Image reconstruction method, device, imaging system and medium for non-uniform radial sampling

Abstract

The present invention provides an image reconstruction method, device, imaging system and medium for non-uniform radial sampling, wherein the method is to obtain initial k-space data of non-uniform radial sampling, obtain a density compensation correction function corresponding to the non-uniform radial sampling type based on the non-uniform radial sampling type, obtain a density compensation function of the initial k-space data based on the density compensation correction function corresponding to the non-uniform radial sampling type and a basic density compensation function corresponding to the density compensation correction function under the same non-uniform radial sampling type, perform density compensation on the initial k-space data based on the density compensation function of the initial k-space data to obtain compensated k-space data, and generate a magnetic resonance image based on the compensated k-space data and a preset reconstruction algorithm. The present invention can effectively reduce the density compensation calculation complexity of non-uniform radial sampling, improve the compensation calculation speed, and thereby improve the reconstruction efficiency while ensuring the reconstruction quality of the magnetic resonance image.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic resonance image reconstruction, and in particular to an image reconstruction method, device, imaging system and medium for non-uniform radial sampling. Background Art

[0002] Radial acquisition is a non-Cartesian acquisition trajectory, which is characterized by a radial trajectory, each acquisition spoke passing through the center of k-space, and multiple spokes covering the entire k-space at their respective angles. Figure 1 The number of sampling points per unit area at different positions in the k-space shown is different. The sampling density of the red box position far away from the center of the k-space is lower than that of the black box position close to the center of the k-space. Figure 2 As shown in the figure, the number of sampling points per unit area (black and red boxes) of all positions in the Cartesian k-space is the same. To ensure that the reconstructed image has a high contrast, it is necessary to calculate the density compensation function (DCF) of each sampling point before reconstruction to compensate for the uneven sampling density.

[0003] In conventional radial acquisition mode, the sampling time window gradient size is constant, such as Figure 1 As shown, the sampling points are equally spaced in the spoke (radial) direction, and the sampling points of the same sampling radius are also equally spaced in the angular direction. Density compensation can be performed by considering only the sampling density on the radial circumference (2D) or radial sphere (3D) (inversely proportional to the sampling radius). However, in practical applications, functions such as free breathing imaging, compressed sensing acquisition, multi-motion state reconstruction, ultra-short TE imaging, and anisotropic field of view acquisition have uneven sampling in the radial direction and / or angular direction. For example, when acquiring ultra-short echoes in the radial direction, Figure 3 As shown in the figure, in order to achieve a shorter echo time, acquisition is usually started during the gradient climbing period rather than when the gradient is stable, resulting in the sampling points not being distributed at equal intervals in the radial direction; Figure 4As shown in the radial acquisition of anisotropic field of view (FOV) or the reconstruction of motion states under motion binning, the distribution of spokes in the angular direction is also not equally spaced (θ1>θ2); of course, there are also cases where the radial spoke direction and the angular direction are non-uniformly distributed at the same time. For the above non-uniform radial sampling, only conventional density compensation methods cannot achieve the ideal compensation effect, and the existing methods that rely on numerical calculation methods to estimate non-uniform sampling density for density compensation, such as the Voronoi area method or the calculation method based on iterative optimization of the point spread function, have high computational complexity and very slow calculation speed when there are many sampling points, which directly affects the reconstruction efficiency and is difficult to meet the needs of efficient magnetic resonance image reconstruction. Summary of the invention

[0004] In order to solve the problems of the prior art, it is necessary to provide an image reconstruction method, device, imaging system and medium for non-uniform radial sampling in response to the above technical problems.

[0005] In a first aspect, an embodiment of the present invention provides a method for reconstructing a magnetic resonance image with non-uniform radial sampling, the method comprising the following steps:

[0006] Acquire initial k-space data of non-uniform radial sampling;

[0007] Based on the non-uniform radial sampling type, obtaining a density compensation correction function corresponding to the non-uniform radial sampling type;

[0008] Obtaining a density compensation function of the initial k-space data based on a density compensation correction function corresponding to the non-uniform radial sampling type and a basic density compensation function corresponding to the density compensation correction function under the same non-uniform radial sampling type;

[0009] Density compensation is performed on the initial k-space data based on a density compensation function of the initial k-space data to obtain compensated k-space data;

[0010] A magnetic resonance image is generated based on the compensated k-space data and a preset reconstruction algorithm.

[0011] In a second aspect, an embodiment of the present invention provides a magnetic resonance image reconstruction device for non-uniform radial sampling, the device comprising:

[0012] A non-uniform radial sampling module, used for acquiring initial k-space data in a non-uniform radial sampling mode;

[0013] A compensation correction function acquisition module, used for obtaining a dimension density compensation correction function corresponding to the non-uniform radial sampling type based on the non-uniform radial sampling type;

[0014] A density compensation correction module, configured to obtain a density compensation function of the initial k-space data based on a density compensation correction function corresponding to the non-uniform radial sampling type and a basic density compensation function corresponding to the density compensation correction function under the same non-uniform radial sampling type;

[0015] A density compensation module, used for performing density compensation on the initial k-space data based on the density compensation function of the initial k-space data to obtain compensated k-space data;

[0016] An image reconstruction module is used to generate a magnetic resonance image based on the compensated k-space data and a preset reconstruction algorithm.

[0017] In a third aspect, an embodiment of the present invention further provides a magnetic resonance imaging system, comprising an imaging controller; the imaging controller comprises a processor and a memory, the processor and the memory are coupled, the memory is used to store computer programs or instructions, and the processor is used to execute the computer programs or instructions in the memory, so that the imaging controller performs the steps of the above-mentioned non-uniform radial sampling magnetic resonance image reconstruction method.

[0018] In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-mentioned non-uniform radial sampling magnetic resonance image reconstruction method.

[0019] Compared with the prior art, the present invention provides a magnetic resonance image reconstruction method for non-uniform radial sampling, which decomposes the multi-dimensional density compensation in k-space into low-dimensional density compensation analysis in radial and angular directions, effectively reducing the density compensation calculation complexity of non-uniform radial sampling scenarios, improving the compensation calculation speed, and thereby improving the reconstruction efficiency while ensuring the quality of magnetic resonance image reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a schematic diagram of the k-space acquisition trajectory of radial acquisition;

[0021] Figure 2 It is a schematic diagram of the k-space acquisition trajectory of Cartesian acquisition;

[0022] Figure 3 This is a schematic diagram of non-uniform sampling of radial sampling points when radially collecting ultra-short echoes;

[0023] Figure 4 It is a schematic diagram of non-uniform sampling in the angular direction during radial acquisition of anisotropic field of view (FOV);

[0024] Figure 5is a schematic flow chart of a magnetic resonance image reconstruction method with non-uniform radial sampling in an embodiment of the present invention;

[0025] Figure 6 is a schematic diagram of sampling point positions in k-space data obtained by radial acquisition in an embodiment of the present invention;

[0026] Figure 7 is a schematic diagram of the principle based on grid interpolation in an embodiment of the present invention;

[0027] Figure 8 is a schematic diagram of a sampling angle field of view region in which the imaging region is an ellipse in two-dimensional sampling in an embodiment of the present invention;

[0028] Fig. 9 is a schematic diagram of non-uniform sampling in the angular direction in a motion reconstruction scenario according to an embodiment of the present invention;

[0029] Fig.10 is a schematic diagram of a sampling angle field of view region in which the imaging region is an ellipsoid in three-dimensional sampling in an embodiment of the present invention;

[0030] Fig.11 is a schematic diagram of comparing the reconstruction quality of an image reconstructed based on the density compensation method provided by the present invention and an image reconstructed after compensation only according to the basic density compensation function in an embodiment of the present invention;

[0031] Fig.12 It is a schematic diagram of the structure of a magnetic resonance image reconstruction system with non-uniform radial sampling in an embodiment of the present invention. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical scheme and beneficial effects of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Obviously, the embodiments described below are part of the embodiments of the present invention and are only used to illustrate the present invention, but are not used to limit the scope of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0033] In the description of the present invention, it should be noted that, unless otherwise defined, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art. The terms used in the specification of the present invention are only for the purpose of describing the embodiments and are not intended to limit the present invention. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood by specific circumstances.

[0034] like Figure 5 As shown, the present invention provides a magnetic resonance image reconstruction method for non-uniform radial sampling, comprising the following steps:

[0035] S1. Acquire initial k-space data of non-uniform radial sampling; wherein the initial k-space data can be understood as data to be density compensated with non-uniform sampling density acquired based on an actual non-uniform radial sampling scene. For example, in some embodiments, Figure 6 The polar coordinates of the sampling point at each position in the initial k-space data are represented as k(r, θ), where r represents the distance of the sampling point from the center of the k-space, and θ represents the angle between the sampling point and a reference direction.

[0036] S2. Based on the non-uniform radial sampling type, a density compensation correction function corresponding to the non-uniform radial sampling type is obtained; wherein the non-uniform radial sampling type includes the cases of non-uniform acquisition in the radial direction and uniform acquisition in the angular direction, uniform acquisition in the radial direction and non-uniform acquisition in the angular direction, and non-uniform acquisition in both the radial direction and the angular direction as described above. In order to ensure that different non-uniform types under radial sampling can improve the corresponding density compensation calculation efficiency while ensuring the reconstruction quality, the density compensation correction function of each non-uniform type is analyzed and designed in a targeted manner.

[0037] Considering the conventional radial acquisition that is uniform in both angular and radial directions, the density compensation function can be directly obtained by analyzing the radius of the sampling point. The implementation principle actually implies three physical meanings: 1) The synthetic gradient intensity-time curve of all spokes is consistent with the sampling interval, so the number of sampling points on the same radius is the same (equal to the total number of spokes); 2) The radial direction is sampled uniformly, and the sampling density of the radial sampling points is the same without the need for density compensation (or the density compensation is 1); 3) For the special case where the angular direction is uniform, taking radial 2d (two-dimensional radial acquisition) and stack of radial (stacked radial acquisition) as examples, for radius r1, N samples are collected within a range of 2*pi*r1 with a circumference of spoke ; For radius r2, N samples were also collected within the range of 2*pi*r1. spoke points, that is, the sampling density is inversely proportional to the sampling radius, and the corresponding sampling density compensation function should be directly proportional to the sampling radius. For the convenience of the following description, the corresponding density compensation function is recorded as the basic density compensation function.

[0038] For the case where only the radial direction is non-uniform, the physical meaning of the above 1) is also valid. Therefore, it is only necessary to calculate the density compensation correction function at the radial direction point, and perform weighted correction on the basic density compensation function that is uniform in both directions to obtain a relatively accurate density compensation function applicable to the sampling point with non-uniform radial direction. Similarly, for the sampling case where only the angular direction is non-uniform, the physical meaning of the above 1) is also valid. Therefore, it is only necessary to calculate the density compensation correction function in the angular direction, and then perform weighted correction on the basic density compensation function that is uniform in both directions to obtain a relatively accurate density compensation function applicable to the sampling point with non-uniform angular direction. In addition, further generalization, for the case where both the angular direction and the radial direction are non-uniform, it also satisfies the condition 1), then the density compensation correction functions in the radial direction and the angular direction can be calculated respectively, and then the basic density compensation function that is uniform in both directions can be weighted corrected to obtain a relatively accurate density compensation function applicable to the sampling point with non-uniform angular direction and non-uniform radial direction. The following is a detailed description of the density compensation correction function acquisition method in the three cases where only the radial direction is non-uniform, only the angular direction is non-uniform, and both the angular direction and the radial direction are non-uniform, in combination with specific embodiments.

[0039] In some embodiments, Figure 3 As shown, the non-uniform radial sampling type is non-uniform acquisition in the radial direction, and when the acquisition is uniform in the angular direction, the density compensation correction function is the density compensation correction function in the radial direction; that is, when the non-uniform radial sampling only has non-uniformity in the radial direction, the corresponding density compensation correction only needs to consider the density compensation correction in the radial direction dimension.

[0040] For the sampling type with non-uniformity in the radial direction, the sampling numbers of sampling points with different radii in the radial direction are exactly the same in the angular direction, that is, the sampling density in the angular direction can still be understood as the sampling density on the radial circumference (2D) or the radial sphere (3D), and the density compensation according to the sampling radius in the angular direction is still effective; that is, for this type of non-uniformity, it is only necessary to consider the correction of the non-uniformity of the sampling density in the radial direction. In some embodiments, the density compensation correction function in the radial direction is obtained in the following manner:

[0041] Based on the accumulated interpolation weights of all adjacent sampling points of each target calculation sampling point within the width range of the preset interpolation kernel function, the radial sampling density corresponding to each target calculation sampling point is obtained; wherein, the target calculation sampling point can be understood as each sampling point in the initial k-space data that needs to be density compensated; the preset interpolation kernel function can be understood as a function used to determine the contribution weight of each adjacent sampling point of the target calculation sampling point to the density calculation of the target calculation sampling point, which can be selected and set according to actual application requirements, for example, set to a trigonometric function or sinc, etc., which is not specifically limited here. The width range of the corresponding preset interpolation kernel function can be understood as a reference range for determining the sampling density of each target calculation sampling point, and the adjacent sampling points used to calculate the sampling density can be determined accordingly. The interpolation weights of each adjacent sampling point of each target calculation sampling point within the width range of the preset interpolation kernel function are set based on the distance between the adjacent sampling point and the target calculation sampling point, and the corresponding radial sampling density corresponding to each target calculation sampling point can be expressed as ∑ i f(rr i ), and r represents the sampling radius of the target calculation sampling point, r i represents the sampling radius of the ith adjacent sampling point of the target calculation sampling point, f(x)=w is the expression of the preset interpolation kernel function, the independent variable x represents the distance between the adjacent sampling point and the target calculation sampling point, and the dependent variable w represents the interpolation weight corresponding to the independent variable x. Based on the expression of the radial sampling density corresponding to the target calculation sampling point obtained, it can be seen that if there are multiple adjacent sampling points near a target calculation sampling point, the larger the accumulated value of the interpolation weight corresponding to the target calculation sampling point, that is, the greater the sampling density of the point.

[0042] In practical applications, each target calculation sampling point for which the sampling density needs to be determined may be a non-Cartesian point or a Cartesian point in the interpolation trajectory of the standard Cartesian sampling trajectory corresponding to the actual sampling trajectory, and each adjacent sampling point corresponding to each target calculation sampling point may also be a non-Cartesian point or a Cartesian point; that is, in some embodiments, the trajectory of the actual sampling point is obtained; the actual sampling point trajectory is interpolated on the standard Cartesian sampling trajectory to obtain an interpolated trajectory, the target calculation sampling point is a non-Cartesian point or a Cartesian point in the interpolation trajectory, and the adjacent sampling points are non-Cartesian points and Cartesian points within the width range of a preset interpolation kernel function; it should be noted that, assuming that the readout gradient intensity G in the radial direction changes with time t and is recorded as G(t), the trajectory of the actual sampling point in the corresponding radial direction can be expressed as The method of interpolating the actual sampling point trajectory to the standard Cartesian sampling trajectory to obtain the interpolation trajectory can be implemented by using the existing spatial interpolation or gridding interpolation based on the Voronoi diagram (Thyssen polygon), which will not be described in detail here.

[0043] In order to facilitate the understanding of the radial sampling density acquisition process of the above target calculation sampling points, the following is an example of the interpolation weight calculation scenario when the preset interpolation kernel function is a trigonometric function:

[0044] Assuming that the preset interpolation kernel function is a trigonometric function and the corresponding width range is recorded as kwidth, the principle of grid interpolation is as follows: Figure 7 As shown in the figure, the solid red dots represent Cartesian grid points, and the solid black dots represent non-Cartesian grid points. Grid-based interpolation is to use the values ​​of the black grid points actually collected to interpolate the values ​​of the red grid points, where the width range of the preset interpolation kernel function is the radius of the circle in the figure, and the vertical height from the point to the cone surface is the weight. It can be understood that the values ​​of non-Cartesian points close to the Cartesian grid points are interpolated with higher weights. Figure 7 In the figure, the kwidth of the central Cartesian point corresponds to three non-Cartesian points, and their corresponding weights are w1, w2, and w3 as shown by the blue arrows. Assuming that the values ​​of these three non-Cartesian points are p1, p2, and p3, the corresponding interpolated Cartesian point values ​​are w1*p1+w2*p2+w3*p3. This interpolation method is similar to convolution and can also be called a convolution kernel. Conversely, non-Cartesian points can also be represented by points on the Cartesian trajectory or other non-Cartesian points in this way. Based on this, the interpolation attribute values ​​of each target calculation sampling point based on grid interpolation can be obtained.

[0045] A similar interpolation processing process based on the above-mentioned method for obtaining the interpolation attribute values ​​of each target calculation sampling point can obtain the sampling density of each target calculation sampling point, that is, it is necessary to calculate how many points (adjacent sampling points) are collected within kwidth for each target calculation sampling point (which may be a non-Cartesian point or a Cartesian point), and obtain the distance / weight of each adjacent sampling point to the target calculation sampling point through a preset interpolation kernel function, and add up the approximate estimated value of the sampling density of the target calculation sampling point, so as to obtain the radial sampling density of each target calculation sampling point.

[0046] According to the inverse of the radial sampling density of each target calculation sampling point, the density compensation correction function of each target calculation sampling point in the radial direction is obtained; that is, the density compensation correction function of each target sampling point in its radial direction can be expressed as:

[0047]

[0048] In the formula, Indicates that the sampling radius is r j The corresponding target calculation sampling point j in the radial direction of the density compensation correction value; ∑ i f(r j -r i ) indicates that the sampling radius is rj The goal is to calculate the radial sampling density corresponding to the sampling points.

[0049] In practical applications, the width range (kwidth value) of the above-mentioned preset interpolation kernel function can in principle be set according to the actual application requirements (at least 1 grid point interval), taking into account that the wider the width range, the more accurate the interpolation but the higher the calculation complexity, and the smaller the width range, the smaller the calculation complexity but the larger the interpolation error, in some embodiments, the width range is twice the interval between Cartesian points in the standard Cartesian sampling trajectory.

[0050] After obtaining the density compensation correction function corresponding to a target calculation sampling point on a spoke in k-space through the above method steps, the density compensation correction function of each target calculation sampling point on the same spoke can be obtained through the above method, that is, the density compensation correction function of the sampling points corresponding to different sampling radii on the same spoke can be obtained based on the same density compensation correction function expression, the only difference is that ∑ i f(r j -r i ) needs to be calculated based on the actual situation of each target sampling point j. Then, for each spoke in the initial k-space data, assuming that there are N read radial sampling points, the corresponding density compensation correction function in the radial direction of the entire spoke can be understood as an N-dimensional density compensation correction function with each target calculation sampling point as its element. read *1 column vector, which can be expressed as:

[0051]

[0052] In the formula, The jth element in the density compensation correction function in the radial direction of the entire spoke is the density compensation correction value in the radial direction of the target calculation sampling point corresponding to the jth sampling radius on the spoke. It should be noted that, from formula (1), it can be seen that the computational complexity corresponding to formula (2) is calculated by N in the traditional density compensation calculation. read *N read Reduce to N read *N kern , where N kern Indicates the number of sampling points in the area with the highest sampling density in the radial direction within the width range of the preset interpolation kernel function (N kern < <N read ), which significantly reduces the computational complexity of density compensation in the radial direction, thereby ensuring the improvement of density compensation efficiency in this direction.

[0053] When the sampling gradients on the spokes in k-space are the same, the distribution pattern of the sampling points is consistent. After obtaining the column vector corresponding to the density compensation correction function in the radial direction of the entire spoke based on the above method, the density compensation correction function in the radial direction of other spokes can be obtained by the same method, and then the density compensation correction function in the radial direction in k-space can be expanded by the following method.

[0054] In some embodiments, the sampling points on each spoke in the k-space have a consistent distribution pattern, the target calculation sampling point is a non-Cartesian point in the interpolation trajectory, and based on the density compensation correction function of the target calculation sampling point on a single spoke in the k-space in the radial direction and the number of spokes in the k-space, a density compensation correction function matrix in the radial direction in the k-space is obtained; that is, assuming that the number of spokes in the k-space is N spoke , then the density compensation correction function matrix in the radial direction of k-space can be expressed as:

[0055]

[0056] In the formula, DCF radial_mod N represents the density compensation correction matrix in the radial direction of k-space; read Indicates the total number of sampling points in the radial direction; N spoke Represents the total number of spokes in k-space.

[0057] In some embodiments, the target calculation point is a Cartesian point in the interpolation trajectory, and based on the density compensation correction function of the target calculation sampling point on a single spoke of the standard Cartesian sampling trajectory in the radial direction and the number of spokes in the k-space, a density compensation correction function matrix in the radial direction in the k-space is obtained; it should be noted that in this case, the density compensation correction function matrix in the radial direction in the k-space can also obtain a similar result as shown in formula (3), and the difference between the two is only that the parameters used in the calculation of the element values ​​in the column vector shown in formula (2) are different, which will not be described in detail here.

[0058] In some embodiments, Figure 4 As shown, the non-uniform radial sampling type is non-uniform acquisition in the angular direction. When the radial direction is uniformly acquired, the density compensation correction function is the density compensation correction function in the angular direction; that is, when the non-uniform radial sampling only has non-uniformity in the angular direction, the number of sampling points in the angular direction of different radii is exactly the same, and the corresponding density compensation correction only needs to consider the density compensation correction in the angular direction dimension.

[0059] Considering that in practical applications, the spacing angles between spokes in k-space are usually affected by anisotropic imaging field of view and resolution parameters, that is, when performing density compensation in the angular direction, it can be processed based on the size of the imaging field of view area or the sampling density. In some embodiments, the density compensation correction function in the angular direction is obtained in the following manner:

[0060] Based on the k-space size and the angular coordinates of each target calculation spoke, the sampling angle field of view of each target calculation spoke in the k-space at the current angular coordinate is obtained; wherein the k-space size can be understood as the maximum imaging area range of the k-space, and the angular coordinates of each target calculation spoke in the k-space vary depending on the actual sampling dimension; similarly, the method for obtaining the sampling angle field of view of each target calculation spoke at the corresponding angular coordinates under different sampling dimensions is also different.

[0061] In some embodiments, when the non-uniform radial sampling is a two-dimensional acquisition, the angular coordinates of the target calculation spokes are based on a two-dimensional rectangular coordinate system with the center of the k-space as the origin, and the angle between the target calculation spokes and a coordinate axis in the two-dimensional rectangular coordinate system; wherein the two-dimensional acquisition can be understood as a 2D radial acquisition, and the corresponding angular coordinates of the target calculation spokes can be understood as Figure 8 The angle φ between the spokes shown and the reference coordinate axis.

[0062] In practical applications, there are two types of angular non-uniformity in two-dimensional radial acquisition, one is the radial acquisition scene of anisotropic field of view (FOV), and the other is the motion state reconstruction scene based on motion binning technology. In order to ensure that the sampling density in the above two angular non-uniform scenes of two-dimensional radial sampling can be effectively compensated to ensure higher image reconstruction quality, the present invention provides corresponding sampling angle field of view area calculation methods for the two scenes, respectively, to provide reliable technical support for sampling angle density compensation based on imaging field of view area.

[0063] In some embodiments, Figure 8 As shown, when the imaging area of ​​the non-uniform radial sampling is elliptical, the sampling angle field of view is obtained in the following manner:

[0064] Based on the angular coordinates of each of the target calculation spokes and the major axis and minor axis of the ellipse, the sampling angle field of view of each of the target calculation spokes is obtained; wherein the sampling angle field of view is as follows: Fig. 9 The figure can be understood as the length through the center of the circle under the angular coordinate φ of the target calculation spoke, that is, the FOV in this angular direction; when the major axis of the imaging area ellipse is x, the minor axis is y, and the angle between the target calculation spoke and the major axis is φ, the FOV in this spoke sampling direction can be obtained by calculation:

[0065] Based on the inverse of the sampling angle field of view of each target calculation spoke, a density compensation correction function of the angular direction of each target calculation spoke is obtained; wherein, after the sampling angle field of view of each target calculation spoke is obtained through the above steps, based on the k-space sampling theorem (full sampling condition: the angular direction sampling density is equal to the inverse of the corresponding sampling angle field of view to ensure that image aliasing does not occur), the unit arc length formula can be obtained Among them, Δk φ like Figure 8 The figure can be understood as the angular spacing between two spokes, Δk φ The larger the spoke is, the larger the distance between the spokes and the spokes on both sides is, the lower the sampling density in the corresponding angular direction is; that is, according to Δk φ The density compensation in the angular direction is performed according to the size of , and the density compensation correction function in the angular direction of the corresponding target calculation spoke can be expressed as:

[0066]

[0067] In the formula, The angle between the major axis of the ellipse and the m The density compensation correction value in the angular direction corresponding to the spoke m. As can be seen from formula (4), its calculation complexity is calculated by N in the traditional density compensation calculation. spoke *N spoke Reduce to N spoke , which significantly reduces the computational complexity of density compensation in the angular direction of two-dimensional sampling, and can effectively ensure the improvement of density compensation efficiency in the angular direction of two-dimensional sampling.

[0068] It should be noted that for non-uniform radial sampling, the imaging area is more generally circular or square (approximately), and the length through the center of the circle in each angular direction is the same. It can be considered that the sampling angle field of view corresponding to each angle is the same, that is, there is no problem of angular non-uniformity, and there is no need to use the above method to perform density compensation in the angular direction.

[0069] In some embodiments, Fig. 9 As shown, the non-uniform radial sampling is sampling in different motion states, that is, the spokes collected in the same motion state are selected from all the acquired spokes (such as the blue spokes in the left figure) and arranged according to the angular coordinates to obtain the angular non-uniform k-space data shown in the right figure, and then the magnetic resonance image is reconstructed. The corresponding angular density compensation correction function is obtained in the following way:

[0070] Based on the interpolation weight accumulation value of the angular coordinates of all adjacent spokes corresponding to the angular coordinates of each target calculation spoke in the k-space data under the target motion state within the width range of the preset interpolation kernel function, the angular sampling density of each target calculation spoke is obtained; wherein, the target motion state can be understood as a certain motion state that needs to be analyzed, which can be determined according to actual application requirements. The target calculation spoke can be understood as each spoke in the k-space data under the target motion state that needs to be compensated for angular density; the preset interpolation kernel function is a function used to determine the contribution weight of each adjacent spoke of the target calculation spoke to the density calculation of the target calculation spoke, as mentioned above, and can also be selected and set according to actual application requirements, and is not specifically limited here. The width range of the corresponding preset interpolation kernel function can be understood as a reference range for determining the angular sampling density of each target calculation spoke, and the adjacent spokes used to calculate the angular sampling density can be determined accordingly. The interpolation weights of each adjacent spoke within the width of the preset interpolation kernel function of each target calculation spoke are set based on the phase difference between the angular coordinates of the adjacent spokes and the angular coordinates of the target calculation spoke. The corresponding angular direction sampling density of each target calculation spoke can be expressed as is the expression of the preset interpolation kernel function, and the independent variable x is Fig. 9 Shown is the interval θ between adjacent spokes and the target calculation spoke (solid line spoke) i , the dependent variable w represents the independent variable θ i Corresponding interpolation weight. Based on the expression of the angular sampling density corresponding to the target calculation spoke, it can be seen that if a target calculation spoke has multiple adjacent spokes within the width range of the preset interpolation kernel function, the greater the cumulative value of the interpolation weight corresponding to the target calculation spoke, that is, the greater the sampling density of the target calculation spoke.

[0071] Based on the inverse of the angular sampling density of each target calculation spoke, a density compensation correction function of the angular direction of each target calculation spoke is obtained; wherein, after the angular sampling density of each target calculation spoke is obtained through the above steps, it can be calculated according to The density compensation in the angular direction is performed according to the size of , and the density compensation correction function in the angular direction of the corresponding target calculation spoke can be expressed as:

[0072]

[0073] In the formula, The angle between the reference axis and the reference coordinate axis is φ m Density compensation correction value in the angular direction corresponding to spoke m; θ l represents the angular coordinate interval between the adjacent spokes and the target calculation spoke. From formula (5), it can be seen that its computational complexity is calculated by N in the traditional density compensation calculation. spoke *N spoke Reduce to Nspoke *N kern , where N kern Represents the number of spokes (N) in the area with the highest sampling density in the angular direction within the width of the preset interpolation kernel function. kern < <N spoke ), which significantly reduces the computational complexity of density compensation in the angular direction, thereby ensuring the improvement of the density compensation efficiency in the angular direction.

[0074] For each spoke in the initial k-space data, when the imaging area is an elliptical scene or a split-motion reconstruction scene, the density compensation correction function of the angular direction on different spokes in the corresponding sampling scene can be used to obtain it. That is, each spoke in the elliptical scene can be obtained based on the formula shown in formula (4), and each spoke in the split-motion reconstruction scene can be obtained based on the formula shown in formula (5). The difference between the density compensation function in the angular direction applied to each spoke is that the parameters in the formula vary depending on the spoke. Based on this, the density compensation correction function in the angular direction of all spokes in the entire k-space can be expanded to 1*N spoke The row vector of can be expressed as:

[0075]

[0076] In the formula, Represents the angular coordinate as φ m Density compensation correction value of the angular direction of spoke m.

[0077] In addition, the angular density compensation correction functions shown in the above equations (4) and (5) are the same for all sampling points on the same radial direction (spoke) in k-space. Assuming that the number of radial sampling points is Nread, the angular density compensation of all sampling points on the same spoke can be understood as repeating N times according to the same compensation value. read times, the computational complexity is only N spoke Based on this, the density compensation correction function matrix of the angular direction of the entire k-space shown in equation (7) can be obtained:

[0078]

[0079] Among them, DCF angular_mod N represents the density compensation correction matrix in the angular direction of k-space; read Indicates the total number of sampling points in the radial direction; N spoke Represents the total number of spokes in k-space.

[0080] The non-uniformity of the angular direction of each spoke in the k-space in a three-dimensional acquisition scenario is mainly affected by its angular coordinates in the three-dimensional rectangular coordinate system with the center of the k-space as the origin. In some embodiments, when the non-uniform radial sampling is three-dimensional acquisition, the angular coordinates of the target calculated spokes are based on the three-dimensional rectangular coordinate system with the center of the k-space as the origin, the first angle between the target calculated spoke and a coordinate plane in the three-dimensional rectangular coordinate system, and the second angle between the projection of the target calculated spoke in the coordinate plane and a coordinate axis of the coordinate plane; that is, the angular coordinates of the target calculated spokes of the three-dimensional acquisition include Fig.11 The angle between the spokes shown and the xoy plane And the angle θ between the projection of the spoke on the xoy plane and the x-axis.

[0081] Taking into account that the sampling density in the angular direction of three-dimensional sampling in practical applications is affected by the anisotropic imaging field of view, density compensation in the angular direction can be performed based on the size of the imaging field of view at the sampling angle. Similar to the case of two-dimensional sampling, the imaging area is a more general sphere, cube or cuboid (approximately), and the size of the imaging field of view in each angular direction is the same, that is, there is no problem of angular non-uniformity, and there is no need to perform density compensation in the angular direction. Based on this, the angular density compensation under three-dimensional sampling considers the scene of the ellipsoidal imaging area with angular non-uniformity; in some implementations, when the imaging area of ​​the non-uniform radial sampling is an ellipsoid, the sampling angle field of view is obtained in the following manner:

[0082] Based on the angular coordinates of each of the target calculation spokes, and the major axis, minor axis and intermediate axis of the ellipsoid, the sampling angle field of view of each of the target calculation spokes is obtained; wherein the sampling angle field of view can be understood as the angular coordinates of the target calculation spoke The length of the ball passing through the center of the sphere is the FOV in this angular direction; Fig.10 As shown in the figure, when the major axis of the imaging area ellipsoid is x, the minor axis is y, and the length of the third axis perpendicular to the plane where the major axis and the minor axis are located is c, the FOV in this spoke sampling direction can be obtained by calculation:

[0083] Similarly, the coordinates of the lower corner of the three-dimensional sampling are The target calculation spoke angular direction density compensation correction function is expressed as:

[0084]

[0085] In the formula, The angular coordinates are The density compensation correction value in the angular direction corresponding to the spoke n is calculated by the complexity of N in the traditional density compensation calculation.spoke *N spoke Also reduced to N spoke , which significantly reduces the computational complexity of density compensation in the angular direction of three-dimensional sampling, and can effectively ensure the improvement of density compensation efficiency in the angular direction of three-dimensional sampling.

[0086] It should be noted that for all spokes in k-space, the corresponding angular coordinates can be used to calculate the density compensation correction value in the corresponding angular direction; and assuming that the total number of sampling points on the same spoke is N read , then N on the same spoke read The density compensation correction values ​​in the angular direction corresponding to different sampling points are the same; extending it to the density compensation correction calculation of all sampling points in the entire k-space, the density compensation function matrix (N) in the angular direction of the entire k-space shown in formula (7) can also be obtained read *N spoke ), which will not be described here.

[0087] In some embodiments, when the non-uniform radial sampling type is non-uniform acquisition in the radial direction or non-uniform acquisition in the angular direction, the density compensation correction function is the product of the density compensation correction function in the angular direction and the density compensation correction function in the radial direction; that is, the density compensation correction function of the sampling point of non-uniform acquisition in the radial direction or non-uniform acquisition in the angular direction can be understood as the product of the density compensation correction function of the target sampling point in its radial direction shown in formula (1) and the density compensation correction function of the target sampling point in its angular direction shown in formula (4) or formula (5). The calculation complexity of the above-mentioned density compensation correction function in the radial direction is N read *N kern The computational complexity of the angular density compensation correction function is N spoke , the computational complexity of the density compensation correction function for radial non-uniform acquisition and angular non-uniform sampling points is N read *N kern +N spoke .

[0088] Similarly, corresponding to all sampling points in the entire k-space, the density compensation correction function can actually be understood as including N read *N spoke The density compensation correction function matrix of the k-space in the radial direction shown in equation (3) and the density compensation correction function matrix in the angular direction of the entire k-space shown in equation (7) are obtained by dot multiplication. read *N spoke dimensional matrix, and each element value in the matrix is ​​the product of equation (1) and equation (4), or the product of (1) and equation (5), which will not be repeated here.

[0089] S3. Based on the density compensation correction function corresponding to the non-uniform radial sampling type and the basic density compensation function corresponding to the density compensation correction function under the same non-uniform radial sampling type, the density compensation function of the initial k-space data is obtained; wherein, the density compensation function of any sampling point in the initial k-space data can be understood as a density compensation function obtained by weighted correction of the basic density compensation function that is uniform in both radial and angular directions based on the specific non-uniform radial sampling type using the corresponding density compensation correction function.

[0090] In some embodiments, the density compensation function of the initial k-space data is obtained based on the product of the density compensation correction function corresponding to the non-uniform radial sampling type and the basic density compensation function corresponding to the density compensation correction function under the same non-uniform radial sampling type; wherein the density compensation function of any sampling point in the initial k-space data can be understood as the product obtained by multiplying the corresponding density compensation correction function with the basic density compensation function that is uniform in radial and angular directions based on the specific non-uniform radial sampling type, including N read *N spoke Matrix of density compensation values ​​of elements:

[0091] 1) When the non-uniform radial sampling type is non-uniform in the radial direction and uniform in the angular direction, the density compensation function matrix of all sampling points in the entire k-space is DCF uniform .*DCF radial_mod , where DCF uniform Represents the basic density compensation function matrix of all sampling points in the entire k-space that is uniform in both radial and angular directions; DCF radial_mod Represents the density compensation correction function matrix in the radial direction of the entire k-space;

[0092] 2) When the non-uniform radial sampling type is non-uniform in the angular direction and uniform in the radial direction, the density compensation function matrix of all sampling points in the entire k-space is DCF angular_mod .*DCF uniform , where DCF uniform Represents the basic density compensation function matrix of all sampling points in the entire k-space that is uniform in both radial and angular directions; DCF angular_mod Represents the density compensation correction matrix in the angular direction of the entire k-space;

[0093] 3) When the non-uniform radial sampling type is non-uniform in the radial direction and non-uniform in the angular direction, the density compensation function matrix of all sampling points in the entire k-space is DCF angular_mod .*DCF radial_mod .*DCF uniform ; Among them, DCF uniformRepresents the basic density compensation function matrix of all sampling points in the entire k-space that is uniform in both radial and angular directions; DCF angular_mod Represents the density compensation correction matrix in the angular direction of the entire k-space; DCF radial_mod Represents the density compensation correction function matrix in the radial direction of the entire k-space.

[0094] Based on the characteristic that the sampling density of the sampling points of the conventional radial acquisition that is uniform in both the angular and radial directions is inversely proportional to the size of the sampling radius, the corresponding basic density compensation function can be designed based on the principle that the sampling density compensation should be proportional to the sampling radius. Considering that the sampling density in the angular direction in the case of two-dimensional acquisition is obtained based on the distribution of sampling points on the circumference of the sampling radius, in order to maximize the calculation efficiency, in some embodiments, the basic density compensation function when the non-uniform radial sampling is two-dimensional acquisition is directly set to an identity function with the distance between the sampling point and the center of the k-space as the independent variable, that is, in, represents the distance between the two-dimensional sampling point d1 and the center of k-space in a two-dimensional rectangular coordinate system with the center of k-space as the origin; abs(·) represents the absolute value function; Represents the basic density compensation function corresponding to the two-dimensional sampling point d1.

[0095] Similarly, considering that the sampling density in the angular direction under three-dimensional acquisition is obtained based on the distribution of sampling points on the circular surface of the sampling radius, in order to maximize the calculation efficiency, in some embodiments, the basic density compensation function when non-uniform radial sampling is used for three-dimensional acquisition is directly set to a square function with the distance between the sampling point and the center of the k-space as the independent variable, that is, in, represents the distance between the three-dimensional sampling point d2 and the center of k-space in the three-dimensional rectangular coordinate system with the center of k-space as the origin; abs(·) represents the absolute value function; Represents the basic density compensation function corresponding to the three-dimensional sampling point d2.

[0096] S4. Density compensation is performed on the initial k-space data based on the density compensation function of the initial k-space data to obtain compensated k-space data; wherein, after the density compensation function of the initial k-space data is obtained through the above-mentioned method steps, the corresponding compensated k-space data can be obtained by multiplying the obtained values ​​of each k-space sampling point with the corresponding density compensation function value.

[0097] S5. Generate a corresponding magnetic resonance image based on the compensated k-space data and a preset reconstruction algorithm; wherein the preset reconstruction algorithm can be selected according to actual application requirements, such as grid-based reconstruction, deep learning-based reconstruction, and compressed sensing-based reconstruction, etc. The specific magnetic resonance image reconstruction process can refer to the existing technology related to the selected preset reconstruction algorithm, which is not described in detail here.

[0098] In a magnetic resonance image reconstruction method for non-uniform radial sampling provided by an embodiment of the present invention, a fast density compensation function calculation method applicable to 2D radial, stack of radial and kooshball 3D radial is designed by utilizing the characteristic that the number of acquisition points in the angular direction of different sampling radii in radial acquisition is exactly the same. As long as the amplitude-time curve of the readout gradient synthesis of each spoke is the same, the method can be directly used to perform fast density compensation calculation on the k-space data obtained by non-uniform radial sampling, and the calculation complexity of the density compensation algorithm is reduced from N of the traditional Voronoi area method to read *N spoke *log(N read *N spoke ) and the iterative optimization point spread function Nread*Nspoke*Nread*Nspoke is reduced to N when only radial non-uniformity exists read *N kern (N kern < <N spoke ), or N when only the angular direction is non-uniform spoke , or N when there is non-uniformity in both radial and angular directions read *N kern +N spoke , greatly improving the calculation speed; at the same time, by comparing the reconstruction quality of the image reconstructed based on the density compensation method provided by the present invention with the image reconstructed after compensation only according to the basic density compensation function, the reconstruction quality is obtained. Fig.11 From the results shown, it can be found that the image reconstruction method provided by the present invention makes the brightness of the image more uniform; that is, the method of the present invention can effectively improve the reconstruction efficiency while ensuring the reconstruction quality.

[0099] It should be noted that although the steps in the above flowchart are shown in sequence according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders.

[0100] like Fig.12 As shown, the present invention provides a magnetic resonance image reconstruction device with non-uniform radial sampling, the device comprising:

[0101] A non-uniform radial sampling module 1, used for acquiring initial k-space data in a non-uniform radial sampling mode;

[0102] A compensation correction function acquisition module 2 is used to obtain a dimensional density compensation correction function corresponding to the non-uniform radial sampling type based on the non-uniform radial sampling type;

[0103] A density compensation correction module 3, configured to obtain a density compensation function of the initial k-space data based on a density compensation correction function corresponding to the non-uniform radial sampling type and a basic density compensation function corresponding to the density compensation correction function under the same non-uniform radial sampling type;

[0104] A density compensation module 4 is used to perform density compensation on the initial k-space data based on the density compensation function of the initial k-space data to obtain compensated k-space data;

[0105] The image reconstruction module 5 is used to generate a corresponding magnetic resonance image based on the compensated k-space data and a preset reconstruction algorithm.

[0106] For the specific definition of the magnetic resonance image reconstruction system with non-uniform radial sampling, please refer to the definition of the magnetic resonance image reconstruction method with non-uniform radial sampling above, and the corresponding technical effects can also be obtained equivalently, which will not be repeated here. Each module in the above-mentioned magnetic resonance image reconstruction system with non-uniform radial sampling can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0107] In some embodiments, the present invention provides a magnetic resonance imaging system, characterized in that the magnetic resonance imaging system includes an imaging controller; the imaging controller includes a processor and a memory, the processor and the memory are coupled, the memory is used to store computer programs or instructions, and the processor is used to execute the computer program or instructions in the memory, so that the imaging controller performs the steps of the above-mentioned non-uniform radial sampling magnetic resonance image reconstruction method.

[0108] In some embodiments, the present invention provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the above-mentioned non-uniform radial sampling magnetic resonance image reconstruction method when executed by a processor.

[0109] In summary, the embodiments of the present invention provide a method, device, imaging system and medium for magnetic resonance image reconstruction with non-uniform radial sampling. By utilizing the characteristic that the number of acquisition points in the angular direction of different sampling radii in radial acquisition is exactly the same, a method for fast density compensation reconstruction of k-space data obtained by non-uniform radial sampling is designed. By decomposing the multi-dimensional density compensation in k-space into low-dimensional density compensation analysis in the radial and angular directions, the density compensation calculation complexity of the non-uniform radial sampling scenario is effectively reduced, and the compensation calculation speed is increased, thereby effectively improving the reconstruction efficiency while ensuring the quality of magnetic resonance image reconstruction.

[0110] Each embodiment in this specification is described in a progressive manner, and the same or similar parts of each embodiment can be directly referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. It should be noted that the technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the above-mentioned embodiments are not described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0111] The above-mentioned embodiments only express several preferred implementation modes of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this technical field, several improvements and substitutions can be made without departing from the technical principle of the present invention, and these improvements and substitutions should also be regarded as the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be based on the protection scope of the claims.

Claims

1. A magnetic resonance image reconstruction method with non-uniform radial sampling, characterized in that: The method comprises the following steps: Acquire initial k-space data of non-uniform radial sampling; Based on the non-uniform radial sampling type, obtaining a density compensation correction function corresponding to the non-uniform radial sampling type; Obtaining a density compensation function of the initial k-space data based on a density compensation correction function corresponding to the non-uniform radial sampling type and a basic density compensation function corresponding to the density compensation correction function under the same non-uniform radial sampling type; Density compensation is performed on the initial k-space data based on a density compensation function of the initial k-space data to obtain compensated k-space data; A magnetic resonance image is generated based on the compensated k-space data and a preset reconstruction algorithm.

2. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 1, characterized in that: The non-uniform radial sampling type is non-uniform sampling in the radial direction, and when the sampling is uniform in the angular direction, the density compensation correction function is a density compensation correction function in the radial direction.

3. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 1, characterized in that: The non-uniform radial sampling type is non-uniform sampling in the angular direction. When the radial direction is uniformly sampled, the density compensation correction function is a density compensation correction function in the angular direction.

4. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 1, characterized in that: When the non-uniform radial sampling type is non-uniform acquisition in the radial direction or non-uniform acquisition in the angular direction, the density compensation correction function is the product of the density compensation correction function in the angular direction and the density compensation correction function in the radial direction.

5. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 2 or 4, characterized in that: The density compensation correction function in the radial direction is obtained in the following manner: Based on the accumulated interpolation weights of all adjacent sampling points of each target calculation sampling point within the width range of a preset interpolation kernel function, a radial sampling density corresponding to each target calculation sampling point is obtained; wherein the interpolation weights of the adjacent sampling points are set based on the distances between the adjacent sampling points and the target calculation sampling point; According to the inverse of the radial sampling density of each of the target calculation sampling points, a density compensation correction function of each of the target calculation sampling points in the radial direction is obtained.

6. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 5, characterized in that: Obtaining the trajectory of the actual sampling points; interpolating the actual sampling point trajectory with the standard Cartesian sampling trajectory to obtain an interpolated trajectory, wherein the target calculation sampling point is a non-Cartesian point or a Cartesian point in the interpolated trajectory, and the adjacent sampling points are non-Cartesian points and Cartesian points within the width range of a preset interpolation kernel function.

7. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 6, characterized in that: The sampling points on each spoke in the k-space have a consistent distribution pattern, the target calculation sampling point is a non-Cartesian point in the interpolation trajectory, and based on the density compensation correction function of the target calculation sampling point on a single spoke in the k-space in the radial direction and the number of spokes in the k-space, a density compensation correction function matrix in the radial direction in the k-space is obtained.

8. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 6, characterized in that: The target calculation point is a Cartesian point in the interpolation trajectory. Based on the density compensation correction function of the target calculation sampling point on a single spoke of the standard Cartesian sampling trajectory in the radial direction and the number of spokes in the k-space, a density compensation correction function matrix in the radial direction in the k-space is obtained.

9. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 8, characterized in that: The width range is twice the interval between Cartesian points in a standard Cartesian sampling trajectory.

10. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 3 or 4, characterized in that: The density compensation correction function in the angular direction is obtained in the following manner: Based on the k-space size and the angular coordinates of each target calculation spoke, obtaining the sampling angle field of view of each target calculation spoke in the k-space at the current angular coordinate; Based on the inverse of the sampling angle field of view of each of the target calculation spokes, a density compensation correction function in the angular direction of each of the target calculation spokes is obtained.

11. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 10, characterized in that: When the non-uniform radial sampling is a two-dimensional acquisition, the angular coordinates of the target calculation spokes are based on a two-dimensional rectangular coordinate system with the center of the k-space as the origin, and the angle between the target calculation spokes and a coordinate axis in the two-dimensional rectangular coordinate system.

12. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 11, characterized in that: When the imaging area of ​​the non-uniform radial sampling is elliptical, the sampling angle field of view is obtained in the following manner: Based on the angular coordinates of each of the target calculation spokes and the major axis and the minor axis of the ellipse, a sampling angle field of view of each of the target calculation spokes is obtained.

13. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 3 or 4, characterized in that: The non-uniform radial sampling is a motion state sampling, and the density compensation correction function in the angular direction is obtained in the following manner: Based on the interpolation weight accumulation value of the angular coordinates of all adjacent spokes corresponding to the angular coordinates of each target calculation spoke in the k-space data under the target motion state within the width range of the preset interpolation kernel function, the angular direction sampling density of each target calculation spoke is obtained; wherein the interpolation weight of the angular coordinates of the adjacent spokes is set based on the phase difference angle between the angular coordinates of the adjacent spokes and the angular coordinates of the target calculation spoke within the width range of the preset interpolation kernel function; Based on the inverse of the angular sampling density of each of the target calculation spokes, a density compensation correction function of the angular direction of each of the target calculation spokes is obtained.

14. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 10, characterized in that: When the non-uniform radial sampling is a three-dimensional acquisition, the angular coordinates of the target calculation spoke are based on a three-dimensional rectangular coordinate system with the center of the k space as the origin, the target calculation spoke and a first angle between a coordinate plane in the three-dimensional rectangular coordinate system, and the projection of the target calculation spoke in the coordinate plane and a second angle between a coordinate axis of the coordinate plane.

15. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 14, characterized in that: When the imaging area of ​​the non-uniform radial sampling is an ellipsoid, the sampling angle field of view is obtained in the following manner: Based on the angular coordinates of each of the target calculation spokes, and the major axis, minor axis and intermediate axis of the ellipsoid, a sampling angle field of view of each of the target calculation spokes is obtained.

16. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 1, characterized in that: The density compensation function of the initial k-space data is obtained based on the product of the density compensation correction function corresponding to the non-uniform radial sampling type and the basic density compensation function corresponding to the density compensation correction function under the same non-uniform radial sampling type.

17. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 14, characterized in that: When the non-uniform radial sampling is two-dimensional acquisition, the basic density compensation function is an identity function with the distance between the sampling point and the center of the k-space as the independent variable.

18. The magnetic resonance image reconstruction method of non-uniform radial sampling according to claim 14, characterized in that: When the non-uniform radial sampling is three-dimensional acquisition, the basic density compensation function is a square function with the distance between the sampling point and the center of the k-space as the independent variable.

19. A magnetic resonance image reconstruction device with non-uniform radial sampling, characterized in that: The device comprises: A non-uniform radial sampling module, used for acquiring initial k-space data in a non-uniform radial sampling mode; A compensation correction function acquisition module, used for obtaining a dimension density compensation correction function corresponding to the non-uniform radial sampling type based on the non-uniform radial sampling type; A density compensation correction module, configured to obtain a density compensation function of the initial k-space data based on a density compensation correction function corresponding to the non-uniform radial sampling type and a basic density compensation function corresponding to the density compensation correction function under the same non-uniform radial sampling type; A density compensation module, used for performing density compensation on the initial k-space data based on the density compensation function of the initial k-space data to obtain compensated k-space data; An image reconstruction module is used to generate a magnetic resonance image based on the compensated k-space data and a preset reconstruction algorithm.

20. A magnetic resonance imaging system, characterized in that: The magnetic resonance imaging system includes an imaging controller; the imaging controller includes a processor and a memory, the processor and the memory are coupled, the memory is used to store computer programs or instructions, and the processor is used to execute the computer programs or instructions in the memory, so that the imaging controller performs the steps of the magnetic resonance image reconstruction method with non-uniform radial sampling as described in any one of claims 1 to 18.

21. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the magnetic resonance image reconstruction method with non-uniform radial sampling according to any one of claims 1 to 18 are implemented.

Images