Fourier stack microscopy LED position error correction method and device

Abstract

This invention relates to the technical field of computational imaging, specifically a Fourier layered microscopy method for correcting LED position errors. The method involves acquiring low-resolution spectral intensity images and periodically smoothing and decomposing them. A convolutional neural network (U-Net) model is trained by inputting the spectral intensity images decomposed by the periodic smoothing method as a dataset. The pre-trained network extracts circular spectra, which are then used to search for optimal position parameters using a simulated annealing algorithm. The optimal solution for global misalignment parameters is obtained when the circular spectrum error is minimized. Finally, based on the AA algorithm and FPM reconstruction, the LED position misalignment parameters obtained in the simulated annealing algorithm are compensated into the AA reconstruction algorithm to generate a SAAS algorithm. The SAAS algorithm reconstructs the amplitude and phase information of the sample image with LED position misalignment, achieving high-precision light field recovery.

Description

Technical Field

[0001] This invention relates to the technical field of computational imaging, and in particular to a method and apparatus for correcting the position error of LEDs in a Fourier layered microscopy system. Background Technology

[0002] High resolution (HR), large field of view (FOV), and quantitative phase imaging have long been the goals pursued in the field of microscopy. However, these goals are difficult to achieve simultaneously in traditional microscopy imaging techniques. Fourier layered microscopy (FPM) is a new type of computational imaging technology that breaks through the diffraction limit of the objective lens by computational reconstruction, and at the same time achieves large field of view and high resolution quantitative phase imaging. It has wide applications in biomedicine such as cytology and digital pathology.

[0003] In the FPM system, different LEDs emit plane waves at different angles to illuminate the sample. The sample spectrum of each LR image corresponds to a sub-aperture. However, the spatial position of the LEDs and the position of the sub-apertures during the reconstruction process will inevitably deviate, which will lead to the generation of frequency domain information with incorrect position during reconstruction. This will continuously reduce the quality of the reconstructed image during iteration, resulting in wrinkles and artifacts.

[0004] LED position error correction using frequency domain feature information is a novel and mainstream method. This method uses frequency domain feature information instead of low-resolution intensity images for correction, avoiding the limitations caused by errors in low-resolution images. Separating the LED position search from the FPM reconstruction step improves the accuracy and efficiency of the correction. However, this method has high requirements for frequency domain feature extraction. The study found that truncating different regions of different sizes causes low-resolution images to produce cross-shaped artifacts of varying degrees in the frequency domain. These artifacts will seriously affect the extraction of frequency domain information and the accuracy of LED position correction, thus affecting the quality of the reconstructed image. Summary of the Invention

[0005] The primary objective of this invention is to provide a Fourier layered microscopy method for correcting LED position errors, aiming to address the problem that low-resolution images produce varying degrees of cross-shaped artifacts in the frequency domain, which affect the accuracy of LED position error correction.

[0006] To address the aforementioned technical problems, a Fourier-multiplexed microscopic LED position error correction method is provided, comprising the following steps:

[0007] S1. Acquire low-resolution spectral intensity images and decompose the spectral intensity images through periodic smoothing;

[0008] S2. Train the convolutional neural network U-Net model. The spectral intensity image decomposed by the periodic smoothing method is used as a dataset and input into the convolutional neural network U-Net model for training. By iteratively comparing the segmentation results of the model with the manually labeled gold standard, and optimizing the model parameters through the backpropagation mechanism, the best-performing model is obtained and used to extract the circular spectrum from the spectral intensity image.

[0009] S3. The pre-trained network extracts the circular spectrum and inputs it into the simulated annealing algorithm to search for the optimal position parameters. The simulated annealing algorithm changes the position of the circular spectrum image by setting the randomly updated illumination wave vector offset direction and step size during the forward propagation of the circular spectrum image, so as to obtain the optimal solution of global misalignment parameters when the error between the circular spectrum image and the one obtained in S2 is minimized.

[0010] S4. FPM reconstruction based on AA algorithm: Based on the LED position misalignment parameters obtained in the simulated annealing algorithm, the AA reconstruction algorithm is compensated to generate SAAS algorithm. The SAAS algorithm reconstructs the amplitude and phase information of the sample image with LED position misalignment to achieve high-precision light field recovery.

[0011] Furthermore, the U-Net convolutional neural network model uses binary cross-entropy as the loss function and mean absolute error as the performance evaluation index during the training phase to measure the deviation between the network output and the real annotation.

[0012] Furthermore, the structure of the convolutional neural network U-Net model is set as follows: the number of channels in the convolutional layers of the encoder part is 8, 16, 32 and 64 respectively; the bottleneck layer is set to 128 channels; the number of channels in the decoder part is 64, 32, 16 and 8 respectively; all convolution operations use 3×3 convolutional kernels, and feature map downsampling is performed through 2×2 max pooling operation.

[0013] Furthermore, the dataset of the spectral intensity images consists of 300 sample images, divided into a training set and a validation set in a 7:3 ratio.

[0014] Furthermore, the network input for the sample images is a single-channel grayscale image with a size of 256×256.

[0015] Furthermore, the expression for the periodically smoothed decomposition spectral intensity image is as follows:

[0016] ;

[0017] ;

[0018] ;

[0019] in, For the input image, It is a periodic component. For smoothing components; For a two-dimensional discrete Laplace operator, Boundary terms constructed for boundary discontinuities; , , , These represent the smoothing values ​​for the left, right, top, and bottom sides, respectively.

[0020] Furthermore, the aforementioned The boundary term constructed for boundary discontinuities is defined as:

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] in, The number of rows and columns of the image. Represents the top boundary row of the image and the lowest boundary line The pixel difference between them; Represents the leftmost column of the image And the rightmost column The jump difference between them This represents the jump difference before the update; Guarantee the construction The diagram shows a closed, compensated structure formed at the boundary, satisfying periodicity. This is for periodic compensation of horizontal jumps.

[0026] Furthermore, regarding the aforementioned Taking a two-dimensional Fourier transform of both sides of the formula yields:

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] in, , These are the frequency components in the horizontal and vertical directions, respectively; For the frequency domain representation of the smooth component, It provides high-precision periodic output results.

[0032] Furthermore, the optimal solution for the global misalignment parameters is obtained when the error between the circular spectrum and the circular spectrum obtained in S2 is minimized: the circular spectrum is continuously updated to approximate and converge to the circular spectrum extracted in step S2.

[0033] The second objective of this invention is to provide a Fourier stacked microscopic LED position error correction device, which aims to solve the problem of varying degrees of cross-shaped artifacts in low-resolution images in the frequency domain.

[0034] To address the aforementioned technical problems, a Fourier layered microscopy LED position error correction device is provided, applied to the aforementioned Fourier layered microscopy LED position error correction method. The device includes a camera, lenses, a Fourier plane, objective lenses, a sample, and an LED array. The camera is used to acquire low-resolution spectral intensity images. The lenses are spaced between the camera and the Fourier plane, the Fourier plane is spaced between the lenses and the objective lenses, and the objective lenses are spaced between the Fourier plane and the sample. The LED array faces directly below the sample, and by illuminating the sample with LEDs at different positions, the camera records low-resolution spectral intensity images corresponding to different sub-regions of the object's spectrum for each illumination angle.

[0035] Implementing the embodiments of the present invention will have the following beneficial effects:

[0036] 1. The Fourier layered microscopy LED position error correction method in this embodiment acquires low-resolution spectral intensity images and decomposes them using periodic smoothing. A convolutional neural network (U-Net) model is trained by inputting the spectral intensity images decomposed by the periodic smoothing method as the dataset. The model's segmentation results are iteratively compared with manually labeled gold standards, and the model parameters are optimized through backpropagation to obtain the best-performing model, which is used to extract circular spectra from the spectral intensity images. The pre-trained network extracts the circular spectra and inputs them into a simulated annealing algorithm to search for the optimal position parameters. The simulated annealing algorithm changes the position of the circular spectral image by setting randomly updated illumination wave vector offset direction and step size during the forward propagation of the circular spectral image, minimizing the error between the circular spectrum and the one obtained in S2, thus obtaining the optimal solution for global misalignment parameters. Finally, based on the AA algorithm's FPM reconstruction, the LED obtained from the simulated annealing algorithm is reconstructed. The positional misalignment parameters are compensated into the AA reconstruction algorithm to generate the SAAS algorithm. The SAAS algorithm reconstructs the amplitude and phase information of the sample image with LED positional misalignment, achieving high-precision light field recovery and overcoming the problem of low-resolution images producing cross-shaped artifacts of varying degrees in the frequency domain in the existing technology.

[0037] 2. The Fourier stacked microscopy LED position error correction device in this embodiment 2 uses a camera to acquire low-resolution spectral intensity images. The lens is spaced between the camera and the Fourier plane, the Fourier plane is spaced between the lens and the objective lens, and the objective lens is spaced between the Fourier plane and the sample. The LED array faces directly below the sample, and by illuminating the sample with LEDs at different positions, the camera records low-resolution spectral intensity images corresponding to different sub-regions of the object's spectrum for each illumination angle. This provides support for solving the problem of different degrees of cross-shaped artifacts generated in the frequency domain of low-resolution images. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 This is a flowchart illustrating the method described in Embodiment 1 of the present invention;

[0040] Figure 2 This is a flowchart of the method described in Embodiment 1 of the present invention;

[0041] Figure 3These are comparison diagrams showing the effects of artifact suppression by the method described in Embodiment 1 of the present invention; wherein, Figure (a) of SAAS is the artifact image before correction according to the present invention, Figure (b) of SAAS is the artifact suppression image after correction according to the present invention; Figure (c) of SAA is the artifact image before correction according to the prior art, and Figure (c) of SAA is the artifact suppression image after correction according to the prior art.

[0042] Figure 4 The image shows a comparison of the reconstruction results of the method described in Embodiment 1 of the present invention on blood smears with other algorithms; wherein, (a) is an LR image taken under the central LED, (a1) is a 512*512 selected reconstruction area map in the center of the field of view; (a2) is a magnified view of (a1); (b)-(f) are the intensity images and phase images reconstructed by the prior art method; (g) is the reconstruction result of the method of the present invention.

[0043] Figure 5 This is a physical diagram of the device described in Embodiment 2 of the present invention;

[0044] Figure 6 This is a schematic diagram of the device described in Embodiment 2 of the present invention;

[0045] Figure 7 This is a schematic diagram of low-resolution spectral intensity images corresponding to different illumination angles of the device described in Embodiment 2 of the present invention;

[0046] Among them: 100, Microscopic LED position error correction device; 110, Camera; 120, Lens; 130, Fourier plane; 140, Objective lens; 150, Sample; 160, LED array. Detailed Implementation

[0047] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0048] It should be noted that when a component is said to be "fixed to" another component, it can be directly attached to the other component or there may be an intervening component. When a component is said to be "connected to" another component, it can be directly connected to the other component or there may be an intervening component. The terms "vertical," "horizontal," "left," "right," and similar expressions used in this document are for illustrative purposes only.

[0049] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0050] Example 1

[0051] Please refer to Figures 1-4 Embodiment 1 of the present invention provides a method for correcting the position error of a Fourier-multiplexed microscopic LED, comprising the following steps:

[0052] S1. Acquire low-resolution spectral intensity images and decompose the spectral intensity images through periodic smoothing;

[0053] S2. Train the convolutional neural network U-Net model. The spectral intensity image decomposed by the periodic smoothing method is used as the dataset input into the convolutional neural network U-Net model for training. By iteratively comparing the model's segmentation results with the manually labeled gold standard, and optimizing the model parameters through the backpropagation mechanism, the best-performing model is obtained, which is used to extract circular spectra from the spectral intensity image.

[0054] S3. The pre-trained network extracts the circular spectrum and inputs it into the simulated annealing algorithm to search for the optimal position parameters. The simulated annealing algorithm changes the position of the circular spectrum image by setting the randomly updated illumination wave vector offset direction and step size during the forward propagation of the circular spectrum image, so as to obtain the optimal solution of global misalignment parameters when the error between the circular spectrum image and the one obtained in S2 is minimized.

[0055] S4. FPM Reconstruction Based on the AA Algorithm: Based on the LED position misalignment parameters obtained from the simulated annealing algorithm, these parameters are compensated into the AA reconstruction algorithm to generate the SAAS algorithm. The SAAS algorithm reconstructs the amplitude and phase information of the sample image with LED position misalignment, achieving high-precision light field restoration. In specific applications, the acquired LR image spectral intensity images are decomposed using Periodic Plus Smooth Image Decomposition to train the U-Net convolutional neural network model. The spectral intensity images decomposed by the periodic smoothing method in the previous step are used as the dataset, approximately 300 images, which are then input into the U-Net convolutional neural network for training. During training, the learning rate is set to 1×10⁻⁶. -4The batch size is 8, and the number of epochs is 500. The Adam optimizer is used to ensure a balance between convergence speed and stability. By iteratively comparing the model's segmentation results with the manually labeled gold standard and optimizing the model parameters using backpropagation, the best-performing model is obtained and used as the pre-trained model for the next step, used to extract circular spectra (e.g., ...) from the frequency domain intensity of LR images. Figure 3 (b) As shown, after extracting the circular spectrum using a pre-trained network, it is input into a simulated annealing algorithm to search for the optimal position parameters. This simulated annealing algorithm uses the circular spectrum obtained in S2 as physical prior knowledge. During the forward propagation of the LR image acquired by Fourier layered microscopy (FPM), the illumination wave vector offset direction and step size are set to change the position of the circular feature in the LR frequency domain. The circular spectrum is continuously updated to approximate and converge to the prior knowledge extracted in S2, obtaining the optimal solution for the global offset parameters. Based on the AA algorithm for FPM reconstruction, the steps of this invention adopt AA (Adaptive Algorithm) as the basic phase reconstruction strategy. The LED position misalignment parameters searched in the simulated annealing algorithm in S3 are used as physical prior knowledge to compensate for the AA reconstruction algorithm. The amplitude and phase information of the sample image with LED position misalignment (e.g.) are reconstructed. Figure 4 As shown, the reconstruction results of blood smear samples using six FPM reconstruction methods (AA algorithm, PC algorithm, AA-C algorithm, SC algorithm, SAA algorithm, and SAAS algorithm, the latter five of which have LED position correction function) are presented. All four algorithms recover LR image data under the condition of unknown LED position error. Figure 4 As seen in (b1)-(b3), the AA algorithm, lacking an LED position correction algorithm, exhibits numerous artifacts caused by positional errors in its reconstruction results. Compared to the PC algorithm (c1)-(c3) and the AA-C algorithm (d1)-(d3), the overall contrast of the AA algorithm is improved. However, due to their tendency to get trapped in local optima during positional error correction, their reconstruction results still cannot be correctly reconstructed, resulting in a large number of artifacts. The SC algorithm (e1)-(e3) shows a significant advantage over the previous methods. Thanks to the advantage of light intensity correction, its reconstructed intensity image has good contrast and significantly reduced artifacts. However, there are still many wrinkles in the intensity and phase image backgrounds, and blood cells in the phase image are difficult to distinguish, as shown in Figure (e3), indicating weak sample information. Similarly, the SAA algorithm (f1)-(f3) still reconstructs images with many artifacts, making it difficult to obtain satisfactory reconstruction results, as shown in Figure (f2). In contrast, the SAAS algorithm of this invention has significant advantages over other algorithms in its reconstruction results and can effectively suppress artifacts, such as... Figure 3 (b) Intensity images are free from artifact effects, such as Figure 4 (g1) presents blood cells with the clearest effect, and the phase image also shows blood cells with distinct details, such as... Figure 4 (g2) thus achieving high-precision light field recovery. This method introduces periodic smoothing decomposition in frequency domain information extraction, decomposing the original image into periodic and smooth components, which can effectively suppress frequency domain artifacts, improve the accuracy of LED global position parameter search, increase the algorithm convergence speed, and obtain higher quality reconstruction results. In addition, the method of this invention not only achieves effective correction of LED position errors, but also improves the robustness and adaptability of the FPM imaging system.

[0056] In one possible implementation, the U-Net convolutional neural network model uses binary cross-entropy as the loss function and mean absolute error (MAE) as the performance evaluation metric to measure the deviation between the network output and the ground truth annotations during the model training phase. Specifically, during model training, the entire network training process takes approximately 2 minutes. During the inference phase, the pre-trained model segments a single image in approximately 5–10 ms, which meets the requirements for efficient processing.

[0057] In one possible implementation, the U-Net convolutional neural network model is structured as follows: the number of channels in the convolutional layers of the encoder part is 8, 16, 32, and 64, respectively; the bottleneck layer is set to 128 channels; the number of channels in the decoder part is 64, 32, 16, and 8, respectively; all convolutional operations use 3×3 convolutional kernels, and feature map downsampling is achieved through 2×2 max pooling. In a specific application, the U-Net model structure is configured as follows: the number of channels in the convolutional layers of the encoder part is 8, 16, 32, and 64, respectively; the bottleneck layer is set to 128 channels; the number of channels in the decoder part is 64, 32, 16, and 8, respectively; all convolutional operations use 3×3 convolutional kernels, and feature map downsampling is achieved through 2×2 max pooling.

[0058] In one possible implementation, the dataset of spectral intensity images consists of 300 sample images, divided into training and validation sets in a 7:3 ratio. Specifically, in data processing, the 300 sample images are divided into training and validation sets in a 7:3 ratio to ensure the model has good generalization ability.

[0059] In one possible implementation, the network input for the sample images is a grayscale image with a size of 256×256. In specific applications, the network input is a single-channel grayscale image with a size of 256×256.

[0060] In one possible implementation, the expression for the periodically smoothed decomposition of the spectral intensity image is:

[0061] ;

[0062] ;

[0063] ;

[0064] in, For the input image, It is a periodic component. For smoothing components; For a two-dimensional discrete Laplace operator, Boundary terms constructed for boundary discontinuities; , , , These represent the smoothing values ​​for the left, right, top, and bottom sides, respectively. In practical applications, the acquired LR image spectral intensity image is subjected to periodic plus smooth image decomposition. The specific mathematical principle is as follows:

[0065] ;

[0066] in For the input image, It is a periodic component (without boundary discontinuity). It is a smoothed component (mean is 0). And... Satisfies the discrete Poisson equation:

[0067] ;

[0068] in The two-dimensional discrete Laplacian operator is defined as follows:

[0069] ;

[0070] , , , These represent the smoothing values ​​for the left, right, top, and bottom sides, respectively.

[0071] In one possible implementation, The boundary term constructed for boundary discontinuities is defined as:

[0072] ;

[0073] ;

[0074] ;

[0075] ;

[0076] in, The number of rows and columns of the image. Represents the top boundary row of the image and the lowest boundary line The pixel difference between them; Represents the leftmost column of the image And the rightmost column The jump difference between them This represents the jump difference before the update; Guarantee the construction The diagram shows a closed, compensated structure formed at the boundary, satisfying periodicity. This is for periodic compensation of horizontal jumps. In practical applications, The boundary term, which is constructed by boundary discontinuities, is defined as follows:

[0077] ;

[0078] ;

[0079] ;

[0080] ;

[0081] in, The number of rows and columns of the image. Represents the top boundary row of the image and the lowest boundary line The pixel difference between them; Represents the leftmost column of the image And the rightmost column The jump difference between them This represents the jump difference before the update; Guarantee the construction The graph forms a closed compensation structure at its boundary, satisfying periodicity (equal beginning and end). This is for periodic compensation of horizontal jumps.

[0082] In one possible implementation, for Taking a two-dimensional Fourier transform of both sides of the formula yields:

[0083] ;

[0084] ;

[0085] ;

[0086] ;

[0087] in, , These are the frequency components in the horizontal and vertical directions, respectively; For the frequency domain representation of the smooth component, This provides high-precision, periodic output results. In practical applications, the formula... Taking a two-dimensional Fourier transform on both sides, we get:

[0088] ;

[0089] The frequency domain properties of the discrete Laplace operator can be utilized:

[0090] ;

[0091] , These are the frequency components in the horizontal and vertical directions, respectively; This is the frequency domain representation of the smooth component. Substituting the above equation into the formula... From:

[0092] ;

[0093] And the formula The frequency domain expression can be transformed into:

[0094] ;

[0095] Will By substituting the values, we can obtain high-precision periodic results. .

[0096] In one possible implementation, the optimal solution for the global offset parameters is obtained when the error between the circular spectrum and the circular spectrum obtained in S2 is minimized: the circular spectrum is continuously updated to approximate and converge to the circular spectrum extracted in step S2. Specifically, in the simulated annealing algorithm, the circular spectrum obtained in S2 is used to set a randomly updated illumination wave vector offset direction and step size during the forward propagation process of acquiring the LR image in Fourier layered microscopy (FPM), changing the position of the circular spectrum in the LR frequency domain. This circular spectrum is continuously updated to approximate and converge to the circular spectrum obtained in S2, thereby obtaining the optimal solution for the global offset parameters.

[0097] Example 2

[0098] This embodiment protects a different subject matter compared to Embodiment 1, specifically:

[0099] Please refer to Figures 5-7 Embodiment 2 of the present invention provides a Fourier layered microscopy LED position error correction device, applied to the aforementioned Fourier layered microscopy LED position error correction method. It includes a camera, lenses, a Fourier plane, objective lenses, a sample, and an LED array. The camera is used to acquire low-resolution spectral intensity images. Lenses are spaced between the camera and the Fourier plane, the Fourier plane is spaced between the lenses and the objective lenses, and the objective lenses are spaced between the Fourier plane and the sample. The LED array faces directly below the sample, and by illuminating the sample with LEDs at different positions, the camera records low-resolution spectral intensity images corresponding to different sub-regions of the object's spectrum at each illumination angle. In specific applications, the Fourier layered microscopy (FPM) process first illuminates the sample by illuminating LEDs at different positions using the LED array. The changing position angles of the LEDs move frequency information originally outside the objective lens cutoff frequency into the objective lens's passband, meaning each illumination angle corresponds to a different sub-region of the object's spectrum. After low-pass filtering by the limited aperture of the microscope objective lens, the camera records a low-resolution spectral intensity image. Then, the low-resolution images from all angles are sequentially stitched together using a phase retrieval algorithm (e.g., ...). Figure 6 (b) shows the iterative reconstruction. Figure 7 This is a schematic diagram of the frequency domain intensity characteristics of LR images corresponding to different lighting angles. (a1) represents the vertical lighting mode of the center lamp, (a2) represents the tilted angle lighting mode, (b1-b2) represents the bright field low-resolution blood smear sample images under different lighting modes, and (c1-c2) are the frequency domain intensity images after Fourier transform of the images within the red boxes in (b1-b2). The circular spectral features in the bright field low-resolution image spectrum are used to determine the LED position misalignment parameters.

[0100] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for correcting the position error of a Fourier-multiplexed microscopic LED, characterized in that, Including the following steps: S1. Acquire low-resolution spectral intensity images and decompose the spectral intensity images through periodic smoothing; S2. Train the convolutional neural network U-Net model. The spectral intensity image decomposed by the periodic smoothing method is used as a dataset and input into the convolutional neural network U-Net model for training. By iteratively comparing the segmentation results of the model with the manually labeled gold standard, and optimizing the model parameters through the backpropagation mechanism, the best-performing model is obtained and used to extract the circular spectrum from the spectral intensity image. S3. The pre-trained network extracts the circular spectrum and inputs it into the simulated annealing algorithm to search for the optimal position parameters. The simulated annealing algorithm changes the position of the circular spectrum image by setting the randomly updated illumination wave vector offset direction and step size during the forward propagation of the circular spectrum image, so as to obtain the optimal solution of global misalignment parameters when the error between the circular spectrum image and the one obtained in S2 is minimized. S4. FPM reconstruction based on AA algorithm: Based on the LED position misalignment parameters obtained in the simulated annealing algorithm, the AA reconstruction algorithm is compensated to generate SAAS algorithm. The SAAS algorithm reconstructs the amplitude and phase information of the sample image with LED position misalignment to achieve high-precision light field recovery.

2. The Fourier layered microscopic LED position error correction method according to claim 1, characterized in that, The U-Net convolutional neural network model uses binary cross-entropy as the loss function and mean absolute error as the performance evaluation index during the training phase to measure the deviation between the network output and the real annotation.

3. The Fourier layered microscopic LED position error correction method according to claim 2, characterized in that, The structure of the U-Net convolutional neural network model is set as follows: the number of channels in the convolutional layers of the encoder part is 8, 16, 32 and 64 respectively; the bottleneck layer is set to 128 channels; the number of channels in the decoder part is 64, 32, 16 and 8 respectively; all convolution operations use 3×3 convolution kernels, and feature map downsampling is performed through 2×2 max pooling operation.

4. The Fourier layered microscopic LED position error correction method according to claim 3, characterized in that, The dataset of the spectral intensity images consists of 300 sample images, divided into a training set and a validation set in a 7:3 ratio.

5. The Fourier layered microscopic LED position error correction method according to claim 3, characterized in that, The network inputs for the sample images are all grayscale images with a size of 256×256.

6. The Fourier layered microscopic LED position error correction method according to claim 1, characterized in that, The expression for the periodically smoothed decomposition spectral intensity image is: ； ； ； in, For the input image, It is a periodic component. For smoothing components; For a two-dimensional discrete Laplace operator, Boundary terms constructed for boundary discontinuities; , , , These represent the smoothing values ​​for the left, right, top, and bottom sides, respectively.

7. The Fourier layered microscopic LED position error correction method according to claim 6, characterized in that, The The boundary term constructed for boundary discontinuities is defined as: ； ； ； ； in, The number of rows and columns of the image. Represents the top boundary row of the image and the lowest boundary line The pixel difference between them; Represents the leftmost column of the image And the rightmost column The jump difference between them This represents the jump difference before the update; Guarantee the construction The diagram shows a closed, compensated structure formed at the boundary, satisfying periodicity. This is for periodic compensation of horizontal jumps.

8. The Fourier layered microscopic LED position error correction method according to claim 6, characterized in that, Regarding the Taking a two-dimensional Fourier transform of both sides of the formula yields: ； ； ； ； in, , These are the frequency components in the horizontal and vertical directions, respectively; For the frequency domain representation of the smooth component, It provides high-precision periodic output results.

9. The Fourier layered microscopic LED position error correction method according to claim 1, characterized in that, The optimal solution for global misalignment parameters is obtained when the error between the circular spectrum and the circular spectrum obtained in step S2 is minimized: the circular spectrum is continuously updated to approximate and converge to the circular spectrum extracted in step S2.

10. A Fourier layered microscopy LED position error correction device, applied to the Fourier layered microscopy LED position error correction method as described in any one of claims 1-9, characterized in that, The system includes a camera, lenses, a Fourier plane, objective lenses, a sample, and an LED array. The camera is used to acquire low-resolution spectral intensity images. The lenses are spaced between the camera and the Fourier plane. The Fourier plane is spaced between the lenses and the objective lenses. The objective lenses are spaced between the Fourier plane and the sample. The LED array faces directly below the sample and illuminates the sample by lighting LEDs at different positions, so that the camera records low-resolution spectral intensity images corresponding to different sub-regions of the object's spectrum for each illumination angle.

Images