Low-quality fluorescent microscopic image reconstruction method based on simulation data and learnable descent algorithm

Abstract

The invention discloses a low-quality fluorescent microscopic image reconstruction method based on simulation data and a learnable descent algorithm, and the method achieves the efficient reconstruction of a low-signal-to-noise-ratio three-dimensional fluorescent microscopic image through the combination of a double-layer optimization frame and a joint optimization mechanism of a fidelity term and a regular term, combines the deep learning and optimization algorithm, and achieves the high-efficiency reconstruction of the low-signal-to-noise-ratio three-dimensional fluorescent microscopic image. Through a mode of combining a learning regularization item and iterative optimization, the method can effectively denoise and recover high-resolution details of the fluorescent microscopic image, thereby improving the image quality, reducing the noise interference, and obtaining a more accurate image reconstruction result under the condition of a low signal-to-noise ratio. The algorithm has strong generalization ability, can be trained on a small amount of simulation data, achieves a good effect in real data inference, reduces dependence on a large-scale real data set, establishes a clear relationship between input and output through a regularization item and a fidelity item with clear physical significance, follows a strict mathematical principle in the whole iteration process, and has high robustness. And the method has good interpretability.

Description

Technical Field

[0001] The present invention relates to the technical field of fluorescence microscopic image reconstruction, and particularly to a method for reconstructing low-quality fluorescence microscopic images based on simulation data and a learnable descent algorithm. Through a joint optimization mechanism that combines a fidelity term and a regularization term in a double-layer optimization framework, efficient reconstruction of three-dimensional fluorescence microscopic images with low signal-to-noise ratio is achieved. Background Art

[0002] Fluorescence microscopic imaging technology is an important means for observing the microscopic structure of cells. The fluorescence microscope images obtained under low-light conditions are mainly affected by two main types of degradation: noise pollution and optical blur. Photon shot noise is an important reason for the degradation of image quality under low-light conditions. Due to the randomness of photon emission and detection, under low photon flux, photon shot noise becomes more obvious. This noise will cause random bright and dark spots to appear in the image, reducing the clarity and contrast of the image, making it difficult to identify the fine structures inside the cells. Detector noise also affects the image quality. The detector of a fluorescence microscope generates electronic noise during operation, and these noises will be superimposed on the image signal, further reducing the signal-to-noise ratio of the image. In addition, optical diffraction also causes optical blur of the image. Due to the diffraction effect of light, the point spread function (PSF) of the imaging system introduces blur in the image, making the fine structures inside the cells become blurred. This optical blur reduces the resolution of the image and affects the observation of the ultrastructure inside the cells. In live-cell imaging, motion blur is also an important problem. The biomolecules and organelles inside the cells are constantly moving, and this movement will cause motion blur to appear in the image, further reducing the image quality and affecting the accurate observation of dynamic biological processes.

[0003] To address the above challenges, various computational methods have been developed to improve the quality of fluorescence microscope images. Traditional deconvolution methods, such as the Richardson-Lucy (RL) deconvolution algorithm, have been widely used for fluorescence image restoration. These methods use an iterative optimization algorithm to reconstruct the original image using the point spread function of the imaging system, thereby improving the resolution and contrast of the image. However, although RL deconvolution is effective in improving image sharpness, it is prone to amplifying noise under low signal-to-noise ratio (SNR) conditions, resulting in overfitting artifacts and loss of fine structure details.

[0004] In recent years, deep learning techniques have been introduced to address the limitations of traditional methods. For example, Patent CN109636733A proposed a deconvolution method based on a deep neural network, which utilized the spatio-temporal redundant information of multiple frames of images and alternately optimized through Fourier transform and denoising network, solving the problem that the design of the regularization term in traditional methods relied on experience. However, this method is sensitive to the temporal redundancy of images, and its performance significantly degrades when the redundancy is insufficient in dynamic scenarios (such as fast cell movement). Patent CN111524078A directly learned the mapping relationship between blurred images and deconvolution results using a dense network, achieving non-iterative fast deblurring. However, its pure data-driven black-box model lacks physical interpretability and may introduce false structural artifacts when dealing with complex noise, especially prone to losing weak signal features under low signal-to-noise ratio conditions.

[0005] In addition, these methods often require a large amount of computing resources and time when dealing with complex images, and it is often difficult to simultaneously achieve denoising and deconvolution, resulting in limited improvement in image quality. Therefore, developing more efficient and generalized image processing methods is of great significance for improving the imaging quality of fluorescence microscopes. Summary of the Invention

[0006] In view of the above, the present invention provides a method for reconstructing low-quality fluorescence microscopy images based on simulation data and a learnable descent algorithm. This method combines deep learning and optimization algorithms, and through the combination of a learning-based regularization term and iterative optimization, can effectively denoise and restore the high-resolution details of fluorescence microscopy images, thereby improving image quality, reducing noise interference, and obtaining more accurate image reconstruction results under low signal-to-noise ratio conditions. The present invention is realized through the following technical solutions:

[0007] The present invention discloses a method for reconstructing low-quality fluorescence microscopy images based on simulation data and a learnable descent algorithm, and the steps are as follows:

[0008] 1) Acquisition of low-dose three-dimensional fluorescence images: Imaging a biological sample labeled with specific fluorescence through a microscopy imaging system. Under imaging conditions with strictly limited low photon dose flux, drive the objective lens through a piezoelectric ceramic to complete multi-focal plane sequence acquisition, and stack and reconstruct the obtained two-dimensional image sequence along the axial dimension to form an original three-dimensional fluorescence image;

[0009] 2) Calculation of the point spread function and isotropic processing: Based on the core parameters such as the numerical aperture of the microscopy imaging system, the magnification of the objective lens, and the refractive index of the imaging medium, obtain the three-dimensional point spread function PSF through wavefront propagation theory calculation or fluorescence microsphere calibration experiment, and use an interpolation algorithm to adjust its axial sampling interval to ensure that its lateral and axial pixel sizes reach an isotropic resolution of 1:1;

[0010] 3) Simulation data construction: Create a three-dimensional zero-value matrix as the basic space, randomly generate three-dimensional geometric structures with dynamic size ranges within a limited spatial domain, where the intensity values of each structure follow a uniform distribution, and finally superimpose a uniform background field to construct the original simulation data;

[0011] 4) Biological imaging property simulation: Apply three-dimensional Gaussian convolution to the original simulation data to eliminate the sharp edge artifacts of the artificially generated structures; subsequently, perform axial downsampling to make the anisotropy ratio of the data volume consistent with that of real microscopic images, and output noiseless reference data;

[0012] 5) Optical degradation reconstruction: Simulate the optical diffraction effect by performing three-dimensional convolution operation on the three-dimensional point spread function PSF in 2) and the noiseless reference data to generate blurred intermediate data; perform matching downsampling on the blurred data along the axial direction to obtain reduced-dimensional blurred data that conforms to the resolution characteristics of the real imaging system;

[0013] 6) Multi-modal noise injection: First, generate Poisson noise according to the signal intensity of the reduced-dimensional blurred data to simulate photon counting noise; then superimpose Gaussian white noise to characterize the readout noise of the microscopic imaging system, and finally synthesize degraded simulation data with a signal-to-noise ratio equivalent to that of the experimental data;

[0014] 7) Large-scale dataset construction: Through parameter space traversal, repeatedly execute steps 3)-6) to generate a large number of data pairs, namely matching reference data and degraded simulation data, ensure the balance of data distribution, and divide the data pairs into a validation set and a training set;

[0015] 8) Construct a deep learning network with parameters updated by a learnable descent algorithm. Use the simulated degraded data in the training set data pairs as the input of the network, and the corresponding reference data as the label of the network output. In the network architecture, first use a 3D convolutional layer with a smooth activation function to extract the key features in the input data, and continue with smooth processing after norm calculation to obtain the feature map and use it as the regularization term function. Apply the regularization term and the gradient calculation of the fidelity term with a learnable gradient operator in the iterative algorithm to solve the iterative result, and train the network by using the iterative result and the label through a composite loss function, and test the network performance with the validation set;

[0016] 9) Input the three-dimensional fluorescence image of the biological sample collected in 1) into the trained deep learning network for inference, so as to output a high-quality reconstructed image.

[0017] As a further improvement, the imaging conditions of the low-dose three-dimensional fluorescence image in step 1) of the present invention are low excitation light intensity or short exposure time, and the collected two-dimensional images contain a large amount of noise and diffraction blur; the point spread function is a three-dimensional matrix structure with a Gaussian distribution.

[0018] As a further improvement, the processing procedure expression of step 4) in the present invention is as follows:

[0019] GT = [Gau(S, σ1)]↓ t ;

[0020] Where: GT is the reference data, S is the simulation data, Gau(S, σ1) represents three-dimensional Gaussian smoothing of the simulation data S with a variance of σ1, and [ ]↓ t represents downsampling the target axis at a magnification of t;

[0021] The processing procedure expression of step 5) is as follows:

[0022]

[0023] Where: i1 is the downsampled blurred data, S is the simulation data, represents the convolution operator, h is the point spread function, and []↓ t represents downsampling the target axis at a magnification of t.

[0024] The processing procedure expression of step 6) is as follows:

[0025] i2 = P(i1) + n;

[0026] Where: i1 is the downsampled blurred data, i2 is the simulated degraded data, P( ) represents the Poisson random process of introducing photon noise during the imaging process, and n represents the Gaussian random noise introduced by the detection device during the imaging process.

[0027] As a further improvement, the simulation data, downsampled blurred data, simulated degraded data, and reference data in the present invention are all three-dimensional volume data, and the ratio of the lateral pixel size to the axial pixel size of the downsampled blurred data, simulated degraded data, and reference data is consistent with the corresponding ratio of the three-dimensional fluorescence microscopy image.

[0028] As a further improvement, the composite loss function in the present invention includes a weighted combination of the mean square error and the structural similarity term:

[0029] L = MSE(x k , y) + ω × [1 - SSIM(x k , y)].

[0030] As a further improvement, the regularization term function in the present invention is implemented by a convolutional neural network, which includes: a feature extraction layer: a three-dimensional convolutional layer, a non-linear activation layer using a smoothing activation function, and a feature normalization layer for L2 norm calculation, that is, extracting the features of the image through a convolutional neural network, and obtaining a piecewise regularization term function limited by a constant threshold after a series of smoothing and normalization processes on the features.

[0031] As a further improvement, for the smooth activation function of the present invention, the activation function adopts a smooth correction unit that remains second-order differentiable within a preset threshold range:

[0032] That is

[0033]

[0034] As a further improvement, for the learnable gradient operator of the data fidelity term of the present invention, its parameter matrix inherits the characteristics of the point spread function of the optical system and is dynamically updated through gradient descent during the training process;

[0035] The gradient calculation expression of the learnable gradient operator satisfies:

[0036]

[0037] where A is the learnable parameter matrix, which maintains a preset proportional relationship with the PSF during initialization.

[0038] As a further improvement, in each iteration of the iterative algorithm stage of the present invention, the following operations are performed. Taking the k-th iteration as an example:

[0039] First, perform the gradient calculation of the fidelity term:

[0040]

[0041] where α k is the step size parameter of the fidelity term. On this basis, two candidate solutions, namely v k+1 and u k+1

[0042] That is

[0043]

[0044] where τ k is the fusion step size parameter;

[0045] Compare the objective function values at the two candidate solutions, and select the relatively smaller one as the new iteration value x k+1 to ensure convergence. At the same time, during this process, the gradient of the entire objective function needs to be calculated and used as a conditional judgment to update the threshold parameter to gradually decrease it;

[0046] When k reaches the preset maximum number of iterations K of the current iteration round or the overall threshold is less than the minimum tolerance, iterate and output x K .

[0047] The beneficial effects of the present invention are as follows:

[0048] The present invention proposes a method for reconstructing low-quality fluorescence microscopy images based on the Learnable Descent Algorithm (LDA), aiming to solve the problems of noise and blurring in fluorescence images under low-light conditions. By combining simulation data generation and deep learning optimization, this method constructs an efficient double-layer reconstruction framework, which can significantly improve the resolution and contrast of three-dimensional fluorescence images and provide a reliable solution for dynamic observation of living cells.

[0049] The method first constructs a simulation topology model through the Monte Carlo algorithm, combines three-dimensional Gaussian smoothing and convolution with the three-dimensional point spread function (PSF), simulates optical degradation and injects Poisson-Gaussian mixed noise to generate a training dataset. During the reconstruction process, this method uses the Learnable Descent Algorithm (LDA) to construct a deep network model. Through the composite loss calculation of the upper optimization module and the joint optimization mechanism of the fidelity term and the regularization term of the lower module, efficient iterative reconstruction is achieved. Innovatively, a learnable gradient operator is introduced to replace the traditional PSF parameters, combined with Nesterov smoothing to handle non-smooth optimization problems, and the image detail recovery ability is enhanced through a feature normalization module. This method effectively suppresses noise artifacts under low signal-to-noise ratio conditions, avoids the overfitting problem of traditional deconvolution algorithms, and significantly improves the image quality.

[0050] The innovation of the present invention lies in its strong generalization ability, which can be trained on a small amount of simulation data and achieve good results in real data inference, reducing the dependence on large-scale real datasets. In addition, through regularization terms and fidelity terms with clear physical meanings, the algorithm establishes a clear relationship between the input and the output. The entire iterative process follows strict mathematical principles and has good interpretability.

[0051] In summary, through an innovative algorithm framework and optimization mechanism, the present invention effectively solves the problems of noise and blurring in image reconstruction under low-light conditions, improves the image quality, and demonstrates strong generalization and interpretability in practical applications, having broad application prospects and technical value. Brief Description of the Drawings

[0052] Figure 1 A low signal-to-noise ratio image obtained by imaging lysosomes in living U2OS cells under low light dose conditions using an instantaneous structured illumination microscopy;

[0053] Figure 2 A schematic flowchart of the method for reconstructing low signal-to-noise ratio fluorescence microscopy data of the present invention based on simulation data and deep learning guided by the Learnable Descent Algorithm;

[0054] Figure 3 (a) is an example diagram of the simulation data S;

[0055] Figure 3 (b) is an example diagram of the simulation clean and noise-free reference data GT;

[0056] Figure 3 (c) is an example diagram of the simulated degradation data i2;

[0057] Figure 4 is a schematic diagram of the deep learning network structure of the learnable descent algorithm double-layer optimization module;

[0058] Figure 5 is a comparison diagram of the reconstructed images of the real low-light dose acquisition data using the method of the present invention and the existing reconstruction method RCAN;

[0059] Among them, (a) is the original acquisition data, that is, the low signal-to-noise ratio data obtained by imaging the endoplasmic reticulum labeled with mEmerald-Tomm20-C-10 in living U2OS cells; (b) is the reconstruction result obtained by the method of the present invention, (c) is the reconstruction result obtained by the existing reconstruction method RCAN, and (d) is the data acquired at a high light dose; scale bar: main Figure 5 Microns, and the inset is 1 micron. Detailed implementation manners

[0060] In order to describe the present invention more specifically, the technical solutions of the present invention will be described in detail below with reference to the accompanying drawings and specific implementation manners.

[0061] A method for reconstructing low-quality fluorescence microscopy images based on simulation data and a learnable descent algorithm. In the field of three-dimensional fluorescence microscopy imaging, fluorescently labeled biological samples emit fluorescence signals after being irradiated with excitation light, and these signals are collected by a microscopy imaging system through an optical path. A series of two-dimensional slice images are obtained by quantitatively adjusting the focal plane position, and then three-dimensional stereoscopic image data is generated through volume reconstruction. However, there are various image degradation factors in this imaging process: First, due to the interference of out-of-focus light, each two-dimensional slice plane inevitably contains out-of-focus signals of non-focal planes; second, limited by the optical diffraction limit, the resolution of the acquired images is reduced, resulting in image blurring, which is one of the main mechanisms of fluorescence microscopy image degradation. In addition, under the condition of low-light dose fluorescence microscopy imaging, due to the use of a lower excitation light intensity and a shorter exposure time, the number of photons emitted by fluorescent molecules is significantly reduced, resulting in a decrease in the intensity of the acquired fluorescence signals. In this scenario, the image quality is severely affected by the decrease in the signal-to-noise ratio, accompanied by photon statistical noise and quantization noise, and finally manifested as signal intensity attenuation, contrast reduction, and resolution loss. This extremely low light dose and quantization noise constitute another main mechanism of image degradation.

[0062] Therefore, under the condition of low-light dose imaging, the acquired original data simultaneously exhibits severe noise interference and image blurring characteristics, such as Figure 1As shown in the figure, to achieve high-quality three-dimensional fluorescence image reconstruction under low light dose conditions, joint optimization processing for noise suppression and blur correction needs to be carried out simultaneously. Deep learning has recently become an effective method for fluorescence microscope image restoration, with significant advantages over traditional model-based methods. Among them, convolutional neural networks have demonstrated advanced performance in tasks such as image denoising, super-resolution reconstruction, and blind deconvolution. By training on pairs of noisy and clear fluorescence images, noise suppression and resolution enhancement can be learned. However, due to the complexity of biological samples and the differences in imaging conditions, it is difficult to obtain a large-scale high-quality training dataset in the field of fluorescence microscopy. To overcome the challenge of data dependence, simulation data can be used to train the network; however, this also poses requirements for the generalization ability of the network. Although traditional iterative methods are not as performant as deep learning methods in specific scenarios, they often have good generalization ability. To address these challenges, therefore, the present invention proposes a method for reconstructing low signal-to-noise ratio fluorescence microscopy data guided by simulation data and a learnable descent algorithm. The learnable descent algorithm (LDA) is used to solve the denoising and deconvolution problems in fluorescence microscopy imaging. LDA is a learnable optimization framework designed for non-smooth and non-convex image reconstruction problems, which combines the principles of deep learning and iterative optimization. Different from traditional deconvolution techniques that are prone to amplifying noise or deep learning methods that require a large amount of labeled training data, LDA combines model-based prior knowledge with learnable features to achieve robust and efficient image restoration. The algorithm uses the Nesterov smoothing technique to handle non-smooth optimization problems and uses a residual learning framework to ensure stable convergence and improve the reconstruction quality. By embedding a convolutional neural network (CNN) into the regularization term, LDA enhances the feature extraction ability and promotes image smoothing, thereby achieving better denoising and deconvolution effects in low signal-to-noise ratio fluorescence images.

[0063] The method for reconstructing low signal-to-noise ratio fluorescence microscopy data guided by simulation data and a learnable descent algorithm according to the present invention includes the following steps, as Figure 2 shown:

[0064] Step S1: Acquisition of real data. Under the imaging conditions of low excitation intensity or short exposure time, biological sample data is collected, and according to the experimental conditions, the corresponding point spread function is obtained through simulation or experimental means, and the compensation sizes represented by the horizontal and axial pixels of the collected data are recorded, where the horizontal pixel size is denoted as s x , and the axial pixel size is denoted as s z , and the corresponding axial downsampling ratio t with respect to the horizontal is t = s z / s x ; through data preprocessing, the background intensity of the collected data is removed.

[0065] Step S2: Point Spread Function Calculation:

[0066] Based on the core parameters such as the numerical aperture, objective magnification, and refractive index of the imaging medium of the microscopic imaging system used to collect real image data, the three-dimensional point spread function PSF is obtained through wavefront propagation theory calculation or fluorescence microsphere calibration experiment. The axial sampling interval is adjusted using an interpolation algorithm to ensure that the lateral and axial pixel sizes reach an isotropic resolution of 1:1.

[0067] Step S3: Simulation Data Creation. Generate a three-dimensional matrix of a certain size (such as a matrix size of 128×128×128). Use a position random function to set spheres, circular rings, and three-dimensional space line structures with random radii or random lengths within a limited size range (4 - 10 pixels) at random positions in the matrix. Each structure has a random intensity within the limited range. The specific intensity range uses the intensity of the real collected data as a reference, and the corresponding number of each structure uses the distribution density of the real sample as a reference. Add a constant background to the entire matrix to obtain the original simulation data S.

[0068] Step S4: Biological Imaging Characteristic Simulation. Perform spatial convolution on the original simulation data S using a three-dimensional Gaussian kernel to smooth the sharp edges of the artificially generated structures, and perform t-fold downsampling on its axis to output the simulation clean and noise-free reference data GT.

[0069] Step S5: Optical Degradation Reconstruction: Degrade the simulation data S according to the imaging equation using the three-dimensional point spread function PSF to make it have a blur similar to that of the real collected data, and perform t-fold downsampling on its axis to obtain the simulation blurred downsampled blurred data i1.

[0070] Step S6: Multi-modal Noise Injection: Introduce random noise into i1 through Poisson random process and Gaussian random process to obtain the simulation degraded data i2, and the noise intensity is close to or slightly stronger than that of the real collected data.

[0071] In steps S4 to S6, the process of obtaining GT and i2 from S can be described by the following process:

[0072] GT = [Gau(S,σ1)]↓ t

[0073]

[0074] i2 = P(i1) + n

[0075] where: Gau(S,σ1) is a three-dimensional Gaussian blur function with a mean of 0 and a variance of σ1, [ ]↓ tIt represents downsampling along the axis at a magnification factor of t. P( ) represents the Poisson random process that introduces photon noise during the simulated imaging process, and n represents the Gaussian random process that introduces noise by the detection device during the imaging process. It represents the convolution operator, and + represents the addition operation. Figure 3 It shows the simulation data S, the simulation clean and noiseless reference data GT, and the simulation degraded data i2.

[0076] Step S7: Large-scale dataset construction:

[0077] By repeating the above GT and i2 data generation process, a large number of {GT, i2} data pairs are generated. At the same time, the data pairs are divided into a training set and a validation set according to a ratio of 8:2.

[0078] Step S8: Network construction and training

[0079] The deep learning network driven by the learnable descent algorithm adopts a two-layer optimization framework. Its upper optimization module is responsible for composite loss calculation and network parameter update, while the lower optimization module jointly iteratively optimizes through a fidelity term and a regularization term, as Figure 4 shown. The input of the upper optimization module is the simulation clean and noiseless reference data y and the current iterative reconstruction result x K . Based on a linear combination of the mean squared error and the structural similarity, a loss function L is constructed to calculate the global composite loss and backpropagate to update the network parameters of the lower module, that is

[0080] L = MSE(x k , y) + ω × [1 - SSIM(x k , y)]

[0081] where the definitions of the mean squared error and the structural similarity are as follows:

[0082]

[0083] where represents the mean of the x k data, and represents the variance of the x k data, represents the covariance of the x k and y data. The objective function of the lower module consists of a regularization term and a fidelity term, that is

[0084] x = argmin f(x) + r(x)

[0085] Among them, the regular term network structure is composed of multiple convolutional modules and feature normalization modules. The multiple convolutional modules include feature extraction units composed of multiple three-dimensional convolutional layers and smooth activation functions. In order to make the activation function differentiable near 0, the ReLU activation function is smoothed.

[0086] That is

[0087]

[0088] where δ is the activation function smoothing threshold, which is a constant.

[0089] The feature normalization module then smooths the features extracted by the convolutional module through the L2,1 norm, that is

[0090]

[0091] where N is the number of layers of the convolutional module. In addition, additional smoothing is also done here to ensure differentiability, that is

[0092]

[0093] where τ represents the threshold, which is calculated by τ = ξ × ε. The former is the adjustment coefficient, used to control the sensitivity of the threshold to gradient changes, and the latter is the basic threshold parameter, corresponding to the minimum convergence tolerance in the algorithm.

[0094] The weights of the convolutional neural network of the regularization term are updated during the backpropagation of the upper-layer composite loss function.

[0095] The fidelity term is the square of the difference between the low signal-to-noise ratio blurred fluorescence image x and the k-th iteration result x k and the convolution of the point spread function, that is

[0096]

[0097] For x k in this case, the conventional gradient calculation should be

[0098]

[0099] To compensate for asymmetric sampling and enhance the generalization ability of the model, the present invention introduces a learnable gradient operator A to replace the PSF, that is

[0100]

[0101] where A maintains a certain proportional relationship with the size of the PSF and is initialized with the parameters of the PSF. It is registered as a network parameter and updated during the forward propagation of the upper-layer optimization module.

[0102] The optimization strategy of the lower-layer optimization module consists of a learnable descent algorithm, which has specific update steps. First, it is necessary to calculate the gradient of the data fidelity term and update the current iteration point, that is

[0103]

[0104] where α k is the step size parameter of the fidelity term. On this basis, two candidate solutions can be obtained by taking the first-order approximation of it through the standard gradient descent path and the proximal gradient descent path respectively, which are v k+1 and u k+1

[0105] that is

[0106]

[0107] where τ k is the fusion step size parameter, and its initial value can be preset through experiments or registered as a learnable parameter during the training process.

[0108] Compare the objective function values at the two candidate solutions and select the relatively smaller one as the new iteration value x k+1 to ensure convergence. At the same time, the gradient of the entire objective function needs to be calculated during this process and used as a conditional judgment to update the threshold parameter to make it decrease initially.

[0109] That is, when it satisfies

[0110]

[0111] let

[0112] ε k+1 =βε k

[0113] where κ is a constant, usually taken as 10 6 , and β is also a constant, representing the ratio of ξ reduction, usually taken as 0.8. When the number of iterations k reaches the maximum number of iterations K preset for the current iteration round or the overall threshold index κε k is less than the minimum tolerance ε tol the lower-layer optimization module outputs x K .

[0114] During the training process, the simulated {GT, i2} data is used as the training set of the network.

[0115] First, normalize GT and i2 in each data pair. The normalization method is: arrange all pixel values from small to large. According to the need, the minimum value in the normalization process is selected from the 3% - 5% position, and the maximum value is selected as 100% value. Specifically as follows:

[0116]

[0117] Where: u represents the value to be normalized, percentile(u, p) represents the value at the p-th percentile, p high and p low are the high value and low value corresponding to the normalization standard respectively

[0118] During the training process, at the initial stage, the iteration number k is selected as a relatively small value, but a relatively large number of training epochs are adopted to preset the network parameters of the model, and only MSE is used as the loss function in the upper-layer optimization module to ensure the stability of parameter update. Then, the iteration number is gradually increased, and the number of training epochs is reduced to ensure efficiency. At the same time, SSIM is added to the loss function to achieve better training results. The model parameters with the best effect on the validation set are saved according to the loss function of the data in the validation set.

[0119] Step S9: Reconstruction of real low signal-to-noise ratio data acquisition. The real low signal-to-noise ratio biological data collected in S1 is input into the saved network model for inference to obtain a high-quality reconstruction result.

[0120] The following experiment uses the low signal-to-noise ratio data obtained by imaging the mitochondria labeled with mEmerald-Tomm20-C-10 in living U2OS cells under low light dose conditions to verify the effectiveness of the present invention. First, according to the real data collected, a series of {GT, i2} data pairs as shown in Figure 3 are generated, and i2 is sent into Figure 4 the network structure shown, and is trained under the supervision of GT to obtain appropriate network parameters. Then, the real low signal-to-noise ratio data of mitochondria collected is put into the trained network for reconstruction.

[0121] The comparison method selected for the experiment is the three-dimensional residual attention network (RCAN) commonly used in fluorescence microscopic image reconstruction, and RCAN is also trained using simulation data. In addition, to illustrate the strong generalization ability of this method, only 1 / 10 of the dataset of the RCAN method is used for training in this experiment. The experimental environment is: Pytorch 2.5.1 framework, using Python 3.9 as the programming language, and executed in the Windows 10 operating system; the running environment for the training and testing process is: 32GB of memory, Intel(R) Core(TM) i9-10900K, 3.70GHz CPU, and 10GB video memory of Nvidia GeForce RTX 3080.

[0122] The simulation data generation process proposed by the present invention greatly reduces the difficulty of data acquisition in the process of fluorescence microscopic image reconstruction. The proposed network structure has excellent generalization ability and can simply and effectively achieve the reconstruction of low signal-to-noise ratio data. As Figure 5 shown, it can be seen that compared with the low signal-to-noise ratio mitochondrial data collected, the reconstruction result of the present invention can effectively remove noise and effectively restore the details of mitochondria; the simulation data generation method proposed by the present invention can effectively promote the network to restore real biological samples, and both RCAN and the method of the present invention have obtained an improvement in image reconstruction quality based on the simulation data. In addition, compared with RCAN, the network structure proposed by the present invention can better maintain the mitochondrial structure and obtain clearer images in both the axial and transverse directions, proving the reliability of its reconstruction, as Figure 5 shown.

[0123] The above description of the embodiments is for those of ordinary skill in the art in this technical field to understand and apply the present invention. It is obvious that those skilled in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative efforts. Therefore, the present invention is not limited to the above embodiments, and all improvements and modifications made by those skilled in the art according to the disclosure of the present invention should be within the protection scope of the present invention.

Claims

1. A method for reconstructing low-quality fluorescence microscopy images based on simulation data and a learnable descent algorithm, the steps of which are as follows: 1) Acquisition of low-dose three-dimensional fluorescence images: The biological sample labeled with specific fluorescence is imaged by a microscopy imaging system. Under the condition of low-light-dose imaging, the multi-focal plane sequence is collected by driving the objective lens, and the obtained two-dimensional image sequence is stacked and reconstructed along the axial dimension to form an original three-dimensional fluorescence image; 2) Calculation of the point spread function and isotropic processing: According to the core parameters such as the numerical aperture of the microscopy imaging system, the magnification of the objective lens, and the refractive index of the imaging medium, the three-dimensional point spread function PSF is obtained by wavefront propagation theory calculation or fluorescence microsphere calibration experiment. The axial sampling interval is adjusted by an interpolation algorithm to ensure that the lateral and axial pixel sizes reach an isotropic resolution of 1:1; 3) Construction of simulation data: A three-dimensional zero matrix is created as the basic space, and three-dimensional geometric structures with dynamic size ranges are randomly generated within the limited spatial domain. The intensity values of each structure follow a uniform distribution, and a uniform background field is superimposed to construct the original simulation data; 4) Simulation of biological imaging characteristics: The original simulation data is spatially convolved with a three-dimensional Gaussian kernel to eliminate the sharp edges of the artificially generated structures; then axial downsampling is performed to make the anisotropy ratio of the data volume consistent with that of the real microscopy image, and noise-free reference data is output; 5) Optical degradation reconstruction: The three-dimensional point spread function PSF in 2) and the noise-free reference data are used to simulate the optical diffraction effect through three-dimensional convolution operation to generate blurred intermediate data; the blurred data is downsampled axially in a matching manner to obtain dimension-reduced blurred data that conforms to the resolution characteristics of the real imaging system; 6) Multi-modal noise injection: First, Poisson noise is generated according to the signal intensity of the dimension-reduced blurred data to simulate photon counting noise; then Gaussian white noise is superimposed to characterize the readout noise of the microscopy imaging system, and finally, degraded simulation data with a signal-to-noise ratio equivalent to the experimental data is synthesized; 7) Construction of a large-scale dataset: Through parameter space traversal, steps 3)-6) are cyclically executed to generate a large number of data pairs, that is, matching reference data and degraded simulation data, ensuring the balance of data distribution, and dividing the data pairs into a validation set and a training set; 8) Construct a deep learning network based on a learnable descent algorithm. Use the simulated degraded data in the training set data pair as the input of the network, and the corresponding reference data as the label of the network output. In the network architecture, first, a 3D convolutional layer with a smooth activation function is used to extract the key features in the input data, and after norm calculation, continue to perform smoothing processing to obtain a feature map and use it as a regular term function. In the iterative algorithm, the regular term and the gradient calculation of the fidelity term with a learnable gradient operator are used to solve the iterative result, and the network is trained by the composite loss function with the iterative result and the label, and the network performance is tested with the validation set; 9) Input the three-dimensional fluorescence image of the biological sample collected in 1) into the trained deep learning network for inference, so as to output a high-quality reconstructed image.

2. The low-quality fluorescence microscopic image reconstruction method according to claim 1, wherein: The imaging condition of the low-dose three-dimensional fluorescence image in step 1) is low excitation light intensity or short exposure time, and the collected two-dimensional image contains a large amount of noise and diffraction blur; The point spread function is a three-dimensional matrix structure with a Gaussian distribution.

3. The low-quality fluorescence microscopic image reconstruction method according to claim 1, wherein: The processing procedure expression in step 4) is as follows: GT = [Gau(S,σ1)]↓ t ; Where: GT is the reference data, S is the simulation data, Gau(S,σ1) represents performing three-dimensional Gaussian smoothing with a variance of σ1 on the simulation data S, and [ ]↓ t represents downsampling the target axis at a magnification of t; The processing procedure expression in step 5) is as follows: where: i1 is the downsampled blurred data, and S is the simulation data, denotes the convolution operator, h is the point spread function, and [ ]↓ t denotes downsampling of the target axis at a magnification of t. The processing procedure expression in step 6) is as follows: i2 = P(i1) + n; Where: i1 is the downsampled blurred data, i2 is the simulated degraded data, P( ) represents the Poisson random process introducing photon noise during the imaging process, and n represents the Gaussian random noise introduced by the detection device during the imaging process.

4. The low-quality fluorescence microscopic image reconstruction method according to claim 1 or 2 or 3, characterized in that: The simulated data, downsampled blurred data, simulated degraded data, and reference data are all three-dimensional volume data, and the ratio of the lateral pixel size to the axial pixel size of the downsampled blurred data, simulated degraded data, and reference data is consistent with the corresponding ratio of the three-dimensional fluorescence microscopy image.

5. The low-quality fluorescence microscopic image reconstruction method according to claim 4, wherein: The composite loss function includes a weighted combination of the mean square error and the structural similarity term: L = MSE(x k , y) + ω × [1 - SSIM(x k , y)]。 6. The method for reconstructing a low-quality fluorescence microscopic image according to claim 4, wherein: The regularization term function is implemented by a convolutional neural network, which includes: a feature extraction layer: a three-dimensional convolutional layer, a non-linear activation layer using a smooth activation function, and a feature normalization layer for L2 norm calculation, that is, the features of the image are extracted by the convolutional neural network, and after a series of smoothing and normalization processes, a piecewise regularization term function limited by a constant threshold is obtained.

7. The method for reconstructing a low-quality fluorescence microscopic image according to claim 6, wherein: For the smooth activation function, its activation function adopts a smooth correction unit that remains second-order differentiable within a preset threshold range: That is 8. The method for reconstructing a low-quality fluorescence microscopic image according to claim 4, characterized in that: The data fidelity term is a learnable gradient operator, whose parameter matrix inherits the characteristics of the point spread function of the optical system and is dynamically updated by gradient descent during the training process; The gradient calculation expression of the learnable gradient operator satisfies: Where A is the learnable parameter matrix, which is initialized to maintain a preset proportional relationship with the PSF.

9. The method for reconstructing a low-quality fluorescence microscopic image according to claim 7, wherein: In each iteration of the iterative algorithm stage, the following operations are performed. Taking the k-th iteration as an example: First, calculate the gradient of the fidelity term: where α k is the fidelity term step parameter. Based on this, two candidate solutions are obtained by taking the first-order approximation of it through the standard gradient descent path and the proximal gradient descent path respectively, which are v k+1 and u k+1 That is where τ k is the fusion step parameter; Compare the objective function values at two candidate solutions and select the relatively smaller one as the new iteration value x k+1 Thus, convergence is ensured. At the same time, during this process, the gradient of the entire objective function needs to be calculated and used as a condition for judgment to update the threshold parameter to gradually decrease it; When k reaches the maximum number of iterations K preset for the current iteration round or the overall threshold is less than the minimum tolerance, the iteration outputs x K .

Images