Medical image reconstruction system based on joint optimization

Abstract

The invention relates to the technical field of medical image reconstruction, and discloses a medical image reconstruction system based on joint optimization, which comprises a data acquisition module, a preprocessing module, a joint optimization reconstruction module, a post-processing module and a data storage and management module. According to the medical image reconstruction system based on joint optimization, various optimization technologies and algorithms are combined through the medical image reconstruction system based on joint optimization, the complex medical image data can be processed more flexibly through joint optimization of multiple parameters and target functions, and through the optimization algorithm and the parallel processing technology, the medical image reconstruction efficiency is improved. According to the method, the image reconstruction precision and detail expressive force can be remarkably improved while the high processing speed is kept, meanwhile, the higher intelligent and automatic level is achieved, parameters can be automatically adjusted, the reconstruction process can be optimized, manual intervention is reduced, and the adaptability and flexibility of the system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of medical image reconstruction, and particularly to a medical image reconstruction system based on joint optimization. Background Art

[0002] Medical images refer to the visual representations of the internal structures of the human body obtained through medical imaging techniques. These images are commonly used in multiple fields such as clinical diagnosis, treatment planning, teaching, and scientific research. Medical imaging techniques include, but are not limited to, X-rays, computed tomography (CT), magnetic resonance imaging (MRI), ultrasound imaging, positron emission tomography (PET), etc.

[0003] A medical image reconstruction system provides doctors with more accurate and intuitive medical image information. Through the reconstructed high-quality images, doctors can more clearly observe the tissue structures and lesion conditions within the patient's body, thereby making more accurate diagnoses. This has important value in the diagnosis of various diseases such as tumors, cardiovascular diseases, and neurological diseases.

[0004] Currently, traditional medical image reconstruction systems usually rely on fixed mathematical models and algorithms, such as filtered back projection. These methods are relatively mature theoretically, but may be difficult to handle complex and variable medical image data. Moreover, traditional medical image reconstruction systems may be relatively fast in processing speed, but their accuracy may be limited, especially when facing interference factors such as noise and artifacts. Additionally, they require a large amount of manual operations and parameter adjustments, increasing the burden on operators and the risk of errors. Summary of the Invention

[0005] In view of the problems of the above-mentioned existing traditional medical image reconstruction systems, which usually rely on fixed mathematical models and algorithms, such as filtered back projection, these methods are relatively mature theoretically, but may be difficult to handle complex and variable medical image data. Moreover, traditional medical image reconstruction systems may be relatively fast in processing speed, but their accuracy may be limited, especially when facing interference factors such as noise and artifacts. Additionally, they require a large amount of manual operations and parameter adjustments, increasing the burden on operators and the risk of errors, the present invention is proposed.

[0006] Therefore, the object of the present invention is to provide a medical image reconstruction system based on joint optimization, and its purpose is as follows: by combining multiple optimization techniques and algorithms, these methods can more flexibly process complex medical image data through jointly optimizing multiple parameters and objective functions. Moreover, through optimization algorithms and parallel processing techniques, while maintaining a relatively high processing speed, the accuracy and detail expressiveness of image reconstruction can be significantly improved. At the same time, it has a higher level of intelligence and automation, can automatically adjust parameters and optimize the reconstruction process, reduce manual intervention, and improve the adaptability and flexibility of the system.

[0007] To solve the above technical problems, the present invention provides the following technical solutions: A medical image reconstruction system based on joint optimization, including a data acquisition module, a preprocessing module, a joint optimization reconstruction module, a postprocessing module, and a data storage and management module;

[0008] The data acquisition module is responsible for obtaining raw medical image data from medical imaging devices (such as CT, MRI, ultrasound, etc.). The data acquisition module includes a signal amplification module, a filtering module, an A / D conversion module, and a phase-sensitive demodulation module;

[0009] The preprocessing module preprocesses the raw image data. The preprocessing module includes an image registration module, an image brightness unification module, an image denoising module, an image enhancement module, and an image segmentation module.

[0010] As a preferred solution of the medical image reconstruction system based on joint optimization of the present invention, wherein: The principle of the image registration module is to calculate the transformation relationship between two images so that they best match spatially or geometrically. This transformation can be translation, rotation, scaling, affine transformation, or even non-linear transformation;

[0011] The core steps of the feature-based image registration algorithm are: feature extraction, feature matching, model parameter estimation, image transformation, and gray-scale interpolation;

[0012] Affine transformation formula:

[0013]

[0014] Where (u, v) are the coordinates in the target image, (x, y) are the coordinates in the original image, and A, B, C, D, E, F are the six parameters of the affine transformation.

[0015] As a preferred solution of the medical image reconstruction system based on joint optimization of the present invention, wherein: The joint optimization reconstruction module includes a sampling matrix optimization module, a reconstruction algorithm optimization module, and a deep learning module.

[0016] As a preferred solution of the medical image reconstruction system based on joint optimization of the present invention, wherein: The sampling matrix optimization module includes an adaptive sampling strategy formulation sub-module, a sampling matrix generation and optimization sub-module, and a sampling matrix performance evaluation sub-module;

[0017] Sampling rate calculation formula:

[0018] The sampling rate is usually expressed as the ratio of the observed value to the original signal. For multi-viewpoint images, the average sampling rate can be expressed as the mean of the sum of the sampling rates of each image;

[0019]

[0020] Among them, T is the number of images, M_i is the number of observations of the i-th image, and N_i is the number of original signals of the i-th image.

[0021] Optimization objective function:

[0022] The optimization of the sampling matrix usually involves an objective function that measures the performance of the sampling matrix; the objective function may include an error term for the reconstructed image, a sparsity constraint for the sampling matrix, etc.;

[0023] A possible objective function is:

[0024]

[0025] Among them, Y is the observed data, X is the original signal, Φ is the sampling matrix, and λ is the regularization parameter used to balance the reconstruction error and the sparsity of the sampling matrix.

[0026] As a preferred solution of the medical image reconstruction system based on joint optimization according to the present invention, wherein: the reconstruction algorithm optimization module uses bilinear interpolation to consider the information of the four nearest neighbor pixels around the pixel to be reconstructed; it uses linear weights to perform weighted averaging on the pixel values of the nearest neighbor pixels to obtain the pixel value of the pixel to be reconstructed; the interpolation formula is as follows:

[0027] G(i + uj + v) = (1 - u)(1 - v)G(ij) + (1 - u)vG(ij + 1) + u(1 - v)G(i + 1j) + uvG(i + 1j + 1)

[0028] Among them, u and v are floating-point numbers in the interval [0, 1), G(i, j) is the pixel value of the low-resolution image at (i, j), and the bilinear interpolation method can effectively overcome the mosaic phenomenon of the nearest neighbor interpolation, but the high-resolution image obtained is still relatively blurred in details such as edges.

[0029] As a preferred solution of the medical image reconstruction system based on joint optimization according to the present invention, wherein: the deep learning module includes Stochastic Gradient Descent (SGD);

[0030] SGD is one of the most commonly used optimization algorithms in deep learning, and its formula is:

[0031]

[0032] Among them, x is the model parameter, η is the learning rate, and is the gradient of the loss function L with respect to x;

[0033] The AdaGrad algorithm adaptively adjusts the learning rate according to the magnitude of the gradient, and its formula is:

[0034]

[0035] y i = yx i + β

[0036] Wherein, gt,i is the gradient of parameter θi at the t-th step, Gt,ii is the cumulative sum of the squared gradients, and ∈ is a very small number to prevent the denominator from being zero.

[0037] As a preferred embodiment of the medical image reconstruction system based on joint optimization according to the present invention, wherein: the post-processing module includes an image segmentation module and a feature extraction module.

[0038] As a preferred embodiment of the medical image reconstruction system based on joint optimization according to the present invention, wherein: the data storage and management module includes a database management module, a file storage management module, a backup and recovery module, a data security control module, and a data indexing and retrieval module.

[0039] Advantages of the present invention: Through the medical image reconstruction system based on joint optimization, which combines multiple optimization techniques and algorithms, these methods can more flexibly process complex medical image data by jointly optimizing multiple parameters and objective functions. And through the optimization algorithm and parallel processing technology, while maintaining a high processing speed, it can significantly improve the accuracy and detail expressiveness of image reconstruction. At the same time, it has a higher level of intelligence and automation, can automatically adjust parameters and optimize the reconstruction process, reduce manual intervention, and improve the adaptability and flexibility of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings. Among them:

[0041] Figure 1 It is a schematic diagram of the overall framework of the medical image reconstruction system based on joint optimization of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0042] In order to make the above objects, features, and advantages of the present invention more obvious and understandable, the following will describe the specific embodiments of the present invention in detail with reference to the drawings of the specification.

[0043] In the following description, many specific details are set forth in order to fully understand the present invention. However, the present invention can also be implemented in other ways different from those described herein. Those skilled in the art can make similar promotions without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

[0044] Reference Figure 1 , which is an embodiment of the present invention, provides a medical image reconstruction system based on joint optimization. This medical image reconstruction system based on joint optimization includes a data acquisition module, a preprocessing module, a joint optimization reconstruction module, a postprocessing module, and a data storage and management module;

[0045] The data acquisition module is responsible for obtaining original medical image data from medical imaging devices (such as CT, MRI, ultrasound, etc.). The data acquisition module includes a signal amplification module, a filtering module, an A / D conversion module, and a phase-sensitive demodulation module. The data acquisition module needs to ensure the accuracy and integrity of the data, and also needs to consider factors such as the data format and resolution for subsequent processing;

[0046] The preprocessing module preprocesses the original image data, including denoising, filtering, enhancement, etc., to improve the quality and readability of the image. The preprocessing module includes an image registration module, an image brightness uniformity module (due to different imaging conditions, the brightness of medical images may vary. Brightness uniformity aims to adjust the brightness of the image to make it consistent among different regions or different images, which usually involves operations such as histogram equalization, contrast adjustment, or brightness correction of the image to improve the visual effect of the image and the accuracy of subsequent processing), an image denoising module (medical images may be interfered by noise during acquisition and transmission, which will affect the image quality and subsequent reconstruction results. Image denoising aims to remove this noise and improve the clarity of the image. Denoising methods include filtering, morphological processing, wavelet transform, etc., and these methods can be selected and applied according to the type and distribution characteristics of the noise), an image enhancement module (image enhancement aims to improve the contrast, sharpness, and clarity of the image for better observation and analysis of the detailed structure in the image, which can be achieved by adjusting the gray level of the image, applying a sharpening filter, performing edge detection, etc.), and an image segmentation module (separating the region of interest (ROI) in the image from the background or other tissues for subsequent analysis and processing).

[0047] The principle of the image registration module is to calculate the transformation relationship between two images so that they best match spatially or geometrically. This transformation can be translation, rotation, scaling, affine transformation, or even non-linear transformation;

[0048] Image registration is an important task in the preprocessing module. It aims to align multiple medical images from different times, different perspectives, or different imaging devices so that they can be spatially consistent. Usually, a reference image is selected for image registration, and then other images are aligned with the reference image, which can be achieved through rigid registration or non-rigid registration, depending on the degree of deformation between the images and the required accuracy.

[0049] The core steps of the feature-based image registration algorithm are: feature extraction, feature matching, model parameter estimation, image transformation, and gray interpolation.

[0050] Affine transformation formula:

[0051]

[0052] Among them, (u, v) are the coordinates in the target image, (x, y) are the coordinates in the original image, and A, B, C, D, E, F are the six parameters of the affine transformation.

[0053] 1. Selection and implementation of reconstruction algorithms

[0054] The joint optimization reconstruction module first needs to select a suitable 3D reconstruction algorithm according to the specific medical application scenario and imaging requirements. These algorithms may include but are not limited to surface rendering algorithms, volume rendering algorithms, iterative reconstruction algorithms, etc. After selecting the algorithm, the module needs to implement these algorithms and optimize them to improve the reconstruction speed and accuracy.

[0055] 2. Formulation and execution of joint optimization strategies

[0056] Joint optimization is the core feature of the joint optimization reconstruction module, which usually involves the balance and coordination of multiple optimization goals, such as image quality, reconstruction speed, computational resource consumption, etc. The module needs to formulate effective joint optimization strategies and achieve the balance of these optimization goals by adjusting algorithm parameters, introducing new optimization methods, or using parallel computing and other technical means. When executing the joint optimization strategy, the module also needs to monitor and adjust the optimization process to ensure the stability and reliability of the optimization results.

[0057] 3. Data fusion and calibration

[0058] During the joint optimization reconstruction process, it may be necessary to fuse image data from different imaging devices or different time points, which requires the module to have the ability of data fusion and be able to effectively integrate and calibrate data from different sources to improve the accuracy and consistency of the reconstruction results. Data fusion may involve preprocessing operations such as image registration, brightness uniformization, noise removal, etc., as well as subsequent image synthesis and calibration steps.

[0059] 4. Evaluation and feedback of reconstruction results

[0060] The joint optimization and reconstruction module also needs to evaluate the reconstruction results to ensure that they meet the requirements of clinical applications. This usually involves quantitative analysis of indicators such as the clarity, contrast, and resolution of the reconstructed images, as well as evaluating the accuracy and reliability of the reconstruction results through expert review or clinical verification. According to the evaluation results, the module may need to adjust the optimization strategy or algorithm parameters to further improve the reconstruction quality.

[0061] The joint optimization and reconstruction module includes a sampling matrix optimization module (the sampling matrix is a core concept in compressed sensing theory, which determines how to extract information from the original image. In medical image reconstruction, the optimization of the sampling matrix is crucial for improving the accuracy and speed of image reconstruction. By optimizing the sampling matrix, key information in the image can be captured more effectively while reducing the acquisition and processing of redundant data, thereby improving the performance of the entire reconstruction system), a reconstruction algorithm optimization module (combining multiple reconstruction algorithms such as iterative reconstruction and deep learning reconstruction, and achieving high-precision reconstruction of images by jointly optimizing multiple objective functions and parameters), and a deep learning module (the main function of the deep learning module in medical image reconstruction is to automatically extract image features, perform classification, segmentation, denoising, and optimize the reconstruction process. By training a deep learning model, key information in the image can be learned and used to guide the image reconstruction process, which can not only improve the resolution and clarity of the image, but also reduce noise and artifacts in the image, thereby improving the diagnostic accuracy of the image).

[0062] The sampling matrix optimization module includes an adaptive sampling strategy formulation sub-module (this sub-module is responsible for formulating an adaptive sampling strategy based on the characteristics of medical images and reconstruction requirements, which includes determining key parameters such as the sampling rate, the distribution of sampling points, and the number of rows and columns of the sampling matrix. The adaptive sampling strategy can dynamically adjust the distribution and number of sampling points according to the information density and importance of different image regions, thereby minimizing the amount of sampled data while ensuring image quality), a sampling matrix generation and optimization sub-module (based on the adaptive sampling strategy, this sub-module is responsible for generating an initial sampling matrix and adjusting and optimizing it through a series of optimization algorithms. The optimization algorithms may include optimization based on sparse representation, optimization based on iterative reconstruction, and optimization based on machine learning, etc. These algorithms aim to improve the efficiency and accuracy of the sampling matrix so that it can better capture key information in the image), and a sampling matrix performance evaluation sub-module (this sub-module is responsible for evaluating the performance of the optimized sampling matrix, which includes evaluating aspects such as the reconstruction accuracy, computational complexity, and performance in practical applications of the sampling matrix. Through performance evaluation, the optimization effect of the sampling matrix can be quantitatively analyzed and provide feedback and guidance for subsequent sampling strategy formulation and optimization);

[0063] Sampling rate calculation formula:

[0064] The sampling rate is usually expressed as the ratio of the observed values to the original signal. For multi-viewpoint images, the average sampling rate can be expressed as the mean of the sum of the sampling rates of each image;

[0065]

[0066] where T is the number of images, M i is the number of observed values of the i-th image, and N i is the number of original signals of the i-th image.

[0067] Optimization objective function:

[0068] The optimization of the sampling matrix usually involves an objective function that measures the performance of the sampling matrix; the objective function may include an error term for the reconstructed image, a sparsity constraint for the sampling matrix, etc.;

[0069] A possible objective function is:

[0070]

[0071] where Y is the observed data, X is the original signal, Φ is the sampling matrix, and λ is the regularization parameter used to balance the reconstruction error and the sparsity of the sampling matrix.

[0072] The reconstruction algorithm optimization module uses bilinear interpolation to consider the information of the four nearest neighbor pixels around the pixel to be reconstructed; it uses linear weights to perform weighted averaging on the pixel values of the nearest neighbor pixels to obtain the pixel value of the pixel to be reconstructed; the interpolation formula is as follows:

[0073] G(i + uj + v) = (1 - u)(1 - v)G(ij) + (1 - u)vG(ij + 1) + u(1 - v)G(i + 1j) + uvG(i + 1j + 1)

[0074] where u, v are floating-point numbers in the interval [0, 1), G(i, j) is the pixel value of the low-resolution image at (i, j), and the bilinear interpolation method can effectively overcome the mosaic phenomenon of the nearest neighbor interpolation, but the high-resolution image obtained is still relatively blurred in details such as edges.

[0075] The deep learning module includes Stochastic Gradient Descent (SGD);

[0076] SGD is one of the most commonly used optimization algorithms in deep learning, and its formula is:

[0077]

[0078] where x is the model parameter, η is the learning rate, and is the gradient of the loss function L with respect to x;

[0079] The AdaGrad algorithm adaptively adjusts the learning rate according to the magnitude of the gradient, and its formula is:

[0080]

[0081]

[0082] y i = yx i + β

[0083] where \(g_{t,i}\) is the gradient of parameter \(\theta_i\) at the \(t\)-th step, \(G_{t,ii}\) is the cumulative sum of the squared gradients, and \(\epsilon\) is a very small number to prevent the denominator from being zero.

[0084] The post-processing module includes an image segmentation module (which segments different tissues or organs in the image for more detailed analysis) and a feature extraction module (which extracts key features in the image, such as edges, textures, etc., to provide valuable information for subsequent diagnosis and treatment).

[0085] The data storage and management module includes a database management module (as the core storage component, the database management module is responsible for storing various structured or unstructured medical image data, which includes raw image data, preprocessed data, reconstructed images, and related metadata, such as patient information, examination time, image type, etc. The database management module provides basic operation functions such as query, update, deletion, and insertion of data, and supports complex data retrieval and analysis requirements. In addition, it is responsible for maintaining the integrity and consistency of the data to ensure the accuracy of the data during storage and access);

[0086] a file storage management module and backup (the file storage management module is specifically used to manage a large number of documents and files, such as design drawings, specification documents, test reports, and medical image files, etc. In a medical image reconstruction system, this module is responsible for storing and processing various image files, including DICOM format files, etc. The file storage management module provides functions such as file upload, download, version control, approval, and sharing. It ensures that all relevant files can be accessed and used as needed, and at the same time supports the secure storage and efficient access of files);

[0087] a backup and recovery module (the backup and recovery module is responsible for regularly backing up medical image data to prevent data loss or damage. When data problems occur, this module can quickly recover the data to ensure the continuous operation of the system and the integrity of the data. The backup and recovery module usually adopts various backup strategies, such as full backup, incremental backup, and differential backup, etc., to meet the data backup requirements in different scenarios. At the same time, it also provides flexible recovery options, allowing users to choose to recover the entire database or specific files as needed);

[0088] Data security control module (The data security control module is responsible for implementing strict data security control mechanisms, including functions such as access control, encryption, and auditing. These mechanisms are designed to prevent data leakage, tampering, and damage, ensuring the confidentiality, integrity, and availability of data. The data security control module uses technical means such as authentication, permission management, and data encryption to ensure that only authorized users can access sensitive data. At the same time, it also provides detailed audit logs to record the access and operation history of data for traceability and investigation in case of problems);

[0089] Data indexing and retrieval module (The data indexing and retrieval module is responsible for indexing medical image data and providing efficient retrieval functions, enabling users to quickly find the required image data, improving the efficiency and accuracy of data access. The data indexing and retrieval module usually adopts advanced indexing techniques and algorithms, such as inverted index, full-text index, etc., to support fast data retrieval. At the same time, it also provides flexible retrieval options, allowing users to retrieve according to conditions such as keywords, dates, patient information, etc.).

[0090] Through this jointly optimized medical image reconstruction system, which combines multiple optimization techniques and algorithms, these methods can more flexibly process complex medical image data by jointly optimizing multiple parameters and objective functions. And through optimization algorithms and parallel processing techniques, while maintaining a high processing speed, it can significantly improve the accuracy and detail representation of image reconstruction. At the same time, it has a higher level of intelligence and automation, can automatically adjust parameters and optimize the reconstruction process, reduce manual intervention, and improve the adaptability and flexibility of the system.

[0091] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not restrictive. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A medical image reconstruction system based on joint optimization, characterized in that: It includes data acquisition module, pre-processing module, joint optimization reconstruction module, post-processing module and data storage and management module; The data acquisition module is responsible for acquiring original medical image data from medical imaging equipment (such as CT, MRI, ultrasound, etc.), and the data acquisition module includes a signal amplification module, a filtering module, an A / D conversion module and a phase-sensitive demodulation module; The preprocessing module preprocesses the original image data, and the preprocessing module includes an image registration module, an image brightness unification module, an image denoising module, an image enhancement module and an image segmentation module.

2. The medical image reconstruction system based on joint optimization according to claim 1, characterized in that: The principle of the image registration module is to calculate the transformation relationship between two images so that they can best match each other spatially or geometrically. This transformation can be translation, rotation, scaling, affine transformation or even nonlinear transformation. The core steps of the feature-based image registration algorithm are: feature extraction, feature matching, model parameter estimation, image transformation and grayscale interpolation; Affine transformation formula: Among them, (u, v) is the coordinate in the target image, (x, y) is the coordinate in the original image, and A, B, C, D, E, and F are the six parameters of the affine transformation.

3. The medical image reconstruction system based on joint optimization according to claim 2, characterized in that: The joint optimization reconstruction module includes a sampling matrix optimization module, a reconstruction algorithm optimization module and a deep learning module.

4. The medical image reconstruction system based on joint optimization according to claim 3, characterized in that: The sampling matrix optimization module includes an adaptive sampling strategy formulation submodule, a sampling matrix generation and optimization submodule, and a sampling matrix performance evaluation submodule; Sampling rate calculation formula: The sampling rate is usually expressed as the ratio of the observed value to the original signal. For multi-view images, the average sampling rate can be expressed as the mean of the sum of the sampling rates of each image. Where T is the number of images, Mi is the number of observations of the i-th image, and Ni is the number of original signals of the i-th image. Optimization objective function: The optimization of the sampling matrix usually involves an objective function that measures the performance of the sampling matrix; the objective function may include the error term of the reconstructed image, the sparsity constraint of the sampling matrix, etc. A possible objective function is: Among them, Y is the observed data, X is the original signal, Φ is the sampling matrix, and λ is the regularization parameter used to balance the reconstruction error and the sparsity of the sampling matrix.

5. The medical image reconstruction system based on joint optimization according to claim 4, characterized in that: The reconstruction algorithm optimization module adopts bilinear interpolation to consider the information of the four nearest neighboring pixels around the pixel to be reconstructed; it uses linear weights to perform weighted average on the pixel values ​​of the nearest neighboring pixels to obtain the pixel value of the pixel to be reconstructed; the interpolation formula is as follows: G(i+uj+v)=(1-u)(1-v)G(ij)+(1-u)vG(ij+1)+u(1-v)G(i+1j)+uvG(i+1j+1)where u and v are floating point numbers in the interval [0,1), and G(i,j) is the pixel value of the low-resolution image at (i,j). The bilinear interpolation method can effectively overcome the mosaic phenomenon of the nearest neighbor interpolation, but the high-resolution image obtained is still relatively blurred in details such as edges.

6. The medical image reconstruction system based on joint optimization according to claim 5, characterized in that: The deep learning module includes stochastic gradient descent (SGD); SGD is one of the most commonly used optimization algorithms in deep learning. Its formula is: Where x is the model parameter, η is the learning rate, and θ is the gradient of the loss function L with respect to x; The AdaGrad algorithm adaptively adjusts the learning rate according to the size of the gradient. Its formula is: and i =yx i +β Among them, gt,i is the gradient of the parameter θi at the tth step, Gt,ii is the cumulative sum of the squared gradients, and ∈ is a very small number to prevent the denominator from being zero.

7. The medical image reconstruction system based on joint optimization according to claim 6, characterized in that: The post-processing module includes an image segmentation module and a feature extraction module.

8. The medical image reconstruction system based on joint optimization according to claim 7, characterized in that: The data storage and management module includes a database management module, a file storage management module, a backup and recovery module, a data security control module and a data index and retrieval module.

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