Nonlinear mapping parallel imaging reconstruction method and device based on manifold theory

Abstract

The present invention relates to the field of magnetic resonance imaging technology, and particularly relates to a non-linear mapping parallel imaging reconstruction method and device based on manifold theory. The method and device include: collecting multi-channel K-space data; setting the neighborhood size according to the collected K-space data, and adaptively optimizing and adjusting the key parameters of the high-dimensional mapping; taking the non-linearly correlated image information and noise components of the K-space data as features and inputting them, and mapping them to a higher-dimensional feature space through the manifold theory method to establish the topological relationship of the high-dimensional feature space; in the high-dimensional feature space, smoothing the differences between neighborhood points through manifold regression, establishing a non-linear model to fit and complement the downsampled K-space part of the signal and noise features, and restoring to the image space based on the reconstructed K-space data through inverse Fourier transform. The present invention improves the accuracy and anti-noise performance of the reconstructed image, expands the applicable range of the algorithm, and solves the problem of low signal-to-noise ratio in low-field magnetic resonance parallel imaging.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic resonance imaging, and in particular, to a non-linear mapping parallel imaging reconstruction method and device based on manifold theory. Background Art

[0002] Magnetic resonance imaging (MRI) has been widely used in medical diagnosis due to its advantages of high resolution for soft tissues and no radiation hazard. However, low-field magnetic resonance has the potential in clinical and scientific research applications due to its low cost and less shielding requirements, but its low signal-to-noise ratio and long scanning time have become the key factors restricting its application. In order to improve the practical applicability of low-field magnetic resonance, it is necessary to shorten the scanning time as much as possible while ensuring image quality. However, traditional parallel imaging methods are difficult to effectively complement undersampled data in low-field magnetic resonance, resulting in a decrease in image quality and an increase in artifacts, further affecting the accuracy of clinical diagnosis and research.

[0003] The main problem of existing parallel imaging techniques lies in the low signal-to-noise ratio of the reconstructed images. On the one hand, this comes from the reduction in the number of samples; on the other hand, it comes from the ill-conditioning of the system matrix, which causes the original noise in the auto-calibrating signal ACS part to be amplified during the inversion process, resulting in a decrease in the signal-to-noise ratio of the reconstructed image and an unsatisfactory quality. Among them, the most representative GRAPPA (Generalized Autocalibrating Partially Parallel Acquisitions) reconstruction algorithm reconstructs complete k-space data from incompletely sampled k-space data through a linear model. However, the GRAPPA algorithm has the following disadvantages: 1. Limited reconstruction accuracy: Since it only relies on linear terms for data fitting, it cannot fully capture the non-linear relationships in the data, resulting in a low accuracy of the reconstructed image. 2. Poor noise resistance performance: The linear model is sensitive to noise, and noise may significantly affect the quality of the reconstruction results. 3. Limited applicability: For complex MR data, the linear model is difficult to provide sufficient reconstruction quality, limiting its application in high-resolution and complex imaging tasks. 4. Insufficient data utilization: The high-order information in the already acquired k-space data is not fully utilized, resulting in information loss during the reconstruction process. Summary of the Invention

[0004] Embodiments of the present invention provide a non-linear mapping parallel imaging reconstruction method and device based on manifold theory to at least solve the technical problem of slow magnetic resonance imaging speed in the prior art.

[0005] According to an embodiment of the present invention, a non-linear mapping parallel imaging reconstruction method based on manifold theory is provided, including the following steps:

[0006] S101: Collect k-space data through multiple channels;

[0007] S102: Set the neighborhood size according to the actually acquired K-space data, and adaptively optimize and adjust the key parameters of the high-dimensional mapping;

[0008] S103: Take the image information and noise components that are non-linearly correlated in the K-space data as features and input them, and map them to a higher-dimensional feature space through the manifold method to establish the topological relationship of the high-dimensional feature space;

[0009] S104: In the high-dimensional feature space, smooth the differences between data points within the neighborhood and the differences between the central points of different neighborhoods through manifold regression, and finally establish a non-linear model with minimized noise features to fit and complete the downsampled part of the K-space. Based on the completed K-space data, perform inverse Fourier transform to restore it to the image space.

[0010] Furthermore, in step S101, use multiple receive coils to acquire K-space data in a low-field magnetic resonance system in parallel.

[0011] Furthermore, step S101 specifically includes:

[0012] Establish a K-space model under low-field magnetic resonance conditions, and determine the acquisition trajectory of the echo signal in the K-space model;

[0013] Determine the time series parameters of the low-field magnetic resonance scan according to the acquisition trajectory, and calculate the encoding gradient required to be applied by the magnetic resonance imaging system;

[0014] Acquire the K-space data of parallel imaging.

[0015] Furthermore, in step S102, determine the neighborhood size according to the actual data characteristics, and adaptively optimize and adjust the key parameters of the high-dimensional mapping. The key parameter is the kernel width.

[0016] Furthermore, step S102 specifically includes:

[0017] Analyze the K-space data, determine the size of each neighborhood divided from the data of the auto-calibration signal ACS part in the high-dimensional mapping, and generate a data analysis result;

[0018] Select an initial kernel width according to the data analysis result;

[0019] During the reconstruction process, dynamically adjust the kernel width through an error feedback mechanism for adaptive iterative optimization.

[0020] Furthermore, step S103 specifically includes:

[0021] Taking the non-linearly correlated image information and noise components of K-space data as feature inputs, mapping them to a higher-dimensional feature space through a manifold method to obtain the non-linear relationship features in the high-dimensional space; minimizing the difference between the actual sampling values at the missing positions of the auto-calibration signal ACS and the eigenvalues of the high-dimensional mapped features after linear combination to perform selection and manifold modeling on the non-linear relationship features;

[0022] Adjusting the high-dimensional feature space to balance the computational complexity and the performance of the manifold model;

[0023] Constructing the topological relationship of the high-dimensional feature space, deeply mining the complex associations between each neighborhood kernel in the manifold through the adjusted high-dimensional data, and combining multi-level manifold feature analysis to reveal the non-linear relationships between signals and noise, and different tissues.

[0024] Further, in step S104, smoothing the differences between data points within the neighborhood through kernel regression includes: using manifold regression to smooth the data within the neighborhood to make the signal intensity more consistent within the local area.

[0025] Further, after smoothing the differences between data within the neighborhood through manifold regression in step S104, it further includes: non-linearly enhancing the center points of different neighborhood kernels through a regression model to make the signal intensity more consistent within the global area.

[0026] Further, in step S104, processing the non-linear relationship between signals and noise in the high-dimensional feature space through manifold regression, and finally establishing a non-linear model with minimized noise features to fit and complement the downsampled part of the K-space. Restoring to the image space based on the complemented K-space data through inverse Fourier transform includes:

[0027] During the interpolation reconstruction process, first, use the manifold regression results adaptively iteratively optimized by the auto-calibration signal ACS data to interpolate the unsampled points in the K-space to complement the downsampled data; perform manifold regression fitting in the high-dimensional space to further reduce the interpolation error; then, combine the interpolated data with the existing sampled points to generate complete K-space data; finally, convert the reconstructed K-space data to the image space through IFT.

[0028] According to another embodiment of the present invention, there is provided a non-linear mapping parallel imaging reconstruction device based on manifold, including:

[0029] An acquisition unit for multi-channel acquisition of K-space data;

[0030] A parameter optimization unit for setting the neighborhood size according to the acquired K-space data and adaptively optimizing and adjusting the key parameters of the high-dimensional mapping;

[0031] A mapping unit that takes the non-linearly correlated image information and noise components of K-space data as features as input, maps them to a higher-dimensional feature space through a manifold method, and establishes the topological relationship of the higher-dimensional feature space;

[0032] A fitting and restoration unit for smoothing the differences between data points within the regression smoothing neighborhood and the differences between central points of different neighborhoods in the higher-dimensional feature space, and finally establishing a non-linear model with minimized noise features to fit and complement the downsampled K-space part, and restoring it to the image space based on the complemented K-space data through inverse Fourier transform.

[0033] A storage medium storing a program file capable of implementing the non-linear mapping parallel imaging reconstruction method based on manifold in any of the above items.

[0034] A processor for running a program, where the program, when running, executes the non-linear mapping parallel imaging reconstruction method based on manifold in any of the above items.

[0035] In the embodiments of the present invention, the non-linear mapping parallel imaging reconstruction method and device based on manifold map the data into a higher-dimensional space without explicitly calculating the high-dimensional features. This method makes the signal and noise more separated, and at the same time can capture complex imaging features, so as to more accurately complement the missing sampled K-space information, more accurately restore the details of the image. By adding interaction terms or non-linear features, the model can more carefully identify potential risk patterns, improve the accuracy and anti-noise performance of the reconstructed image, expand the applicable range of the algorithm, solve the problem of low signal-to-noise ratio in low-field magnetic resonance parallel imaging, and significantly improve the quality and diagnostic value of the reconstructed image. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0037] Figure 1 It is a flowchart of the non-linear mapping parallel imaging reconstruction method based on manifold of the present invention;

[0038] Figure 2 It is a schematic diagram of the K-space data acquisition method, showing the way of scanning data. One part acquires the data of the central part of the K-space, and the other part acquires the uniformly downsampled full K-space data, and the echo train calibration technology is used to correct the error between the two;

[0039] Figure 3 It is a flowchart of low-field parallel imaging based on manifold;

[0040] Figure 4This is a comparison diagram of the GRAPPA method and the nonlinear modeling method based on manifold in water film imaging, where: Figure 4 a in the figure is the reference image reconstructed using the SOS method based on the full acquisition data. Figure 4 b and Figure 4 The d in the figure are the reconstructed image and its residual image by GRAPPA method, Figure 4 c and Figure 4 The e in the figure are the reconstructed image and its residual image by the manifold nonlinear modeling method;

[0041] Figure 5 is the comparison result of the GRAPPA method and the nonlinear modeling method based on manifold in human brain imaging, where: Figure 5 a in the figure is the reference image reconstructed using the SOS method based on the full acquisition data. Figure 5 b and Figure 5 The c in the figure are the reconstructed image and its residual image by GRAPPA method, Figure 5 d and Figure 5 The e in the figure are the reconstructed image and its residual image by the manifold nonlinear modeling method;

[0042] Figure 6 It is a module diagram of the nonlinear mapping parallel imaging reconstruction device based on manifold in the present invention. DETAILED DESCRIPTION

[0043] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0044] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0045] Example 1

[0046] According to an embodiment of the present invention, a parallel imaging reconstruction method based on manifold nonlinear mapping is provided. Refer to Figure 1 , which includes the following steps:

[0047] S101: Collect K-space data through multiple channels;

[0048] S102: Set the neighborhood size according to the collected K-space data, and adaptively optimize and adjust the key parameters of the high-dimensional mapping;

[0049] S103: Take the image information and noise components that are nonlinearly related to the K-space data as features and input them, and map them to a higher-dimensional feature space through the manifold method to establish the topological relationship of the high-dimensional feature space;

[0050] S104: In the high-dimensional feature space, smooth the differences between data points within the neighborhood and the differences between the central points of different neighborhoods through manifold regression. Finally, establish a nonlinear model with minimized noise features to fit and complete the downsampled part of the K-space, and restore it to the image space based on the complementary K-space data through inverse Fourier transform.

[0051] In the parallel imaging reconstruction method based on manifold nonlinear mapping in the embodiment of the present invention, the data is mapped into a high-dimensional space without explicitly calculating high-dimensional features. This method makes the signal and noise more separated, and at the same time can capture complex imaging features, so that it can more accurately complete the missing sampled K-space information, more accurately restore the details of the image. By adding interaction terms or nonlinear features, the model can more carefully identify potential risk patterns, improve the accuracy and anti-noise performance of the reconstructed image, expand the applicable range of the algorithm, solve the problem of low signal-to-noise ratio in low-field magnetic resonance parallel imaging, and significantly improve the quality and diagnostic value of the reconstructed image.

[0052] Specifically, in order to solve the problem of slow magnetic resonance imaging speed, parallel imaging technology is a major breakthrough in magnetic resonance imaging technology. This method can accelerate the magnetic resonance imaging (MRI) scanning process by using multiple radio frequency coils to receive signals simultaneously. These coils cover different spatial regions and can capture more spatial information, thus reducing the required k-space (frequency domain space) sampling points. This method can significantly reduce the scanning time, improve the temporal resolution of the image, and improve the patient's comfort. However, reducing sampling will increase the complexity of image reconstruction, such as obvious aliasing artifacts, so effective reconstruction algorithms are needed to restore high-quality images.

[0053] In low-field magnetic resonance imaging, the signal-to-noise ratio (SNR) is relatively low, which further limits the scanning speed and image quality. In this case, the manifold method can separate signals and noise more effectively through projection operations in a high-dimensional space. Meanwhile, it can capture complex imaging features, thus more accurately restoring the details of the image, more accurately complementing the missing sampled K-space information, and significantly improving the quality and diagnostic value of the reconstructed image.

[0054] To address the above drawbacks, the present invention proposes a non-linear mapping parallel imaging reconstruction method based on manifold theory, which is applicable to low-field magnetic resonance image reconstruction and aims to solve the problems of low SNR and slow imaging speed in low fields. The present invention adopts multi-channel acquisition and non-linear modeling based on manifold theory to improve the clarity and contrast of images by more precisely complementing K-space data. Specifically, this method maps the data into a high-dimensional space without explicitly calculating high-dimensional features. This method separates signals and noise more effectively, captures complex imaging features, can more accurately complement the missing sampled K-space information, and more accurately restore the details of the image. By adding interaction terms or non-linear features, the model can more carefully identify potential risk patterns, improve the accuracy and anti-noise performance of the reconstructed image, expand the applicable range of the algorithm, solve the problem of low SNR in low-field magnetic resonance parallel imaging, and significantly improve the quality and diagnostic value of the reconstructed image.

[0055] The basic technical solution of this method is as follows:

[0056] Collect K-space data in a low-field magnetic resonance system. Use multiple receive coils to collect K-space data in parallel. The data collected by each coil is undersampled (i.e., there are data points that are not collected), but it is ensured that the central part of the K-space data in each channel is completely collected. These data are called autocalibration signals (lines). These autocalibration signal ACS lines provide complete K-space information for non-linear modeling.

[0057] Adaptive parameter optimization. In this process, adaptive optimization parameters (such as kernel width and neighborhood size) can be adjusted according to the actual data characteristics to adapt to different imaging conditions and noise levels, further enhancing the flexibility and applicability of the model.

[0058] Non-linear modeling based on manifold theory. Since the collected K-space autocalibration signal ACS partial data contains non-linearly related image and noise features, it is initially used as a feature and mapped to a higher dimension through the manifold method. By adjusting the mapped high-dimensional feature space, the noise is more separated, minimizing noise interference, and finally establishing the topological relationship of the high-dimensional feature space, which helps to more clearly extract the true structural features of the image.

[0059] Manifold regression and image reconstruction. In the high-dimensional feature space, manifold regression establishes a non-linear model with minimized noise features to fit and complete the downsampled K-space part by smoothing the differences between data points within the smooth neighborhood and the differences between the central points of different neighborhoods. Finally, based on the inverse Fourier transform (IFT) of the reconstructed K-space data, this information is restored to the image space to generate higher-quality images.

[0060] See Figure 2 , and the detailed description of the technical solution of the present invention is as follows:

[0061] 1. Collect K-space data in a low-field magnetic resonance system

[0062] The schematic diagram of the acquisition method of K-space data is as Figure 3 shown. In this sampling method, full sampling is strictly performed for the auto-calibration signal ACS part in accordance with the Nyquist sampling law, and downsampling is performed for the part outside the auto-calibration signal ACS, ensuring that while shortening the sampling time, low-resolution complete K-space information is provided for non-linear modeling. The specific steps are as follows:

[0063] Step 1: Establish a K-space model under low-field magnetic resonance conditions and determine the acquisition trajectory of the echo signal in the model.

[0064] Specifically, the acquisition trajectory of the echo signal is as follows: all echo signals are collected in parallel along one coordinate direction. Among them, the central region of K-space is fully sampled (the auto-calibration signal ACS part), strictly following the Nyquist sampling law to ensure that complete high-resolution data is obtained for reconstruction coefficient estimation, and at the same time providing an accurate benchmark for subsequent image reconstruction; the edge region of K-space is downsampled to reduce the amount of data acquisition and improve the acquisition speed.

[0065] Step 2: Determine the time series of ultra-low-field magnetic resonance scanning according to the acquisition trajectory and calculate the encoding gradient required by the magnetic resonance imaging system. The specific steps include: calculating the scanning time series parameters and encoding gradient of the fully sampled region (the auto-calibration signal ACS part) to ensure the integrity of data acquisition in the central region; calculating the scanning time series parameters and encoding gradient of the downsampled region to ensure the uniformity and efficiency of data acquisition in the edge region. In a low-field environment, the signal-to-noise ratio is relatively low, so it is necessary to specifically optimize the time series and encoding gradient to maximize the signal intensity and data acquisition efficiency. For example, the present invention adopts the FSE sequence with a fast acquisition speed.

[0066] Step 3: Acquire the K-space data of parallel imaging. Specifically, the three-dimensional multi-slice K-space data acquired in this embodiment includes fully sampled data in the central region of each slice and downsampled data in the edge region: Full sampling in the central region (the auto-calibration signal ACS part): The central part of the K-space is fully sampled according to the Nyquist sampling law to ensure the acquisition of complete high-resolution data. This is particularly important for low-field environments. Downsampling in the edge region: Uniform downsampling is performed in the edge part of the K-space to reduce the data acquisition time. First, dense phase-encoding acquisitions are performed on the adaptive calibration scan (the auto-calibration signal ACS) part to obtain complete central K-space data. Then, the phase-encoding interval is gradually increased to make the phase-encoding steps sparse and expand the range of phase-encoding, thereby acquiring a uniformly downsampled K-space data.

[0067] 2. Adaptive parameter optimization

[0068] The kernel width in the kernel method of manifold learning determines the projection effect of data blocks in the high-dimensional feature space and directly affects the separation accuracy of signals and noise. In a low signal-to-noise ratio environment, increasing the kernel width can reduce the noise impact, make similar signals more concentrated, and enhance signal consistency. In a high signal-to-noise ratio environment, moderately reducing the kernel width helps capture more subtle local features and details. The specific process is as follows:

[0069] Step 1: Data analysis. First, analyze the K-space data to determine the "kernel" size, that is, the size of each neighborhood divided from the data of the auto-calibration signal ACS part for high-dimensional mapping.

[0070] Step 2: Set the initial kernel width. Select the initial kernel width according to the data analysis results , which determines the initial dimension size of the high-dimensional mapping of the data.

[0071] Step 3: Adaptive iterative optimization. In each iteration, use the current estimate to calculate , and then calculate the approximate (that is, calculate the estimate of through empirical formula 2 based on the current value and determine its dimension size). Then, use the new estimate to calculate the next . This step updates the kernel width by the least squares method, and the specific formula is as follows:

[0072] [1]

[0073] Among them, A represents a matrix composed of the non-undersampled position points of the automatic calibration signal ACS. The size of matrix A is m×k, where m is the total number of "kernels" divided in the automatic calibration signal ACS data, and k is the number of neighborhood points in each "kernel". represents performing a high-dimensional mapping on A using the manifold method with a kernel width of ; represents the combination of the estimates of the linear representations of the high-dimensional mappings of each data at the non-undersampled positions of the automatic calibration signal ACS, with a dimension of , where is the dimension of the new feature space, which is usually much higher than k.

[0074]

[0075] Formula 2 is the empirical formula for performing high-dimensional mapping on each sampling point in A, where represents the K-space signal of the data at the partially missing positions of the automatic calibration signal ACS on the target coil ; represents the acquired undersampled signal, where is the coil index, and t and h respectively represent the offsets of the neighboring K-space data in the and directions. R represents the undersampling rate (ORF, sampling rate factor), that is, the undersampling factor. and respectively represent the coordinates along the frequency encoding and phase encoding directions. and are the basic sampling intervals in the K-space, which are respectively used to describe the distances between points in the frequency encoding and phase encoding directions. is the integer offset along the phase encoding direction, which determines the position of the target point. n represents the offset that is still n frequency encoding intervals different from the neighboring K-space data. The larger n is, the more non-linear relationships between higher-dimensional K-space data are extracted. Generally, for the conventional empirical formula 2 to reduce the computational amount, n is set to 3.

[0076] 3. Nonlinear Modeling Based on Manifold

[0077] All existing GRAPPA-derived algorithms are based on the linear model in formula [3]. Due to the low signal-to-noise ratio of low-field magnetic resonance, it is difficult to separate the non-linearly related signals and noise in the automatic calibration signal ACS data, resulting in model deviation.

[0078]

[0079]

[0080] Among them Indicates the K-space signal not acquired on the target coil The K-space signal not acquired on the target coil Indicates the undersampled signal that has been acquired, where is the coil index, and t and h respectively represent the offsets of the neighboring K-space data in the and directions. Indicates the combination coefficients of the linear model, which are used to linearly combine the neighboring sampled signals into the unsampled signal on the target coil. L represents the total number of coils, R represents the undersampling rate (ORF, sampling rate factor), that is, the undersampling factor. l traverses the indices of all coils. and respectively represent the coordinates along the frequency encoding and phase encoding directions. r is the integer offset along the phase encoding direction. Equation [3] only performs linear combination in one dimension, does not fully separate the image from the noise, and loses a lot of image information.

[0081] To solve the common non-linear and noise-like error problems in the GRAPPA reconstruction process, the present invention proposes an innovative method based on manifold theory, which improves the reconstruction accuracy by identifying and adjusting the non-linear relationships between image features. This method utilizes the statistical characteristics of the data and the trend distribution in the sample space to effectively suppress noise and artifacts, thereby achieving more accurate signal reconstruction.

[0082] Step 1: Feature selection and non-linear modeling. First, select and perform manifold theory modeling on the non-linear relationship features mapped to the high-dimensional space. For example, use a method (kernel method) in manifold theory to separate the non-linear relationship signals and noise through high-dimensional mapping to identify the error sources in the reconstruction process. A typical kernel (inhomogeneous polynomial kernel) has the following form:

[0083] [4]

[0084] Where, and are scalars, is the order of the polynomial (which is also the kernel width of the inhomogeneous polynomial kernel function), which helps to map the non-linear relationships in the data to the high-dimensional space so that they can be separated. Where represents the th and th "kernel" extracted from the ACS part of the data of the auto-calibration signals of all channels. .

[0085] The present invention maps the input space through non-linear mapping The data in (the auto - calibration signal ACS non - undersampled position data, i.e., the initial features) is mapped to a high - dimensional feature space (a high - dimensional feature that can separate signals and noise with non - linear relationships), and using Equation 4 for The linear combination after non - linear mapping to high - dimensions is expressed as Then:

[0086] [5]

[0087] Based on the least - squares method of Equation 5, the coefficients of each dimension from the high - dimensional mapping of the manifold model from the non - undersampled position data matrix A to the undersampled position data matrix B are calculated, so as to combine Equation [2] and [4] to obtain the parameters used in the manifold model. Specifically here, it refers to the and These two parameters.

[0088] Improper setting of the parameters may lead to the mapping dimension being very high or even infinite. Therefore, it is necessary to select high - dimensional features. In this example of the non - homogeneous polynomial kernel, it is found that retaining the dimensional features above the quadratic term is difficult to further reduce the error of the manifold model. Therefore, they are discarded.

[0089] Step 2: Adjustment of the feature space. Assume using a non - homogeneous polynomial kernel and = 1, = 1, = 2, then the non - linear mapping of the manifold Can be specifically expressed as:

[0090]

[0091] Adopting the non - linear mapping in the above form , helps to effectively process non - linearly inseparable data in the high - dimensional space. Among them, is The k elements included in "kernel". Specifically: This mapping form includes first - order and second - order terms to retain the basic information and non - linear features of the original data in the high - dimensional space, especially suitable for the need to observe the feature trend in manifold modeling. The first - order term retains the basic manifold trend of the data, and the second - order term captures the sum of squares and interaction terms of each feature, which enables the mapped feature space to reveal the non - linear manifold trend. The higher the mapping order, the more completely the non - linearly related information is separated, but at the same time, the calculation is more complex. Adjusting the appropriate feature space of the mapping is the key to this step. There are three terms in the quadratic term as shown in Equation [2]. To further reduce the computational complexity, only the first two terms of the quadratic term can be retained without affecting the performance of the manifold model.

[0092] Step 3: Establish the topological relationship of the high-dimensional feature space. When constructing the topological relationship of the high-dimensional feature space, the adjusted high-dimensional data is used to deeply explore its complex associations in manifold theory. This process combines multi-level manifold feature analysis to reveal the potential patterns of the image and the local structure of the data. Modeling the topological relationship of the high-dimensional feature space helps to capture the non-linear relationships between signals and noise, and different tissues. As shown in Equation [7], each neighborhood "kernel" divided in the automatic calibration signal ACS part data of multiple channels is mutually correlated. is the nth "kernel" drawn from the automatic calibration signal ACS part data of all channels, for the automatic calibration signal ACS part data divided by all channels except other than ), with respect to is the integer offset, which further affects . Equation 7 represents the relationship of mutual influence between all "kernels" of all channels. Among them, can be estimated by the convolution sum of the matrix composed of the remaining neighborhoods and the coefficient matrix . Finally, Equations [2], [4], [5], and [7] are combined to further fuse the relationships between different neighborhood "kernels" in the same channel, and the relationships between the data of different neighborhood "kernels" in different channels, further improving the accuracy of the manifold theory model.

[0093]

[0094] 4. Manifold Regression and Signal Reconstruction

[0095] Construct a manifold regression model to handle the non-linear relationship between signals and noise in the high-dimensional feature space. The specific steps are as follows:

[0096] Step 1: Smoothing processing. Use manifold regression to smooth the data within the neighborhood to make the signal intensity more consistent in the local area.

[0097] Step 2: Non-linear enhancement of the center point. Non-linearly enhance the center points of different "kernels" through the regression model to make the signal intensity more consistent in the global area.

[0098] Step 3: Interpolation and reconstruction. During the interpolation and reconstruction process, first, the manifold regression results adaptively iteratively optimized using the auto-calibration signal ACS data are used to interpolate the unsampled points in the K-space to complete the downsampled data; manifold regression fitting is performed in the high-dimensional space to further reduce the interpolation error; then, the interpolated data is combined with the existing sampled points to generate the complete K-space data; finally, the reconstructed K-space data is transformed to the image space through IFT.

[0099] The key points and the points to be protected in the present invention are:

[0100] The core innovation of the present invention lies in proposing a non-linear mapping parallel imaging reconstruction method based on manifold theory, which provides an effective technical solution for improving image quality and accelerating the scanning process in the face of problems such as low signal-to-noise ratio and slow imaging speed in low-field magnetic resonance imaging. The following are the key innovation points and the technical content to be protected in the present invention:

[0101] Non-linear mapping method based on manifold theory. By adopting the non-linear mapping technology in manifold theory, the K-space data is mapped to a high-dimensional space, so as to separate the non-linearly related image and noise features in the raw data collected by low-field magnetic resonance. This method can overcome the deficiencies of traditional linear methods under low signal-to-noise ratio and improve the accuracy of image reconstruction. The present invention takes the kernel method in manifold theory as an example, and the high-dimensional feature space mapping methods in manifold theory such as polynomial feature expansion and high-dimensional representation in deep learning are also applicable to the present invention.

[0102] Combination of multi-channel acquisition and manifold modeling. The present invention combines multi-channel parallel acquisition and non-linear modeling based on manifold theory. Signals are received simultaneously through multi-channel radio frequency coils to reduce the K-space sampling points, and at the same time, the under-sampled data is accurately completed through non-linear modeling. This technical solution significantly improves the image quality of low-field magnetic resonance imaging, especially in terms of the signal-to-noise ratio and detail performance of the reconstructed image.

[0103] Effective separation of signals and noise. Using the manifold method to perform high-dimensional mapping on the raw data collected by low-field magnetic resonance, the non-linearly related image and noise features are effectively separated into a linearly combinable form. By removing the "kernel" of the noise term, the adverse effects caused by the amplification of noise in traditional methods are avoided. By separating the noise features, the present invention can more accurately restore the image details and significantly improve the clarity and contrast of the image.

[0104] Precisely complete the undersampled K-space data. The present invention accurately calculates the coefficients of various high-dimensional image features through the manifold regression technique, and combines the data smoothing processing within the neighborhood and the non-linear enhancement of the central point data to more accurately restore the undersampled K-space data in low-field magnetic resonance imaging, reducing the image artifacts caused by data loss in traditional methods. This technical solution effectively improves the reconstruction accuracy of low-field magnetic resonance imaging.

[0105] Enhanced anti-noise performance and adaptability. The present invention completes the downsampled K-space data by introducing the manifold reconstruction method, enabling the model to maintain strong anti-noise ability when dealing with noise in low-field magnetic resonance imaging. This innovation significantly broadens the application scope of this method in various magnetic resonance imaging tasks and is also applicable in complex high-resolution imaging tasks.

[0106] Kernel function selection and optimization iteration process. In the kernel method of the present invention, the selection of the kernel function is crucial for the performance of high-dimensional mapping. To ensure the best imaging quality and reconstruction effect, the present invention allows the selection of various kernel functions, including non-uniform polynomial kernels, Gaussian kernels (RBF kernels), and hybrid kernel functions, etc. By evaluating the performance of different kernel functions and combining the requirements of specific tasks, the best kernel function is iteratively selected automatically or through optimization algorithms (such as the alternating least squares method, gradient descent method, etc.), and its relevant parameters are tuned.

[0107] Sequence scanning model. The sequence used in the present invention has a fast scanning speed, and at the same time can collect fully sampled data in the central part and uniformly downsampled K-space data. The present invention scans in two times, once scanning the central part data and once scanning the downsampled data, and finally calibrates through the echo train. Including but not limited to fast spin echo (FSE), gradient echo (GRE), balanced steady-state free precession (bSSFP), etc., such MRI sequences are all applicable to the present invention.

[0108] Compared with the traditional GRAPPA method, the present invention significantly improves the image quality, data completion ability, and computational efficiency by introducing the manifold non-linear modeling method and combining the application environment of low-field magnetic resonance, enhances the adaptability to complex imaging environments, and improves the signal-to-noise ratio and image stability, having important application value and promotion prospects. Specifically as follows:

[0109] (1) Stronger non-linear modeling ability. GRAPPA relies on a linear model and cannot effectively capture the non-linear relationships in the data. In contrast, the present invention adopts non-linear manifold mapping, which can more accurately capture complex imaging features and improve the image reconstruction accuracy.

[0110] (2) Better anti-noise performance. GRAPPA is prone to amplifying noise in low signal-to-noise ratio data, resulting in a decline in image quality. Through the manifold method, the present invention can effectively separate signals and noise, improve the anti-noise ability, thereby reducing artifacts and enhancing image clarity.

[0111] (3) More accurate K-space data completion. GRAPPA uses linear interpolation to fill in missing K-space data, with limited accuracy. The present invention can more accurately complete the missing K-space data through high-dimensional non-linear mapping, retaining more imaging details.

[0112] (4) Higher adaptability. The applicability of GRAPPA is limited, especially when dealing with complex MR data. The present invention supports multiple kernel functions (such as Gaussian kernel, non-uniform polynomial kernel, etc.), and can be flexibly adjusted according to the characteristics of the data to adapt to different imaging tasks.

[0113] (5) Higher computational efficiency. Although non-linear methods have a higher computational complexity, the present invention can maintain a high computational efficiency while maintaining image quality through manifold mapping and high-dimensional modeling, especially performing better on large datasets.

[0114] (6) Optimized data utilization and information recovery. GRAPPA does not fully utilize the high-order information of K-space data, resulting in information loss. The present invention effectively utilizes all the acquired K-space data through non-linear mapping, improves the information recovery degree, and thus enhances the image quality.

[0115] The present invention has been proven feasible through experiments, simulations, and usage. The present invention has been tested on a self-developed zero-liquid-helium 0.23T superconducting low-field magnetic resonance system with a water phantom and a human brain. The scanning sequence is based on the FSE sequence, and the phase encoding position of the FSE sequence is adjusted according to the K-space acquisition template specified by the present invention, confirming the feasibility of the present invention. Figure 4 For the comparison of the imaging results of the water phantom for GRAPPA technology and the present invention based on manifold non-linear modeling, where a is the water phantom image reconstructed using the sum of squares method (SOS) based on fully sampled data as the reference image; b and d are the difference maps between the images reconstructed using the GRAPPA method and the reference image based on the full sampling of the central 48 rows and the uniform undersampling of the remaining part by a factor of two; c and e are the difference maps between the images reconstructed using the manifold method and the reference image based on the full sampling of the central 48 rows and the uniform undersampling of the remaining part by a factor of two; comparing the parallel imaging results of the water phantom of these two methods, it can be clearly seen that when improving the same scanning speed, the performance of the method based on the manifold method is significantly better than the GRAPPA method, and the NMSE between the reconstructed image and the reference image is only 0.28, which is 32.7% lower than the GRAPPA method.

[0116] Figure 5 For the comparison of the GRAPPA technique and the human brain imaging results of the parallel imaging based on manifold nonlinear modeling of the present invention, where a is a human brain image reconstructed by the sum of squares method (SOS) based on fully sampled data and serves as a reference image; b and c are the difference maps between the images reconstructed by the GRAPPA method and the reference image respectively, based on the full sampling of the central 48 lines and the uniform undersampling of the remaining part by a factor of two; d and e are the difference maps between the images reconstructed by the manifold method and the reference image respectively, based on the full sampling of the central 48 lines and the uniform undersampling of the remaining part by a factor of two; it can be clearly seen from the comparison of the parallel imaging results of the human brain by these two methods that, when the same scanning speed is improved, the performance of the method based on the manifold method is significantly better than that of the GRAPPA method, and the NMSE between the reconstructed image and the reference image is only 0.43, which is reduced by 33% compared with the GRAPPA method.

[0117] Example 2

[0118] According to another embodiment of the present invention, a parallel imaging reconstruction device based on manifold nonlinear mapping is provided. Refer to Figure 6 , including:

[0119] An acquisition unit 201 for multi-channel acquisition of K-space data;

[0120] A parameter optimization unit 202 for setting the neighborhood size according to the actually acquired K-space data and adaptively optimizing and adjusting the key parameters of the high-dimensional mapping;

[0121] A mapping unit 203 for taking the K-space data (including non-linearly related image information and noise components) as features and mapping them to a higher-dimensional feature space by the manifold method to establish the topological relationship of the high-dimensional feature space;

[0122] A fitting and recovery unit 204 for smoothing the differences between data points within the neighborhood and the differences between the central points of different neighborhoods in the high-dimensional feature space by manifold regression, and finally establishing a non-linear model with minimized noise features to fit and complete the undersampled part of the K-space, and restoring it to the image space based on the inverse Fourier transform of the reconstructed K-space data.

[0123] In the method for parallel imaging reconstruction based on manifold learning in the embodiments of the present invention, data is mapped into a high-dimensional space without explicitly calculating high-dimensional features. This method separates signals and noise more effectively, while being able to capture complex imaging features, so as to more accurately complete the missing sampled K-space information, more accurately restore the details of the image. By adding interaction terms or non-linear features, the model can more carefully identify potential risk patterns, improve the accuracy and anti-noise performance of the reconstructed image, expand the applicable range of the algorithm, solve the problem of low signal-to-noise ratio in low-field magnetic resonance parallel imaging, and significantly improve the quality and diagnostic value of the reconstructed image.

[0124] Specifically, to solve the problem of slow magnetic resonance imaging speed, parallel imaging technology is a major breakthrough in magnetic resonance imaging technology. This method can accelerate the magnetic resonance imaging (MRI) scanning process by using multiple radio frequency coils to receive signals simultaneously. These coils cover different spatial regions and can capture more spatial information, thereby reducing the required sampling points in k-space (frequency domain space). This method can significantly reduce the scanning time, improve the temporal resolution of the image, and improve the patient's comfort. However, reducing sampling leads to an increase in the complexity of image reconstruction, such as obvious aliasing artifacts, so effective reconstruction algorithms are needed to restore high-quality images.

[0125] In low-field magnetic resonance imaging, the signal-to-noise ratio (SNR) is relatively low, which further limits the scanning speed and image quality. In this case, the projection operation of the manifold learning method in the high-dimensional space can separate signals and noise more effectively, while being able to capture complex imaging features, so as to more accurately restore the details of the image, and thus more accurately complete the missing sampled K-space information, significantly improving the quality and diagnostic value of the reconstructed image.

[0126] Aiming at the above-mentioned drawbacks, the present invention proposes a method for parallel imaging reconstruction based on manifold learning, which is applicable to low-field magnetic resonance image reconstruction, aiming to solve the problems of low signal-to-noise ratio and slow imaging speed in low fields. The present invention adopts multi-channel acquisition and non-linear modeling based on manifold learning to improve the clarity and contrast of the image by more accurately completing the K-space data. Specifically, the present invention maps the data into a high-dimensional space through this method without explicitly calculating high-dimensional features. This method separates signals and noise more effectively, while being able to capture complex imaging features, so as to more accurately complete the missing sampled K-space information, more accurately restore the details of the image. By adding interaction terms or non-linear features, the model can more carefully identify potential risk patterns, improve the accuracy and anti-noise performance of the reconstructed image, expand the applicable range of the algorithm, solve the problem of low signal-to-noise ratio in low-field magnetic resonance parallel imaging, and significantly improve the quality and diagnostic value of the reconstructed image.

[0127] The basic content of the technical solution of this method is as follows:

[0128] Collect K-space data in a low-field magnetic resonance system. Use multiple receive coils to collect K-space data in parallel. The data collected by each coil is undersampled (i.e., there are uncollected data points), but ensure that the central part of the K-space data in each channel is completely collected. These data are called autocalibration signal (ACS) lines. These ACS lines of autocalibration signals provide complete K-space information for non-linear modeling.

[0129] Adaptive parameter optimization. In this process, adaptive optimization parameters (such as kernel width and neighborhood size) can be adjusted according to the actual data characteristics to adapt to different imaging conditions and noise levels, further improving the flexibility and applicability of the model.

[0130] Non-linear modeling based on manifold theory. Since the ACS part of the K-space autocalibration signal collected contains non-linear related image and noise characteristics, initially use it as a feature and map it to a higher dimension through manifold theory methods. By adjusting the mapped high-dimensional feature space, the noise is more separated, minimizing noise interference, and finally establishing the topological relationship of the high-dimensional feature space, which helps to more clearly extract the true structural features of the image.

[0131] Manifold regression and image reconstruction. In the high-dimensional feature space, manifold regression minimizes the differences between data points within a smooth neighborhood and the differences between the central points of different neighborhoods, thereby establishing a non-linear model with minimized noise characteristics to fit and complete the undersampled part of the K-space. Finally, based on the inverse Fourier transform (IFT) of the reconstructed K-space data, restore this information to the image space to generate higher-quality images.

[0132] See Figure 2 , the detailed elaboration of the technical solution of the present invention is as follows:

[0133] 1. Collect K-space data in a low-field magnetic resonance system

[0134] The schematic diagram of the acquisition method of K-space data is as Figure 3 shown. This sampling method strictly follows the Nyquist sampling law for full sampling in the ACS part of the autocalibration signal, and at the same time performs undersampling on the part outside the ACS of the autocalibration signal, ensuring that while shortening the sampling time, it provides low-resolution complete K-space information for non-linear modeling. The specific steps are as follows:

[0135] Step 1: Establish a K-space model under low-field magnetic resonance conditions and determine the acquisition trajectory of the echo signal in the model.

[0136] Specifically, the acquisition trajectory of the echo signals is as follows: all echo signals are acquired in parallel along one coordinate direction. The central region of the K-space is fully sampled (the auto-calibration signal ACS part), strictly following the Nyquist sampling law to ensure obtaining complete high-resolution data for reconstruction coefficient estimation, and at the same time providing an accurate benchmark for subsequent image reconstruction; the edge region of the K-space is downsampled to reduce the amount of data acquisition and improve the acquisition speed.

[0137] Step 2: Determine the time series of the ultra-low field magnetic resonance scan according to the acquisition trajectory, and calculate the encoding gradients required to be applied by the magnetic resonance imaging system. The specific steps include: calculating the scan time series parameters and encoding gradients of the fully sampled region (the auto-calibration signal ACS part) to ensure the integrity of data acquisition in the central region; calculating the scan time series parameters and encoding gradients of the downsampled region to ensure the uniformity and efficiency of data acquisition in the edge region. In a low-field environment, the signal-to-noise ratio is relatively low, so it is necessary to specifically optimize the time series and encoding gradients to maximize the signal intensity and data acquisition efficiency. For example, the present invention adopts the fast spin-echo (FSE) sequence with a fast acquisition speed.

[0138] Step 3: Acquire the K-space data of parallel imaging. Specifically, the three-dimensional multi-slice K-space data acquired in this embodiment includes the fully sampled data of the central region of each slice and the downsampled data of the edge region: Full sampling of the central region (the auto-calibration signal ACS part): The central part of the K-space is fully sampled according to the Nyquist sampling law to ensure obtaining complete high-resolution data. This is particularly important for a low-field environment. Downsampling of the edge region: Uniform downsampling is performed in the edge part of the K-space to reduce the data acquisition time. First, dense phase-encoding acquisitions are performed on the adaptive calibration scan (the auto-calibration signal ACS) part to obtain complete central K-space data. Then, the phase-encoding interval is gradually increased to make the phase-encoding steps sparse and expand the range of phase-encoding, thereby acquiring a uniformly downsampled K-space data.

[0139] 2. Adaptive parameter optimization

[0140] The kernel width in the kernel method of manifold learning determines the projection effect of data blocks in the high-dimensional feature space and directly affects the separation accuracy of signals and noise. For a low signal-to-noise ratio environment, increasing the kernel width can reduce the influence of noise, make similar signals more concentrated, and enhance signal consistency; while in a high signal-to-noise ratio environment, moderately reducing the kernel width helps to capture more subtle local features and details. The specific process is as follows:

[0141] Step 1: Data analysis. First, analyze the K-space data to determine the "kernel" size, that is, the size of each neighborhood divided from the data of the auto-calibration signal ACS part for high-dimensional mapping.

[0142] Step 2: Initial kernel width setting. Select the initial kernel width according to the data analysis results , and determine the initial dimension size of the high-dimensional mapping of the data.

[0143] Step 3: Adaptive iterative optimization. In each iteration, use the current estimate to calculate , and then calculate the approximate (that is, calculate the estimate of through empirical formula 2 based on the current value, and at the same time determine its dimension size). Then, use the new estimate to calculate the next . This step updates the kernel width by the least squares method, and the specific formula is as follows:

[0144] [1]

[0145] where A represents the matrix composed of the non-undersampled position points of the auto-calibration signal ACS. The size of matrix A is m×k, where m is the total number of "kernels" divided in the auto-calibration signal ACS data, and k is the number of neighborhood points in each "kernel". represents the high-dimensional mapping of A using the manifold method with kernel width , represents the combination of the estimates of the linear representations of the high-dimensional mappings of each data at the non-undersampled positions of the auto-calibration signal ACS, with dimension , where is the dimension of the new feature space, which is usually much higher than k.

[0146]

[0147] Formula 2 is the empirical formula for the high-dimensional mapping of each sampling point in A, where represents the K-space signal of the data at the partially missing positions of the auto-calibration signal ACS on the target coil , represents the acquired undersampled signal, where is the coil index, and t and h respectively represent the offsets of the adjacent K-space data in the and directions. R represents the undersampling rate (ORF, sampling rate factor), that is, the undersampling factor. and respectively represent the coordinates along the frequency encoding and phase encoding directions. and is the basic sampling interval in k-space, which is used to describe the distance between points in the frequency encoding and phase encoding directions respectively. r is the integer offset along the phase encoding direction, which determines the position of the target point. n represents the offset that is still n frequency encoding intervals away from the adjacent k-space data. The larger n is, the more it means that in order to extract the non-linear relationship between higher-dimensional k-space data, the conventional empirical formula 2 generally sets n to 3 to reduce the computational amount.

[0148] 3. Nonlinear Modeling Based on Manifold

[0149] All existing GRAPPA-derived algorithms are based on the linear model in formula [3]. Due to the low signal-to-noise ratio of low-field magnetic resonance, it is difficult to separate the non-linearly related signals and noise in the auto-calibration signal ACS data, resulting in a deviation of the model.

[0150]

[0151]

[0152] where represents the k-space signal not acquired on the target coil ; represents the acquired undersampled signal, where is the coil index, and t and h respectively represent the offsets of the adjacent k-space data in the and directions; represents the combination coefficients of the linear model, and these coefficients are used to linearly combine the adjacent sampled signals into the unsampled signal on the target coil. L represents the total number of coils, R represents the undersampling rate (ORF, sampling rate factor), that is, the undersampling factor, and l traverses the indices of all coils. and respectively represent the coordinates along the frequency encoding and phase encoding directions. r is the integer offset along the phase encoding direction. Formula [3] only performs linear combination in one dimension, does not completely separate the image and noise, and loses a lot of image information.

[0153] To solve the common non-linear and noise-like error problems in the GRAPPA reconstruction process, the present invention proposes an innovative method based on manifold, which improves the reconstruction accuracy by identifying and adjusting the non-linear relationship between image features. This method utilizes the statistical characteristics of the data and the trend distribution in the sample space to effectively suppress noise and artifacts, thereby achieving more accurate signal reconstruction.

[0154] Step 1: Feature Selection and Nonlinear Modeling. First, select the non-linear relationship features mapped to the high-dimensional space and perform manifold modeling. For example, use a method in manifold theory (kernel method) to separate the signals and noises of non-linear relationships through high-dimensional mapping in order to identify the error sources in the reconstruction process. A typical kernel (inhomogeneous polynomial kernel) has the following form:

[0155] [4]

[0156] where and are scalars, is the order of the polynomial (also the kernel width of the kernel function for the inhomogeneous polynomial kernel function), which helps to map the non-linear relationships in the data to the high-dimensional space so that they can be separated. Among them represents the th and th "kernel" extracted from the ACS part of the data of the auto-calibration signals of all channels, .

[0157] Through the non-linear mapping The in the input space the data (the data at the non-undersampled positions of the auto-calibration signal ACS, that is, the initial features) are mapped to the high-dimensional feature space (the high-dimensional features that can separate the signals and noises of non-linear relationships). Using formula 4, the linear combination after non-linear mapping to high dimensions is expressed as , then: , then:

[0158] [5]

[0159] Based on the least squares method of formula 5, calculate the coefficients of each dimension from the high-dimensional mapping of the non-undersampled position data matrix A to the undersampled position data matrix B of the manifold model, so as to obtain the parameters used by the manifold model by combining formula [2] and [4]. Here, specifically, it refers to the and two parameters in the kernel function.

[0160] Improper setting of the parameters may lead to a very high or even infinite mapped dimension. Therefore, it is necessary to select the high-dimensional features. It is found in this example of the inhomogeneous polynomial kernel that retaining the dimensional features above the quadratic term is difficult to further reduce the error of the manifold model. Therefore, they are discarded.

[0161] Step 2: Adjustment of the Feature Space. Assume that the inhomogeneous polynomial kernel is used and = 1, = 1, = 2, the non - linear mapping of the manifold theory can be specifically expressed as:

[0162]

[0163] Using the non - linear mapping in the above form , helps to effectively process non - linearly separable data in a high - dimensional space, where is k elements contained in "kernel". Specifically: This mapping form contains first - order and second - order terms to retain the basic information and non - linear characteristics of the original data in a high - dimensional space, which is especially suitable for the need to observe the feature trend in manifold theory modeling. The first - order term retains the basic manifold trend of the data, and the second - order term captures the sum of squares and interaction terms of each feature, which enables the mapped feature space to reveal the non - linear manifold trend. The higher the mapping order, the more completely the non - linear - related information is separated, but at the same time the calculation is more complex. Adjusting the appropriate feature space of the mapping is the key to this step. The quadratic term has three terms as shown in formula [2]. To further reduce the computational complexity, only the first two terms of the quadratic term can be retained without affecting the performance of the manifold theory model.

[0164] Step 3: Establish the topological relationship of the high - dimensional feature space. When constructing the topological relationship of the high - dimensional feature space, the adjusted high - dimensional data is used to deeply explore its complex associations in manifold theory. This process combines multi - level manifold feature analysis to reveal the potential patterns of the image and the local structure of the data. Modeling the topological relationship of the high - dimensional feature space helps to capture the non - linear relationships between signals and noises, different tissues. As shown in formula [7], each neighborhood "kernel" divided from the data of the automatic calibration signal ACS part of multiple channels is mutually related, is the nth "kernel" drawn from the data of the automatic calibration signal ACS part of all channels, is other "kernels" ( ) divided from the data of the automatic calibration signal ACS part of all channels except with respect to the integer offset, which further affects . Formula 7 represents the relationship of mutual influence between all "kernels" of all channels, where can be estimated by the convolution sum of the matrix composed of the remaining neighborhoods and the coefficient matrix . Finally, combining formulas [2], [4], [5] and [7] further fuses the relationships between different neighborhoods "kernels" of the same channel, as well as the relationships between the data of different neighborhoods "kernels" of different channels, further improving the accuracy of the manifold theory model.

[0165]

[0166] 4. Manifold Regression and Signal Reconstruction

[0167] Construct a manifold regression model to handle the non - linear relationship between signals and noise in a high - dimensional feature space. The specific steps are as follows:

[0168] Step 1: Smoothing. Use manifold regression to smooth the data in the neighborhood, making the signal intensity more consistent in the local area.

[0169] Step 2: Non - linear Enhancement of the Central Point. Non - linearly enhance different "kernel" central points through the regression model, making the signal intensity more consistent in the global area.

[0170] Step 3: Interpolation Reconstruction. In the interpolation reconstruction process, first, use the manifold regression result obtained by adaptively iteratively optimizing the automatic calibration signal ACS data to interpolate the unsampled points in the K - space to complete the down - sampled data; perform manifold regression fitting in the high - dimensional space to further reduce the interpolation error; then, combine the interpolated data with the existing sampled points to generate the complete K - space data; finally, transform the reconstructed K - space data to the image space through IFT.

[0171] The key points and the points to be protected by the present invention are as follows:

[0172] The core innovation of the present invention lies in proposing a non - linear mapping parallel imaging reconstruction method based on manifolds. Aiming at problems such as low signal - to - noise ratio and slow imaging speed in low - field magnetic resonance imaging, it provides an effective technical solution to improve image quality and accelerate the scanning process. The following are the key innovation points and the technical content to be protected by the present invention:

[0173] Non - linear mapping method based on manifolds. By adopting the non - linear mapping technology in manifolds, map the K - space data to a high - dimensional space, so as to accurately model the complex data relationship in low - field magnetic resonance imaging. This method can capture the non - linear features in the data, overcome the deficiencies of traditional linear methods under low signal - to - noise ratio, and improve the accuracy of image reconstruction. The present invention takes the kernel method in manifolds as an example, and the high - dimensional feature space mapping methods in manifolds such as polynomial feature expansion and high - dimensional representation in deep learning are also applicable to the present invention.

[0174] Nonlinear mapping method based on manifold theory. By adopting the nonlinear mapping technology in manifold theory, the K-space data is mapped into a high-dimensional space, so as to separate the nonlinearly related image and noise features in the original data collected by low-field magnetic resonance. This method can overcome the deficiencies of traditional linear methods under low signal-to-noise ratio and improve the accuracy of image reconstruction. Taking the kernel method in manifold theory as an example in the present invention, the high-dimensional feature space mapping methods in manifold theory such as polynomial feature expansion and high-dimensional representation in deep learning are also applicable to the present invention.

[0175] Combination of multi-channel acquisition and manifold theory modeling. The present invention combines multi-channel parallel acquisition and nonlinear modeling based on manifold theory. Signals are received simultaneously by multi-channel radio frequency coils to reduce the sampling points in the K-space, and at the same time, the undersampled data is accurately complemented through nonlinear modeling. This technical solution significantly improves the image quality of low-field magnetic resonance imaging, especially in terms of the signal-to-noise ratio and detail performance of the reconstructed image.

[0176] Effective separation of signals and noise. Using the manifold theory method to perform high-dimensional mapping on the original data collected by low-field magnetic resonance, the nonlinearly related image and noise features are effectively separated into a form that can be linearly combined. By removing the "kernel" of the noise term for modeling, the adverse effects caused by the amplification of noise in traditional methods are avoided. By separating the noise features, the present invention can more accurately restore the image details and significantly improve the clarity and contrast of the image.

[0177] Accurately complement the undersampled K-space data. The present invention accurately calculates the coefficients of each item of the high-dimensional image features through the manifold regression technology, and combines the data smoothing processing in the neighborhood and the nonlinear enhancement of the central point data to more accurately restore the undersampled K-space data in low-field magnetic resonance imaging, reducing the image artifacts caused by data loss in traditional methods. This technical solution effectively improves the reconstruction accuracy of low-field magnetic resonance imaging.

[0178] Enhanced noise resistance performance and adaptability. The present invention complements the downsampled K-space data by introducing the manifold reconstruction method, enabling the model to maintain strong noise resistance when dealing with noise in low-field magnetic resonance imaging. This innovation significantly broadens the application scope of this method in various magnetic resonance imaging tasks and is also applicable to complex high-resolution imaging tasks.

[0179] Kernel function selection and optimization iteration process. In the kernel method of the present invention, the selection of the kernel function is crucial for the performance of high-dimensional mapping. To ensure the best imaging quality and reconstruction effect, the present invention allows the selection of various kernel functions, including non-uniform polynomial kernels, Gaussian kernels (RBF kernels), and hybrid kernel functions, etc. Through the performance evaluation of different kernel functions and in combination with the requirements of specific tasks, the best kernel function is iteratively selected automatically or through optimization algorithms (such as alternating least squares method, gradient descent method, etc.), and its related parameters are tuned.

[0180] Sequence scanning model. The scanning speed of the sequence premise used in the present invention is fast, and at the same time, it can collect fully sampled data in the central part and K-space data that can be uniformly undersampled. The present invention scans in two times, one time scans the central part data, and one time scans the undersampled data, and finally calibrates through an echo train. Including but not limited to fast spin echo (FSE), gradient echo (GRE), balanced steady-state free precession (bSSFP), etc., such MRI sequences are applicable to the present invention.

[0181] Compared with the traditional GRAPPA method, the present invention significantly improves the image quality, data completion ability, and computational efficiency by introducing a manifold-based nonlinear modeling method and combining it with the application environment of low-field magnetic resonance, enhances the adaptability to complex imaging environments, improves the signal-to-noise ratio and image stability, and has important application value and promotion prospects. Specifically as follows:

[0182] (1) Stronger nonlinear modeling ability. GRAPPA relies on a linear model and cannot effectively capture the nonlinear relationships in the data. In contrast, the present invention uses a nonlinear manifold mapping, which can more accurately capture complex imaging features and improve the image reconstruction accuracy.

[0183] (2) Better noise resistance performance. GRAPPA is prone to amplifying noise in low signal-to-noise ratio data, resulting in a decrease in image quality. Through the manifold method, the present invention can effectively separate signals and noise, improve the noise resistance ability, thereby reducing artifacts and improving image clarity.

[0184] (3) More accurate K-space data completion. GRAPPA uses linear interpolation to fill in the missing K-space data, with limited accuracy. The present invention can more accurately complete the missing K-space data through high-dimensional nonlinear mapping, retaining more imaging details.

[0185] (4) Higher adaptability. The applicability of GRAPPA is limited, especially when dealing with complex MR data. The present invention supports a variety of kernel functions (such as Gaussian kernels, non-uniform polynomial kernels, etc.), and can be flexibly adjusted according to the data characteristics to adapt to different imaging tasks.

[0186] (5) Higher computational efficiency. Although the computational complexity of non-linear methods is relatively high, through manifold mapping and high-dimensional modeling, the present invention can maintain high computational efficiency while maintaining image quality, especially performing better on large data sets.

[0187] (6) Optimized data utilization and information recovery. GRAPPA does not fully utilize the high-order information of K-space data, resulting in information loss. The present invention effectively utilizes all the collected K-space data through non-linear mapping, improves the degree of information recovery, and thus enhances the image quality.

[0188] The present invention has been proven feasible through experiments, simulations, and applications. The present invention has been tested on a self-developed zero-liquid-helium 0.23T conventional low-field magnetic resonance system with a water phantom and a human brain. The scanning sequence is based on the FSE sequence, and the phase encoding position of the FSE sequence is adjusted according to the K-space acquisition template specified by the present invention, verifying the feasibility of the present invention. Figure 4 For the comparison of the imaging results of the water phantom between the GRAPPA technique and the present invention based on manifold non-linear modeling, where a is the water phantom image reconstructed using the sum of squares method (SOS) based on fully sampled data and serves as the reference image; b and d are the difference maps between the images reconstructed using the GRAPPA method with the center 48 rows fully sampled and the remaining part uniformly undersampled by a factor of two and the reference image, respectively; c and e are the difference maps between the images reconstructed using the manifold method with the center 48 rows fully sampled and the remaining part uniformly undersampled by a factor of two and the reference image, respectively. By comparing the parallel imaging results of the water phantom of these two methods, it can be clearly seen that when the same scanning speed is increased, the performance of the method based on the manifold method is significantly better than that of the GRAPPA method. The NMSE between the reconstructed image and the reference image is only 0.28, which is 32.7% lower than that of the GRAPPA method.

[0189] Figure 5 For the comparison of the imaging results of the human brain between the GRAPPA technique and the present invention based on manifold non-linear modeling parallel imaging, where a is the human brain image reconstructed using the sum of squares method (SOS) based on fully sampled data and serves as the reference image; b and c are the difference maps between the images reconstructed using the GRAPPA method with the center 48 rows fully sampled and the remaining part uniformly undersampled by a factor of two and the reference image, respectively; d and e are the difference maps between the images reconstructed using the manifold method with the center 48 rows fully sampled and the remaining part uniformly undersampled by a factor of two and the reference image, respectively. By comparing the parallel imaging results of the human brain of these two methods, it can be clearly seen that when the same scanning speed is increased, the performance of the method based on the manifold method is significantly better than that of the GRAPPA method. The NMSE between the reconstructed image and the reference image is only 0.43, which is 33% lower than that of the GRAPPA method.

[0190] Example 3

[0191] A storage medium stores a program file capable of implementing any of the above-mentioned parallel imaging reconstruction methods based on manifold non-linear mapping.

[0192] Embodiment 4

[0193] A processor is used to run a program. When the program runs, it executes any of the above-mentioned parallel imaging reconstruction methods based on manifold non-linear mapping.

[0194] The serial numbers of the above-mentioned embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0195] In the above embodiments of the present invention, the descriptions of the respective embodiments have their own emphases. For the parts not detailed in a certain embodiment, reference may be made to the relevant descriptions of other embodiments.

[0196] In the several embodiments provided by the present application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the system embodiments described above are only illustrative. For example, the division of units can be a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling or direct coupling or communication connection between each other can be through some interfaces. The indirect coupling or communication connection of units or modules can be in an electrical or other form.

[0197] The units described as separate components may or may not be physically separated. The components displayed as units may or may not be physical units, that is, they can be located in one place or distributed to multiple units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0198] In addition, in each embodiment of the present invention, the functional units can be integrated in a processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit. The above-mentioned integrated units can be implemented in the form of hardware or in the form of software functional units.

[0199] When the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes: various media such as USB flash drives, read-only memories (ROM), random access memories (RAM), mobile hard disks, magnetic disks, or optical discs that can store program codes.

[0200] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A parallel imaging reconstruction method based on manifold learning, characterized in that, It includes the following steps: S101: Collect K-space data through multiple channels; S102: Set the neighborhood size according to the collected K-space data, and adaptively optimize and adjust the key parameters of high-dimensional mapping; S103: Take the non-linearly correlated image information and noise components of the K-space data as features and map them to a higher-dimensional feature space through a manifold method to establish the topological relationship of the high-dimensional feature space; S104: In the high-dimensional feature space, smooth the differences between data points within the neighborhood and the differences between the central points of different neighborhoods through manifold regression. Finally, establish a non-linear model with minimized noise features to fit and complete the downsampled K-space part, and restore it to the image space based on the completed K-space data through inverse Fourier transform.

2. The non-linear mapping parallel imaging reconstruction method based on manifold according to claim 1, characterized in that In step S101, multiple receive coils are used to collect K-space data in a low-field magnetic resonance system in parallel.

3. The non-linear mapping parallel imaging reconstruction method based on manifold theory according to claim 1, characterized in that Step S101 specifically includes: Establish a K-space model under low-field magnetic resonance conditions and determine the acquisition trajectory of the echo signal in the K-space model; Determine the time series parameters of low-field magnetic resonance scanning according to the acquisition trajectory and calculate the encoding gradient required to be applied by the magnetic resonance imaging system; Collect the K-space data of parallel imaging.

4. The method for parallel imaging reconstruction of non-linear mapping based on manifold theory according to claim 1, characterized in that In step S102, determine the neighborhood size according to the actual data characteristics, and adaptively optimize and adjust the key parameters of high-dimensional mapping. The key parameter is the kernel width.

5. The non-linear mapping parallel imaging reconstruction method based on manifold theory according to claim 1, wherein Step S102 specifically includes: Analyze the K-space data, determine the size of each neighborhood divided from the data of the auto-calibration signal (ACS) part in high-dimensional mapping, and generate a data analysis result; Select the initial kernel width according to the data analysis result; During the reconstruction process, dynamically adjust the kernel width through an error feedback mechanism for adaptive iterative optimization.

6. The method for parallel imaging reconstruction of non-linear mapping based on manifold according to claim 1, wherein Step S103 specifically includes: Take the non-linearly correlated image information and noise components of the K-space data as features and map them to a higher-dimensional feature space through a manifold method to obtain the non-linear relationship features of the high-dimensional space; Select and perform manifold modeling on the non-linear relationship features according to minimizing the difference between the actual sampling value at the missing position of the auto-calibration signal (ACS) and the eigenvalue after high-dimensional mapping of the linear combination; Adjust the high-dimensional feature space to balance the computational complexity and the performance of the manifold model; Construct the topological relationship of the high-dimensional feature space, deeply explore the complex associations between each neighborhood kernel in the manifold through the adjusted high-dimensional data, and combine multi-level manifold feature analysis to reveal the non-linear relationships between signals and noise, and different tissues.

7. The non-linear mapping parallel imaging reconstruction method based on manifold theory according to claim 1, wherein In step S104, smoothing the differences between data points within the neighborhood through manifold regression includes: using manifold regression to smooth the data within the neighborhood to make the signal intensity more consistent in the local area.

8. The method for parallel imaging reconstruction of non-linear mapping based on manifold theory according to claim 1, characterized in that, After smoothing the differences between data within the neighborhood through manifold regression in step S104, it also includes: non-linearly enhancing the central points of different neighborhood kernels through a regression model to make the signal intensity more consistent in the global area.

9. The method for parallel imaging reconstruction of non-linear mapping based on manifold theory according to claim 1, wherein In step S104, the nonlinear relationship between the signal and the noise is processed in the high-dimensional feature space through manifold regression, and finally a nonlinear model with minimized noise features is established to fit and complete the downsampled K-space part. The restoration to the image space based on the completed K-space data by inverse Fourier transform includes: In the interpolation reconstruction process, first, the manifold regression results adaptively iteratively optimized using the auto-calibration signal ACS data are used to interpolate the unsampled points in the K-space to complete the downsampled data; manifold regression fitting is performed in the high-dimensional space to further reduce the interpolation error; then, the interpolated data is combined with the existing sampled points to generate the complete K-space data; finally, the reconstructed K-space data is transformed to the image space through IFT.

10. A non-linear mapping parallel imaging reconstruction device based on manifold theory, characterized in that, Including: An acquisition unit for acquiring K-space data in multiple channels; A parameter optimization unit for setting the neighborhood size according to the acquired K-space data and adaptively optimizing and adjusting the key parameters of the high-dimensional mapping; A mapping unit that takes the image information and noise components nonlinearly related to the K-space data as features and maps them to a higher-dimensional feature space through a manifold method to establish the topological relationship of the high-dimensional feature space; A fitting and restoration unit for smoothing the differences between data points within the neighborhood and the differences between the central points of different neighborhoods through manifold regression in the high-dimensional feature space, and finally establishing a nonlinear model with minimized noise features to fit and complete the downsampled K-space part, and restoring to the image space based on the completed K-space data by inverse Fourier transform.

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