injection forms can be adjusted according to parameters such as imaging wavelength, numerical aperture, and propagation distance discretization method, thereby adapting to different system configurations and application requirements without changing the overall framework. Attached Figure Description

[0034] Figure 1 This is a flowchart of a fluorescence microscopy super-resolution reconstruction method based on propagation-constrained inverse diffraction dynamics; Figure 2 The results of the method test on a standard resolution test board using the method provided in this invention; Figure 3 This is a cross-modal example of using the method provided by the present invention; Figure 4 This is another cross-modal example of using the method provided by the present invention; Figure 5 This invention provides a method for 3D imaging at resolutions ranging from confocal to STED. Detailed Implementation

[0035] like Figure 1 As shown, this invention presents the overall framework of a fluorescence microscopy super-resolution reconstruction method based on propagation-constrained inverse diffraction dynamics: an inverse diffraction fitting stage and an inverse diffraction calculation stage. The upper part represents the inverse diffraction fitting stage: a diffraction layer constructed according to discrete propagation distances is used, and the propagation differences are learned by a propagation-conditionalized residual network to learn a physically interpretable inverse propagation trajectory. The lower part represents the inverse diffraction calculation stage: diffraction-constrained measurement data is acquired, inverse diffraction reconstruction is performed, high-frequency information lost during diffraction is compensated, and finally, inverse diffraction super-resolution imaging is achieved. Specifically, this is achieved through the following steps: S1) Acquire super-resolution training data: Acquire super-resolution fluorescence microscopy image data (which may come from SIM, STED, SMLM or other super-resolution imaging / reference reconstruction results); S2) Establish a forward diffraction degradation model and generate a hierarchical degradation sequence: Establish an optical diffraction forward propagation model and discretize the propagation distance into multiple propagation levels; based on the forward propagation model, perform diffraction degradation modeling on the super-resolution training data to generate a diffraction state sequence corresponding to each propagation level, where larger propagation levels correspond to stronger diffraction degradation states, serving as training inputs or intermediate supervision targets; the implementation process is as follows: Figure 1 The upper half of the middle; S3) Training the propagation-conditional inverse diffraction reconstruction model: Using the aforementioned hierarchical diffraction state sequence, train a super-resolution reconstruction model containing propagation-conditional residual operators. This enables the model to learn to perform progressive inverse diffraction updates along the propagation hierarchy, gradually recovering from a strongly degenerate state to the super-resolution state of the object plane. The implementation process is as follows: Figure 1The upper half of the middle section is the weight update part; S4) Super-resolution inference reconstruction: The diffraction-limited fluorescence microscopy image to be processed (low-resolution observation) is input into the trained super-resolution reconstruction model. The model performs stepwise inverse diffraction updates along the propagation hierarchy and outputs the super-resolution reconstruction result. The implementation process is as follows: Figure 1 The lower half of the middle; The training phase does not require real-world acquisition and strict registration of low-resolution / super-resolution paired images, while the inference phase only requires input of diffraction-limited observations to output super-resolution results.

[0036] The above steps S2 and S3 will be explained below through specific embodiments.

[0037] 1. Forward model: Modeling diffraction-induced degradation This invention models the information loss of diffraction limitation from the perspective of wave optics: the high spatial frequency components of the sample plane (object plane) field are gradually suppressed as they propagate along the propagation direction due to the exponential decay of the evanescent components, thus forming a physically explainable degradation process.

[0038] In this embodiment, the angular spectrum propagation model is used to describe the propagation field distribution of the object plane field at a distance z, and its expression is: ; in, This represents the complex amplitude field at a propagation distance of z in the plane; Represents the spectrum of the planar field of an object in the spatial frequency domain; For the transverse wave vector component in the spatial frequency domain; For wave number, The wavelength is used for imaging.

[0039] Longitudinal wave vector component satisfy: ; From equation (2), we can see that: when hour, It is a purely imaginary number, corresponding to the evanescent component; this component decays exponentially with z during propagation, making it difficult to detect high spatial frequency information carrying subwavelength details in far-field observations, thus resulting in diffraction-limited degradation.

[0040] Since fluorescence microscopy records intensity rather than complex amplitude fields, this invention preferably introduces latent variable complex fields for physical propagation interpretation and correlates them to the observed intensity domain via an intensity-forming map, enabling training / inference in the intensity domain during implementation. Intensity mapping formula: In fluorescence microscopy imaging, the detector typically records intensity images, and the observation can preferably be modeled as: in This represents the noise term (e.g., a combination of Poisson noise and readout noise). Based on the above forward model, diffraction degradation modeling can be performed on the super-resolution reference sample to generate diffraction-limited training inputs, thereby constructing training sample pairs.

[0041] 2. Inverse Model: Stepwise Inverse Diffraction Dynamics with Propagation Conditions Unlike the approach of "directly constructing an analytical inverse propagation operator and performing explicit inversion," this invention describes super-resolution reconstruction as a stepwise inverse diffraction update process constrained by a known forward propagation model and parameterized by propagation parameters. Since the evanescent component decays exponentially during propagation, explicit analytical inversion of the propagation operator or direct backpropagation extrapolation can easily amplify noise and lead to instability. Therefore, this invention does not construct an explicit analytical inverse operator, but instead uses learned residual updates to gradually compensate for the high-frequency information loss induced by diffraction at the propagation level, thereby improving stability while maintaining physical consistency.

[0042] 2.1 Propagation hierarchy and reverse update sequence Preferably, a set of discrete propagation distances is pre-selected to form a propagation hierarchy set: ; in Represents the object plane or reference plane. This represents the propagation level corresponding to the observation (i.e., the level with the strongest diffraction degradation). During inference, the initial estimate corresponding to the diffraction-limited observation is used as the starting point, and the propagation proceeds along the predefined propagation levels. Gradually updated to The stepwise reconstruction sequence was obtained. ,in This is the output of the super-resolution reconstruction result.

[0043] 2.2 Residual inverse diffraction update with propagation condition In the At each propagation level, this invention uses propagation-conditionalized residual mapping to update the current estimate.

[0044] In this embodiment, the update follows the following form: ; in: Indicates the level of propagation The current estimate below; This indicates the updated estimate, corresponding to a level closer to the object plane (with weaker degradation); Indicates hierarchy The corresponding forward propagation operator (or its discrete implementation / parameter representation); For parameters The propagation conditional residual operator is used to predict the propagation from the hierarchical level. arrive The residual correction amount.

[0045] By using the stepwise residual update of equation (4), this invention decomposes the “difficult and pathological inverse diffraction reflection” into multiple local, better-condition inverse update steps, so that the inverse process forms a consistent inverse evolution trajectory along the physically defined propagation hierarchy, thereby gradually compensating for the high spatial frequency information suppressed by diffraction and avoiding unstable direct inversion.

[0046] 2.3 Methods of injecting propagation conditions into the model (hierarchical specific updates) To enable different propagation levels to have different reverse update strategies, this invention performs conditional injection at the propagation level.

[0047] In this embodiment, the discrete propagation distance is... (or hierarchical index) Mapped to an embedding vector: ; And the embedded vector is used to pair the residual operator The internal features are modulated (e.g., scaling and translating the normalization parameters of the residual block, or gating / additively biasing the channel features) to achieve level-specific inverse diffraction updates: focusing on noise suppression and main structure recovery at strongly degenerate levels, and gradually enhancing high-frequency details at levels close to the object plane.

[0048] 2.4 Implementation of the Network Structure (Propagation Conditional U-Net) In this embodiment, the residual operator The implementation uses propagation-conditionalized U-Net and includes residual blocks and attention mechanisms to improve fine-structure recovery and cross-structure generalization capabilities: the normalization method is Group Normalization; the activation function is SiLU; the base channel width is 128, and the channel ratio is (1, 2, 2); each scale contains 4 residual blocks; a self-attention module is introduced at the preset scale; Dropout is set to 0.1; during training, EMA (exponential moving average) is used to update parameters, and the decay coefficient can be 0.9999.

[0049] The above structure and parameters are preferred implementations. In actual implementation, equivalent encoder-decoder structures, residual network structures or attention network structures can also be used to realize propagation conditional residual mapping, as long as they can realize the stepwise inverse diffraction update along the propagation level as described in equation (5).

[0050] 3. Gradual dissemination of consistency supervision (training) To learn the inverse update of the aforementioned propagation constraints, this invention constructs a stepwise propagation consistency supervision objective based on a forward diffraction model. This training strategy utilizes a physical forward propagation model to generate a "truth state sequence" of propagation levels and requires the network to output a prediction consistent with the physical state of the corresponding level at each inverse update step, thereby guiding the network to learn stable and interpretable inverse diffraction trails along the propagation levels.

[0051] 3.1 Construction of Multilayer Diffraction State Sequence Given super-resolution parameters of the object plane (e.g., reference reconstructions from SIM, STED, or SMLM), the corresponding object field (or its equivalent representation). Based on the forward propagation operator Generate the diffraction state sequence at the discrete propagation level: ; in Indicates the distance of transmission The physical propagation state at the location (or its intensity domain equivalent representation). This yields the training sample pairs: and the need for intermediate-level supervision .

[0052] 3.2 Stepwise Supervision of the Objective Function During training, the network at different levels Predict based on the current state (or estimate) And compare it with the corresponding real state obtained from equation (6). Alignment. In this embodiment, the parameters are optimized using the following stepwise loss function: ; Among them, expectations The average can be taken from the training data distribution and the sampling distribution of the propagation hierarchy.

[0053] In this embodiment, the losses at different levels can be weighted and summed: ; in This is a weighting coefficient used to balance the learning difficulty of each level.

[0054] Through this training strategy, the model learns the stepwise inverse diffraction update rules under propagation constraints without relying on real registered LR-HR paired images, thereby achieving stable super-resolution reconstruction of real diffraction-constrained observations during the inference stage.

[0055] As another possible implementation, the input during the training phase can be a diffraction-limited intensity image or a combination of it and a latent variable field; the output is the super-resolution reconstruction result of the object plane or the intermediate reconstruction result of the corresponding level. Training can be implemented using a mini-batch stochastic gradient descent optimization method, combined with EMA to improve inference stability. The above training details are preferred embodiments and do not constitute a limitation on the scope of protection of this invention.

[0056] To further illustrate the reconstruction method of the present invention, a super-resolution reconstruction model trained with different super-resolution fluorescence microscopy image data is used to perform super-resolution reconstruction of diffraction-limited fluorescence microscopy images.

[0057] (1) Taking the resolution plate microscopic images captured by structured light illumination microscope (SIM) as training data as an example The training data consists only of resolution plate microscopic images taken by structured light illumination microscope (SIM), without WF data. After performing steps S2 and S3, the trained super-resolution reconstruction model NID is obtained. WF data is the test data, which is input into NID to perform super-resolution reconstruction, resulting in a resolution of 60nm (which exceeds the original resolution of SIM).

[0058] like Figure 2 As shown: The first row, WF, is a resolution plate micrograph taken with a diffraction-limited wide-field microscope (WF), displaying a resolution of 300 nm (the physical diffraction limit is 200 nm); the second row, SIM, is a resolution plate micrograph taken with a structured light illumination microscope (SIM), displaying a resolution of 120 nm (exceeding the physical diffraction limit of 200 nm, indicating super-resolution microscopy capability). From Figure 2 It can be seen that the reconstruction method provided by the present invention does not require training the data with images, but can achieve super-resolution reconstruction of diffraction-limited fluorescence microscopy image data by using only super-resolution fluorescence microscopy image data as training data.

[0059] (2) Taking the microscope images directly acquired by stimulated emission depletion microscopy (STED) as training data as an example Microscopic images directly acquired using stimulated emission depletion microscopy (STED) were used as training data, excluding confocal data. After executing steps S2 and S3, a trained super-resolution reconstruction model NID was obtained. Confocal data was then input into NID as test data, and step S4 was executed to perform super-resolution reconstruction, resulting in an inverse diffraction reconstructed image.

[0060] like Figure 3 As shown, Figure 3The top of the image shows the full field of view, from left to right: a microscope image directly acquired by stimulated emission depletion microscopy (STED) (exceeding the diffraction limit, super-resolution image), a microscope image taken by confocal microscopy (resolution not exceeding the diffraction limit), and an image reconstructed by inverse diffraction (which can be compared with the STED reference). Figure 3 The lower part of the image shows magnified views of the three microscopes mentioned above, along with the grayscale values ​​of the cross-section with the yellow line within those magnified views. From Figure 3 The comparison shows that the inverse diffraction reconstructed the super-resolution information, indicating that the reconstruction method provided by the present invention does not require training the data with images, but can achieve super-resolution reconstruction of diffraction-limited fluorescence microscopy image data by using only super-resolution fluorescence microscopy image data as training data.

[0061] (3) Images captured by structured light illumination microscope (SIM) were used as training data. Using only images captured by a structured light illumination microscope (SIM) as training data, excluding microscope images captured by a wide field microscope (WF), after executing steps S2 and S3, a trained super-resolution reconstruction model NID is obtained. Microscope images captured by a wide field microscope (WF) are input into NID as test data, and step S4 is executed to perform super-resolution reconstruction, resulting in an inverse diffraction reconstructed image.

[0062] like Figure 4 As shown, the left side is the full-field image, from top to bottom: a wide-field (WF) microscope image (resolution not exceeding the diffraction limit) and an image reconstructed by inverse diffraction. The right side is a magnified view, from left to right: an image taken by a simulated illumination microscope (SIM) as a super-resolution reference; a wide-field microscope image, diffraction-limited, with a resolution below 200 nm; and the result of inverse diffraction reconstruction, with a resolution close to that of the SIM. Figure 4 The comparison shows that the inverse diffraction reconstructed the super-resolution information, indicating that the reconstruction method provided by the present invention does not require training the data with images, but can achieve super-resolution reconstruction of diffraction-limited fluorescence microscopy image data by using only super-resolution fluorescence microscopy image data as training data.

[0063] (4) Stimulated emission depletion microscopy (STED) was used as training data. Using only stimulated emission depletion microscopy (STED) as training data, without including confocal microscopy images and 3D images, after executing steps S2 and S3, a trained super-resolution reconstruction model NID is obtained. The confocal microscopy images are input into NID as test data and step S4 is executed to perform super-resolution reconstruction, resulting in an inverse diffraction reconstructed image.

[0064] like Figure 5The image shown is a 3D imaging image: the top is the 3D map reconstructed by inverse diffraction, with the heatmap color representing the imaging depth; the bottom is a cross-sectional view at the dashed line in the larger image, indicating that the resolution in the xz direction can be maintained, only the resolution in the xy direction changes. From Figure 5 The comparison shows that the inverse diffraction reconstructed the super-resolution information, indicating that the reconstruction method provided by the present invention does not require training the data with images, but can achieve super-resolution reconstruction of diffraction-limited fluorescence microscopy image data by using only super-resolution fluorescence microscopy image data as training data.

[0065] In summary, the reconstruction method provided by this invention is an interpretable stepwise inverse propagation / inverse diffraction reconstruction mechanism formed under the constraints of an explicit forward propagation model, which can solve the problems of insufficient physical consistency and interpretability in existing technologies. In the absence of real registration paired training data, the reconstruction method provided by this invention utilizes only super-resolution samples and combines them with a forward diffraction / propagation model to generate diffraction degradation sequences that can be used for training, thereby learning propagation-constrained inverse diffraction updates and achieving super-resolution inference on real diffraction-limited observations. The reconstruction method provided by this invention avoids explicit analytical inverse operators and possesses a noise-resistant and stable inverse diffraction solution, thus solving the problem of instability in inverse propagation in existing technologies. The reconstruction method provided by this invention introduces a constraint mechanism on observations during the reconstruction process, ensuring measurement consistency between intermediate estimates and the final result, thus solving the problem of difficulty in guaranteeing measurement consistency in existing technologies. The reconstruction method provided by this invention can adapt to reconstruction frameworks with different modes and system deviations to achieve stable super-resolution reconstruction, thereby solving the problem of limited generalization across modes / systems in existing technologies.

Claims

1. A fluorescence microscopy super-resolution reconstruction method based on inverse diffraction dynamics, characterized in that, The method includes: S1) Obtain super-resolution fluorescence microscopy image data as training data; S2) Establish an optical diffraction forward propagation model and discretize the propagation distance into multiple propagation levels; based on the forward propagation model, perform diffraction degradation modeling on the super-resolution training data to generate diffraction state sequences corresponding to each propagation level; S3) Train a super-resolution reconstruction model containing propagation conditional residual operators using a hierarchical diffraction state sequence, so that the super-resolution reconstruction model learns to perform stepwise inverse diffraction updates along the propagation hierarchy, gradually recovering from a strongly degenerate state to the super-resolution state of the object plane, and obtains a trained super-resolution reconstruction model. S4) Input the diffraction-limited fluorescence microscopy image to be processed into the trained super-resolution reconstruction model. The super-resolution reconstruction model performs stepwise inverse diffraction updates along the propagation level and outputs the super-resolution reconstruction result.

2. The fluorescence microscopy super-resolution reconstruction method based on inverse diffraction dynamics according to claim 1, characterized in that, In S1, super-resolution fluorescence microscopy image data are derived from structured illumination microscopy (SIM), stimulated emission depletion microscopy (STED), or single-molecule localization microscopy (SMLM).

3. The fluorescence microscopy super-resolution reconstruction method based on inverse diffraction dynamics according to claim 1, characterized in that, In S2, the method for establishing the forward propagation model of optical diffraction and discretizing the propagation distance into multiple propagation levels is as follows: S21) The angular spectrum propagation model is used to describe the propagation field distribution of the object's planar field at a distance z; S22) The complex amplitude field is converted into fluorescence microscopy recording intensity to establish a forward propagation model: S23) The working distance of the microscope is evenly divided into K parts, thereby discretizing the propagation distance into K propagation levels.

4. The fluorescence microscopy super-resolution reconstruction method based on inverse diffraction dynamics according to claim 3, characterized in that, K propagation levels are represented as follows: ； in, Represents the object plane or reference plane. This indicates the propagation level corresponding to the observation.

5. The fluorescence microscopy super-resolution reconstruction method based on inverse diffraction dynamics according to claim 1, characterized in that, In S2, the method for modeling diffraction degradation of the super-resolution training data based on the forward propagation model and generating diffraction state sequences corresponding to each propagation level is as follows: Given object plane super-resolution parameters Based on the forward propagation operator Generate the diffraction state sequence at the discrete propagation level: ； in Indicates the level of propagation The physical propagation state at the location; thus, the training sample pairs are obtained: and the supervision required for intermediate propagation levels .

6. The fluorescence microscopy super-resolution reconstruction method based on inverse diffraction dynamics according to claim 1, characterized in that, In S3, this specifically includes: propagating along predefined levels by... Gradually updated to The stepwise reconstruction sequence was obtained. ,in This is the output of the super-resolution reconstruction result.

7. The fluorescence microscopy super-resolution reconstruction method based on inverse diffraction dynamics according to claim 6, characterized in that, Starting with the initial estimate corresponding to the diffraction-limited observation, in the first... At the propagation level, the current estimate is updated using propagation-conditionalized residual mapping to obtain the th propagation level. -1 level of propagation estimation; Inverse diffraction updates follow the following form: in: Indicates the level of propagation The current estimate below; This indicates the updated estimate, corresponding to a propagation level closer to the object plane; Representation and propagation hierarchy The corresponding forward propagation operator; For parameters The propagation conditional residual operator.

8. The fluorescence microscopy super-resolution reconstruction method based on inverse diffraction dynamics according to claim 7, characterized in that, During training, at the propagation level Based on current estimates and forecasts and compare it with the corresponding real state. Alignment.

9. The fluorescence microscopy super-resolution reconstruction method based on inverse diffraction dynamics according to claim 8, characterized in that, During training, the parameters are optimized using the following stepwise loss function: ； Among them, expectations The average can be taken from the training data distribution and the sampling distribution of the propagation hierarchy.

10. The fluorescence microscopy super-resolution reconstruction method based on inverse diffraction dynamics according to claim 9, characterized in that, Weighted summation of losses at different propagation levels: ； in, This is a weighting coefficient used to balance the learning difficulty of each level.

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