Undersampling point recovery method and device in magnetic resonance imaging and magnetic resonance imaging system

Abstract

The embodiment of the invention discloses an under-sampling point recovery method and device in magnetic resonance imaging and a magnetic resonance imaging system. The method comprises the following steps: in the process of performing magnetic resonance scanning on an imaging target, acquiring magnetic resonance signals of each channel in an undersampling mode, and putting the acquired magnetic resonance signals of each channel into a K space of each channel; and for any under-sampling point in the K space of each channel of the imaging target, recovering the under-sampling point by adopting a mode of performing high-order interpolation on the surrounding data points of the under-sampling point. According to the embodiment of the invention, the recovery accuracy of the under-sampling point in MR imaging is improved, so that the quality of the MR image is further improved.

Description

Technical Field

[0001] This invention relates to the field of medical imaging technology, and in particular to a method, apparatus and system for recovering undersampled points in magnetic resonance imaging. Background Technology

[0002] In MR (Magnetic Resonance) imaging, undersampling is usually used when acquiring K-space data in order to speed up the acquisition process. However, if the undersampled K-space data is used directly for image reconstruction, it will lead to image aliasing. Therefore, the undersampled data must be recovered before image reconstruction.

[0003] Figure 1 This is a simplified example of the signal acquisition and image reconstruction process in existing MR imaging. In the diagram, 111 represents fully sampled K-space data, 112 is the image obtained when reconstructing the image from 111, 121 represents undersampled K-space data, 122 is the image obtained when reconstructing the image from 121 (obvious aliasing is visible in 122), 123 is the K-space data obtained after restoring the undersampled points from 121, and 124 is the image obtained when reconstructing the image from 123 (obvious aliasing is no longer visible in 124).

[0004] When using the GRAPPA (GeneRalized Autocalibrating Partially Parallel Acquisitions) method for image reconstruction, undersampled points in K-space are usually recovered by first-order interpolation of the sampling points in the neighborhood. The interpolation factor is calculated from reference data, which is also called ACS (Auto Calibrating Signal).

[0005] In two-dimensional MR imaging, the formula for recovering undersampled points in K-space is shown in the following formula (1):

[0006]

[0007] Where y is the recovered value of any undersampled point in the K-space, and x ijk W is the signal value of any data point within the neighborhood of y in K-space. ijk It is x ijk The interpolation factor is denoted by i, where i represents the readout dimension, N is the size of the neighborhood of y in the readout dimension, j represents the phase encoding dimension, M is the size of the neighborhood of y in the phase encoding dimension, k represents the channel or coil dimension, and K is the size of the neighborhood of y in the channel or coil dimension.

[0008] Figure 2 This diagram illustrates the recovery of undersampled points in K-space during existing 2D imaging. Points 211, 221, and 231 represent the K-space data for channels 1, 2, and 3, respectively. The horizontal direction in K-space is the readout direction, and the vertical direction is the phase encoding direction. Samples are taken along every other line along the phase encoding direction. Figure 2 As shown, 201 points to a sampled point, and 202 points to an undersampled point. Taking the recovery of an undersampled point within 221 as an example, let the green-marked point within 222 be the undersampled point to be recovered. The interpolation range, i.e., the neighborhood of the undersampled point to be recovered, is shown as: 212 (i.e., the interpolation range in channel 1), 222 (i.e., the interpolation range in channel 2), and 232 (i.e., the interpolation range in channel 3). By performing first-order interpolation on the sampled points within 212, 222, and 232, the undersampled point to be recovered can be obtained. Here, 233 represents ACS data, and the interpolation factor can be calculated using the full sampled data within 233.

[0009] Compared to two-dimensional MR imaging, three-dimensional MR imaging adds a layer dimension. Therefore, in three-dimensional MR imaging, the formula for recovering undersampled points in K-space is as shown in the following formula (2):

[0010]

[0011] Where y is the recovered value of any undersampled point in the K-space, and x ijhk W is the signal value of any data point within the neighborhood of y in K-space. ijhk It is x ijhk The interpolation factor is denoted by i, where i represents the readout dimension, N is the size of the neighborhood of y in the readout dimension, j represents the phase encoding dimension, M is the size of the neighborhood of y in the phase encoding dimension, h represents the layer dimension, H is the size of the neighborhood of y in the layer dimension, k represents the channel or coil dimension, and K is the size of the neighborhood of y in the channel or coil dimension.

[0012] In practical applications, formulas (1) and (2) are usually simplified as follows:

[0013]

[0014] Where y is the recovered value of any undersampled point in the K-space, and x p W is the signal value of the p-th data point in the neighborhood of y in K-space. p It is x pThe interpolation factor is p, where p represents the index of the data point in the neighborhood of y, and P is the total number of data points in the neighborhood of y. For two-dimensional MR imaging, P = N*M*K, and for three-dimensional MR imaging, P = N*M*H*K, where N is the size of the neighborhood of y in the readout dimension, M is the size of the neighborhood of y in the phase encoding dimension, K is the size of the neighborhood of y in the channel or coil dimension, and H is the size of the neighborhood of y in the layer dimension.

[0015] In practical applications, the neighborhood for interpolation of undersampled points is usually selected based on experience. For example, for each undersampled point in a two-dimensional K-space, the size of its neighborhood is 5 in the readout dimension and 3 in the phase coding dimension.

[0016] The existing method of using first-order interpolation to recover undersampled points in K-space has the disadvantage that artifacts will exist in the reconstructed image when using this method. Summary of the Invention

[0017] In view of this, the embodiments of the present invention provide, on the one hand, a method and apparatus for recovering undersampled points in MR imaging to improve the accuracy of undersampled point recovery in MR imaging; on the other hand, an MR imaging system is proposed to improve the accuracy of undersampled point recovery in MR imaging.

[0018] A method for recovering undersampled points in magnetic resonance imaging, the method comprising:

[0019] During the magnetic resonance scanning of the imaging target, the magnetic resonance signals of each channel are acquired by undersampling, and the acquired magnetic resonance signals of each channel are placed into the K-space of each channel respectively.

[0020] For any undersampled point in the K-space of each channel of the imaging target, the undersampled point is recovered by performing high-order interpolation on the surrounding data points.

[0021] The method of recovering the undersampled point by performing high-order interpolation on the surrounding data points includes:

[0022] Second-order interpolation is performed on all reference data points of the undersampled point to obtain the recovered signal value of the undersampled point;

[0023] The reference data points are data points located within the preset interpolation range.

[0024] The step of performing second-order interpolation on all reference data points of the undersampled point to obtain the recovered signal value of the undersampled point includes:

[0025] Construct a quadratic function with any reference data point of the undersampled point as the independent variable and a constant term of 0;

[0026] The signal value of each reference data point of the undersampled point is substituted into the quadratic function as the independent variable value to obtain the quadratic function value. The obtained quadratic function values ​​are added together to obtain the recovered signal value of the undersampled point. The preset interpolation range is the preset neighborhood of the undersampled point in the K space of each channel.

[0027] During the magnetic resonance scanning of the imaging target, the magnetic resonance signals of each channel are acquired using an undersampling method, and the acquired magnetic resonance signals of each channel are placed into the K-space of each channel, further including:

[0028] During the magnetic resonance scanning of the imaging target, the automatic calibration signal (ACS) of each channel is acquired through full sampling, and the acquired ACS of each channel is placed into the K-space of each channel.

[0029] The coefficients of the quadratic and linear terms of the quadratic function are obtained as follows:

[0030] Select multiple ACS in the K-space of each channel. For each selected ACS, construct a quadratic equation. Combine all the constructed quadratic equations into a system of quadratic equations. Solve the system of quadratic equations to obtain the coefficients of the quadratic and linear terms of the quadratic function.

[0031] The quadratic equation is constructed as follows:

[0032] Each ACS within the preset neighborhood of the selected ACS is substituted into the quadratic function as the independent variable value to obtain the quadratic function value. The obtained quadratic function values ​​are then added together, and the sum is set to be equal to the selected ACS.

[0033] The step of performing second-order interpolation on all reference data points of the undersampled point to obtain the recovered signal value of the undersampled point includes:

[0034] Construct the following function, which includes: a linear term with any first-class reference data point of the undersampled point as the independent variable; a linear term with any second-class reference data point of the undersampled point as the independent variable; and a quadratic term with the product of any first-class reference data point and any second-class reference data point of the undersampled point as the independent variable;

[0035] Adding the two linear terms and one quadratic term above yields the function.

[0036] All first-type reference data points and all second-type reference data points of the undersampled point are combined in pairs. The signal values ​​of the first-type reference data points and the second-type reference data points of each pair are substituted into the above function to obtain the function values. The function values ​​are then added together to obtain the recovered signal value of the undersampled point.

[0037] The preset interpolation range includes: a preset first interpolation range and a preset second interpolation range. The first type of reference data point is: a data point located within the preset first interpolation range. The preset first interpolation range is: a preset neighborhood of the undersampled point in the K-space of each channel. The second type of reference data point is: a data point located within the preset second interpolation range. The preset second interpolation range is: the area in the K-space of each channel excluding the preset neighborhood.

[0038] During the magnetic resonance scanning of the imaging target, the magnetic resonance signals of each channel are acquired using an undersampling method, and the acquired magnetic resonance signals of each channel are placed into the K-space of each channel, further including:

[0039] During the magnetic resonance scanning of the imaging target, the automatic calibration signal (ACS) of each channel is acquired through full sampling, and the acquired ACS of each channel is placed into the K-space of each channel.

[0040] The coefficients of the two linear terms and the coefficient of the quadratic term of the function are obtained as follows:

[0041] Multiple ACS are selected in the K-space of each channel. For each selected ACS, a quadratic equation is constructed. All the constructed quadratic equations form a system of quadratic equations. The system of quadratic equations is solved to obtain the coefficients of the two linear terms and the coefficient of the quadratic term of the function.

[0042] The quadratic equation is constructed as follows:

[0043] All ACS within the preset first interpolation range and all ACS within the preset second interpolation range of the selected ACS are combined in pairs. The two ACS in each pair are substituted into the above function to obtain the function values. The obtained function values ​​are added together and the sum is set to be equal to the selected ACS.

[0044] An undersampling point recovery device for magnetic resonance imaging, the device comprising:

[0045] The acquisition module is used to: acquire magnetic resonance signals from each channel by undersampling during the magnetic resonance scanning of the imaging target, and put the acquired magnetic resonance signals from each channel into the K-space of each channel respectively;

[0046] The recovery module is used to recover any undersampled point in the K-space of each channel of the imaging target by performing high-order interpolation on the surrounding data points of the undersampled point.

[0047] The recovery module recovers the undersampled point by performing high-order interpolation on the surrounding data points, including:

[0048] Second-order interpolation is performed on all reference data points of the undersampled point to obtain the recovered signal value of the undersampled point;

[0049] The reference data points are data points located within the preset interpolation range.

[0050] The recovery module performs second-order interpolation on all reference data points of the undersampled point to obtain the recovered signal value of the undersampled point, including:

[0051] Construct a quadratic function with any reference data point of the undersampled point as the independent variable and a constant term of 0;

[0052] The signal value of each reference data point of the undersampled point is substituted into the quadratic function as the independent variable value to obtain the quadratic function value. The obtained quadratic function values ​​are added together to obtain the recovered signal value of the undersampled point. The preset interpolation range is the preset neighborhood of the undersampled point in the K space of each channel.

[0053] The acquisition module is further used for:

[0054] During the magnetic resonance scanning of the imaging target, the automatic calibration signal (ACS) of each channel is acquired through full sampling, and the acquired ACS of each channel is placed into the K-space of each channel.

[0055] Furthermore, the coefficients of the quadratic and linear terms of the quadratic function in the recovery module are obtained in the following manner:

[0056] Select multiple ACS in the K-space of each channel. For each selected ACS, construct a quadratic equation. Combine all the constructed quadratic equations into a system of quadratic equations. Solve the system of quadratic equations to obtain the coefficients of the quadratic and linear terms of the quadratic function.

[0057] For each selected ACS, the recovery module constructs a quadratic equation, including:

[0058] Each ACS within the preset neighborhood of the selected ACS is substituted into the quadratic function as the independent variable value to obtain the quadratic function value. The obtained quadratic function values ​​are then added together, and the sum is set to be equal to the selected ACS.

[0059] The recovery module performs second-order interpolation on all reference data points of the undersampled point to obtain the recovered signal value of the undersampled point, including:

[0060] Construct the following function, which includes: a linear term with any first-class reference data point of the undersampled point as the independent variable; a linear term with any second-class reference data point of the undersampled point as the independent variable; and a quadratic term with the product of any first-class reference data point and any second-class reference data point of the undersampled point as the independent variable;

[0061] Adding the two linear terms and one quadratic term above yields the function.

[0062] All first-type reference data points and all second-type reference data points of the undersampled point are combined in pairs. The signal values ​​of the first-type reference data points and the second-type reference data points of each pair are substituted into the above function to obtain the function values. The function values ​​are then added together to obtain the recovered signal value of the undersampled point.

[0063] The preset interpolation range includes: a preset first interpolation range and a preset second interpolation range. The first type of reference data point is: a data point located within the preset first interpolation range. The preset first interpolation range is: a preset neighborhood of the undersampled point in the K-space of each channel. The second type of reference data point is: a data point located within the preset second interpolation range. The preset second interpolation range is: the area in the K-space of each channel excluding the preset neighborhood.

[0064] The acquisition module is further used for:

[0065] During the magnetic resonance scanning of the imaging target, the automatic calibration signal (ACS) of each channel is acquired through full sampling, and the acquired ACS of each channel is placed into the K-space of each channel.

[0066] The coefficients of the two linear terms and the coefficient of the quadratic term of the function in the recovery module are obtained as follows:

[0067] Multiple ACS are selected in the K-space of each channel. For each selected ACS, a quadratic equation is constructed. All the constructed quadratic equations form a system of quadratic equations. The system of quadratic equations is solved to obtain the coefficients of the two linear terms and the coefficient of the quadratic term of the function.

[0068] For each selected ACS, the recovery module constructs a quadratic equation, including:

[0069] All ACS within the preset first interpolation range and all ACS within the preset second interpolation range of the selected ACS are combined in pairs. The two ACS in each pair are substituted into the above function to obtain the function values. The obtained function values ​​are added together and the sum is set to be equal to the selected ACS, thus obtaining a quadratic equation.

[0070] A magnetic resonance imaging system, the system comprising an undersampling point recovery device as described in any of the above magnetic resonance imaging methods.

[0071] In this embodiment of the invention, by performing high-order interpolation on the surrounding data points of any undersampled point in the K-space of each channel of the imaging target, the accuracy of undersampled point recovery in MR imaging is improved, thereby further improving the quality of MR images. Attached Figure Description

[0072] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which will make the above and other features and advantages of the present invention more apparent to those skilled in the art. In the drawings:

[0073] Figure 1 A simplified example diagram illustrating the signal acquisition and image reconstruction process in existing MR imaging.

[0074] Figure 2 This is a schematic diagram illustrating the recovery of undersampled points in K-space during existing two-dimensional imaging.

[0075] Figure 3 This is a flowchart of an undersampling point recovery method in MR imaging according to an embodiment of the present invention;

[0076] Figure 4 In this invention, the contribution of points distributed outside the interpolation range is increased to ensure a. i A schematic diagram illustrating the accuracy analysis process;

[0077] Figure 5 This is an example of verifying the effectiveness of the embodiments of the present invention by using MR images of the brain as a reference and combining them with simulated coil diagrams in an application example of the present invention.

[0078] Figure 6 This is a schematic diagram of the undersampling point recovery device in MR imaging provided in an embodiment of the present invention.

[0079] The reference numerals in the attached figures are as follows:

[0080]

[0081]

[0082] Detailed Implementation

[0083] To make the objectives, technical solutions, and advantages of the present invention clearer, the following embodiments are provided to further illustrate the present invention in detail.

[0084] Figure 3This is a flowchart of an undersampling point recovery method in MR imaging according to an embodiment of the present invention. Figure 3 As shown, the specific steps are as follows:

[0085] Step 301: During the MR scanning of the imaging target, the MR signals of each channel are acquired by undersampling, and the acquired MR signals of each channel are placed into the K space of each channel respectively.

[0086] Step 302: For any undersampled point in the K-space of each channel of the imaging target, the undersampled point is recovered by performing high-order interpolation on the surrounding data points.

[0087] After recovering all undersampled points in the K-space, image reconstruction methods such as GRAPPA can be used to reconstruct the K-space data to obtain an MR image.

[0088] In one optional embodiment, in step 302, the undersampled point is recovered by performing high-order interpolation on the surrounding data points of the undersampled point, including: performing second-order interpolation on all reference data points of the undersampled point to obtain the recovered signal value of the undersampled point; wherein, the reference data points are data points located within a preset interpolation range.

[0089] In one optional embodiment, second-order interpolation is performed on all reference data points of the undersampled point to obtain the recovered signal value of the undersampled point. This includes: constructing a quadratic function with any reference data point of the undersampled point as the independent variable and a constant term of 0; substituting the signal value of each reference data point of the undersampled point as the independent variable value of the quadratic function to obtain each quadratic function value; and summing the obtained quadratic function values ​​to obtain the recovered signal value of the undersampled point; wherein, the preset interpolation range is: a preset neighborhood of the undersampled point in the K-space of each channel.

[0090] That is, the undersampled points are recovered using the following formula (4):

[0091]

[0092] Where y is any undersampled point in the K-space of the imaging target; x p W represents the p-th data point within the preset interpolation range of the undersampled point, where 1 ≤ p ≤ P; P is the number of data points within the preset interpolation range of the undersampled point; p H is the coefficient of the linear term. pFor quadratic term coefficients, P = N*M*K for two-dimensional MR imaging and P = N*M*H*K for three-dimensional MR imaging, where N is the size of the preset interpolation range of y in the readout dimension, M is the size of the preset interpolation range of y in the phase encoding dimension, K is the size of the preset interpolation range of y in the channel or coil dimension, and H is the size of the preset interpolation range of y in the layer dimension. It can be seen that W p ·x p +H p ·x p 2 W is a quadratic function with a constant term of 0. p H represents the degree of a linear term. p The coefficient of the quadratic term.

[0093] In an optional embodiment, step 301 further includes: during the MR scanning of the imaging target, acquiring the ACS of each channel through a full sampling method, and placing the acquired ACS of each channel into the K space of each channel;

[0094] The coefficients of the quadratic term and the linear term of the above quadratic function (i.e., H in formula (4)) p and W p The following method is used to obtain the quadratic equations: Select multiple ACS in the K-space of each channel, and construct a quadratic equation for each selected ACS; form a system of quadratic equations from all the constructed quadratic equations; solve the system of quadratic equations to obtain the coefficients of the quadratic and linear terms of the quadratic function.

[0095] In one optional embodiment, a quadratic equation is constructed as follows: for each selected ACS, each ACS in a preset neighborhood of the selected ACS is substituted into the quadratic function as the independent variable value to obtain each quadratic function value. The obtained quadratic function values ​​are added together and the sum is set to be equal to the selected ACS, thereby obtaining a quadratic equation.

[0096] In one optional embodiment, solving the quadratic equation system includes: using a numerical algorithm to solve the quadratic equation system.

[0097] Numerical algorithms include, for example, the conjugate gradient and isogradient descent algorithm.

[0098] In one optional embodiment, second-order interpolation is performed on all reference data points of the undersampled point to obtain the recovered signal value of the undersampled point, including: constructing a function comprising: a linear term with any first-type reference data point of the undersampled point as the independent variable; a linear term with any second-type reference data point of the undersampled point as the independent variable; and a quadratic term with the product of any first-type reference data point and any second-type reference data point of the undersampled point as the independent variable; adding the two linear terms and the quadratic term to obtain the function; and combining all first-type reference data points and all second-type reference data points of the undersampled point in pairs. The signal values ​​of the first type of reference data points and the second type of reference data points in each combination are substituted into the above function to obtain the function values. The obtained function values ​​are then added together to obtain the recovered signal value of the undersampled point. The preset interpolation range includes a preset first interpolation range and a preset second interpolation range. The first type of reference data points are data points located within the preset first interpolation range. The preset first interpolation range is a preset neighborhood of the undersampled point in the K-space of each channel. The second type of reference data points are data points located within the preset second interpolation range. The preset second interpolation range is the region in the K-space of each channel excluding the preset neighborhood.

[0099] That is, the undersampled points are recovered using the following formula (5):

[0100]

[0101] Where y is any undersampled point in the K-space of the imaging target; x p x is the p-th data point within the first preset interpolation range of the undersampled point, where 1 ≤ p ≤ P, and P is the number of data points within the first preset interpolation range of the undersampled point; q W represents the q-th data point within the second preset interpolation range of the undersampled point, where 1 ≤ q ≤ Q, and Q is the number of data points within the preset second interpolation range of the undersampled point. p W q H is the coefficient of the linear term. pq This is the coefficient of the quadratic term. Therefore, W... p ·x p For x p W is a linear term of the independent variable. q ·x q For x q H is a linear term of the independent variable. pq ·x p ·x q For x p and x q The product of these terms is a quadratic term of the independent variable.

[0102] In an optional embodiment, step 301 further includes: during the MR scanning of the imaging target, acquiring the ACS of each channel through a full sampling method, and placing the acquired ACS of each channel into the K space of each channel;

[0103] The coefficients of the two linear terms and the coefficient of the quadratic term of the above function (i.e., W in formula (5)) p W q and H pq The following method is used to obtain the equation: Select multiple ACS in the K space of each channel, and construct a quadratic equation for each selected ACS; form a system of quadratic equations from all the constructed quadratic equations; solve the system of quadratic equations to obtain the coefficients of the two linear terms and the coefficient of the quadratic term of the function.

[0104] In one optional embodiment, the quadratic equation is constructed as follows: For each selected ACS, all ACS within a preset first interpolation range and all ACS within a preset second interpolation range of the selected ACS are combined in pairs. The two ACS in each combination are substituted into the above function to obtain the function values. The obtained function values ​​are added together and the sum is set to be equal to the selected ACS, thereby obtaining the quadratic equation.

[0105] In one optional embodiment, solving the quadratic equation system includes: using a numerical algorithm to solve the quadratic equation system.

[0106] Numerical algorithms include, for example, the conjugate gradient and isogradient descent algorithm.

[0107] In the above embodiments, by performing high-order interpolation on the surrounding data points of any undersampled point in the K-space of each channel of the imaging target, the undersampled point is recovered. This indirectly increases the contribution of the data points outside the neighborhood of the undersampled point to the recovery of the undersampled point, thereby indirectly increasing the size of the reconstruction convolution kernel, improving the accuracy of the recovery of undersampled points in MR imaging, and further improving the quality of MR images.

[0108] Formulas (4) and (5) above are obtained through the following process:

[0109] Let f(s) (s∈[-L,L],L>0) be a continuous signal, then the Fourier transform of f(s) can be expressed as:

[0110]

[0111] Where, k i Let i be the index or position of the i-th signal in the frequency domain, i∈[-M,M],M>0.

[0112] For a digital image f(s) (s∈[-L,L],L>0), the Fourier series of f(s) can be expressed as:

[0113]

[0114] Where n is an integer, b n is a coefficient.

[0115] Substituting equation (7) into equation (6), we get:

[0116]

[0117] because

[0118]

[0119] therefore

[0120]

[0121] Let A in =sinc(π(nk) i Then we have:

[0122]

[0123] a i It can be regarded as the signal value of any data point in the K-space. From equation (8), it can be seen that when a i When unknown, a i By examining the surrounding point b n Perform sinc interpolation (A) in It is obtained by the sinc function.

[0124] At the same time, according to n∈(-∞,∞) in equation (8), it can be seen that: a i This requires sinc interpolation of all other points in the K-space. However, in practical applications, image reconstruction speed needs to be considered. Performing sinc interpolation on all other points in the K-space results in a large computational load and slow reconstruction speed, which is unacceptable in practical applications. Therefore, how can we ensure that a is obtained while reducing the number of points involved in sinc interpolation? i How about accuracy? It can be improved by increasing the distribution across the interpolation range (i.e., a). i The contribution of points outside the preset neighborhood is used to guarantee a. i The accuracy.

[0125] Figure 4 In this invention, by increasing the distribution within the interpolation range (i.e., a) i The contribution of points outside the preset neighborhood is used to guarantee a. iA schematic diagram illustrating the accuracy analysis process. Where: 41, 42, and 43 are undersampled K-space data from a certain channel, then:

[0126] Based on signal recovery theory and equation (8), it can be seen that any point in K space can be obtained by sinc interpolation of other points in K space. For example, the undersampled point 0 marked in green in 41 can be obtained by sinc interpolation of all other points in 41 (i.e., the points in the red box except for the undersampled point) (in this example, it is assumed to be two-dimensional MR imaging and there is only one channel).

[0127] However, in practical applications, considering the reconstruction speed, it is necessary to narrow the interpolation range. The narrowed interpolation range is shown in the red box in 42. Since any point outside the interpolation range of the undersampled point 0, such as points 1 and 2 in 43, can also be approximated by sinc interpolation of the points within their respective interpolation ranges, when calculating the undersampled point 0, if the contribution of the points outside its interpolation range is considered, then the characteristic that the points outside its interpolation range are also obtained by sinc interpolation can be considered. At this time, the superposition phenomenon of sinc functions will occur, and the superposition of sinc functions will produce higher-order terms. Therefore, the recovery formula of the undersampled point in K space can be expressed as shown in the above formula (5):

[0128]

[0129] Specifically, when p = q, the above formula (5) is expressed as the above formula (4):

[0130]

[0131] Figure 5 This is an application example of the present invention, using a brain MR image as a reference and combined with a simulated coil pattern to verify the effectiveness of the embodiments of the present invention. Specifically, 51 is a brain MR image reconstructed using fully sampled K-space data; 521, 531, and 541 are simulated coil patterns with significantly different gains (wherein, the simulated coil pattern of the coil closer to the imaging target has a greater gain); 522 is a brain MR image obtained by undersampling the K-space data acquired by coil a simulated in simulated coil pattern 521 using the sampling mask shown in 55, and then reconstructing the image from the undersampled K-space data; 532 is a brain MR image obtained by undersampling the K-space data acquired by coil b simulated in simulated coil pattern 531 using the sampling mask shown in 55, and then reconstructing the image from the undersampled K-space data; 542 is a brain MR image obtained by undersampling the K-space data acquired by coil c simulated in simulated coil pattern 541 using the sampling mask shown in 55, and then reconstructing the image from the undersampled K-space data.

[0132] 56 is a brain MR image obtained by reconstructing the brain based on the recovered K-space data of coils a, b, and c after recovering the undersampled K-space data acquired by coils a, b, and c using existing first-order interpolation methods. The image reconstruction uses the GRAPPA algorithm, and the interpolation range, i.e. the size of the neighborhood, is P = 3 * 5 * 3. Here, the first 3 is the size of the neighborhood in the readout dimension, the 5 is the size of the neighborhood in the phase encoding dimension, and the second 3 is the size of the neighborhood in the coil dimension.

[0133] 57 is a brain MR image obtained by reconstructing the brain based on the recovered K-space data of coils a, b, and c after recovering the undersampled K-space data acquired by coils a, b, and c using the method provided in this embodiment of the invention. The image reconstruction uses the GRAPPA algorithm, and the interpolation range, i.e. the size of the neighborhood, is P = 3 * 5 * 3. Here, the first 3 is the size of the neighborhood in the readout dimension, the 5 is the size of the neighborhood in the phase encoding dimension, and the second 3 is the size of the neighborhood in the coil dimension.

[0134] Comparing 57 and 56, it can be found that the artifact pointed to by the arrow in 56 has disappeared in 57. That is, the method provided by the embodiments of the present invention can reduce artifacts in MR images.

[0135] Figure 6 This is a schematic diagram of the undersampling point recovery device 60 in MR imaging provided in an embodiment of the present invention. Figure 6 As shown, the device 60 mainly includes: a data acquisition module 61 and a data recovery module 62, wherein:

[0136] The acquisition module 61 is used to: acquire MR signals of each channel by undersampling during the MR scanning of the imaging target, and put the acquired MR signals of each channel into the K space of each channel respectively.

[0137] The recovery module 62 is used to: recover any undersampled point in the K-space of each channel of the imaging target by performing high-order interpolation on the surrounding data points of the undersampled point.

[0138] In one optional embodiment, the recovery module 62 recovers the undersampled point by performing high-order interpolation on the surrounding data points of the undersampled point, including: performing second-order interpolation on all reference data points of the undersampled point to obtain the recovered signal value of the undersampled point; wherein, the reference data points are data points located within a preset interpolation range.

[0139] In one optional embodiment, the recovery module 62 performs second-order interpolation on all reference data points of the undersampled point to obtain the recovered signal value of the undersampled point, including: constructing a quadratic function with any reference data point of the undersampled point as the independent variable and a constant term of 0; substituting the signal value of each reference data point of the undersampled point as the independent variable value of the quadratic function to obtain each quadratic function value; and summing the obtained quadratic function values ​​to obtain the recovered signal value of the undersampled point; wherein, the preset interpolation range is: the preset neighborhood of the undersampled point in the K space of each channel.

[0140] In one optional embodiment, the acquisition module 61 is further configured to: during the MR scanning of the imaging target, acquire the automatic calibration signal ACS of each channel in a full sampling manner, and put the acquired ACS of each channel into the K space of each channel;

[0141] Furthermore, the quadratic and linear coefficients of the quadratic function in the recovery module 62 are obtained as follows: multiple ACS are selected in the K-space of each channel, and a quadratic equation is constructed for each selected ACS; all the constructed quadratic equations form a system of quadratic equations; the system of quadratic equations is solved to obtain the quadratic and linear coefficients of the quadratic function.

[0142] In one optional embodiment, the recovery module 62 constructs a quadratic equation for each selected ACS, including: substituting each ACS in a preset neighborhood of the selected ACS as the independent variable value of the quadratic function to obtain each quadratic function value, adding the obtained quadratic function values, and setting the sum to be equal to the selected ACS, thereby obtaining a quadratic equation.

[0143] In one optional embodiment, the recovery module 62 solves the quadratic equation system by using a numerical algorithm to solve the quadratic equation system.

[0144] In one optional embodiment, the recovery module 62 performs second-order interpolation on all reference data points of the undersampled point to obtain the recovered signal value of the undersampled point, including: constructing a function comprising: a linear term with any first-type reference data point of the undersampled point as the independent variable; a linear term with any second-type reference data point of the undersampled point as the independent variable; and a quadratic term with the product of any first-type reference data point and any second-type reference data point of the undersampled point as the independent variable; adding the above two linear terms and one quadratic term to obtain the function; and performing pairwise interpolation on all first-type reference data points and all second-type reference data points of the undersampled point. The signal values ​​of the first and second types of reference data points in each combination are substituted into the above function to obtain the function values. The obtained function values ​​are then added together to obtain the recovered signal value of the undersampled point. The preset interpolation range includes a preset first interpolation range and a preset second interpolation range. The first type of reference data point is a data point located within the preset first interpolation range, and the preset first interpolation range is a preset neighborhood of the undersampled point in the K-space of each channel. The second type of reference data point is a data point located within the preset second interpolation range, and the preset second interpolation range is the region in the K-space of each channel excluding the preset neighborhood.

[0145] In one optional embodiment, the acquisition module 61 is further configured to: during the MR scanning of the imaging target, acquire the automatic calibration signal ACS of each channel in a full sampling manner, and put the acquired ACS of each channel into the K space of each channel;

[0146] The coefficients of the two linear terms and the coefficient of the quadratic term of the function in recovery module 62 are obtained as follows: Select multiple ACS in the K space of each channel, and construct a quadratic equation for each selected ACS; form a system of quadratic equations from all the constructed quadratic equations; solve the system of quadratic equations to obtain the coefficients of the two linear terms and the coefficient of the quadratic term of the function.

[0147] In one optional embodiment, the recovery module 62 constructs a quadratic equation for each selected ACS, including: combining all ACS within a preset first interpolation range and all ACS within a preset second interpolation range of the selected ACS in pairs, substituting the two ACS in each combination into the above function to obtain function values, adding the obtained function values, and setting the sum to be equal to the selected ACS, thereby obtaining a quadratic equation.

[0148] In one optional embodiment, the recovery module 62 solves the quadratic equation system by using a numerical algorithm to solve the quadratic equation system.

[0149] This invention also provides an MR imaging system, which includes an undersampling point recovery device 60 as described in any of the above MR imaging embodiments.

[0150] It should be noted that the undersampling point recovery method, apparatus, and MR imaging system provided in the embodiments of the present invention can all be methods, apparatus, and systems applied in medical imaging.

[0151] This invention also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement the steps of the undersampling point recovery method in MR imaging as described in any of the above embodiments.

[0152] This invention also provides a computer-readable storage medium storing instructions that, when executed by a processor, can perform the steps of the undersampling point recovery method in MR imaging as described above. In practical applications, the computer-readable medium may be included in the devices / apparatus / systems described above, or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium stores instructions that, when executed by a processor, can perform the steps of the undersampling point recovery method in MR imaging as described above.

[0153] This invention also provides an electronic device. The electronic device may include a processor with one or more processing cores, a memory of one or more computer-readable storage media, and a computer program stored in the memory and executable on the processor. When the program in the memory is executed, the undersampling point recovery method in MR imaging described above can be implemented.

[0154] Those skilled in the art will understand that the features described in the various embodiments and / or claims disclosed in this application can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in this application. In particular, without departing from the spirit and teachings of this application, the features described in the various embodiments and / or claims of this application can be combined and / or combined in various ways, and all such combinations and / or combinations fall within the scope of this application.

[0155] This document uses specific embodiments to illustrate the principles and implementation methods of this application. The descriptions of the embodiments above are only for the purpose of helping to understand the methods and core ideas of this application, and are not intended to limit this application. For those skilled in the art, changes can be made to the specific implementation methods and application scope based on the ideas, spirit and principles of this application. Any modifications, equivalent substitutions, improvements, etc., made should be included within the scope of protection of this application.

Claims

1. A method for point recovery from undersampling in magnetic resonance imaging, characterized in that, The method comprises: In the process of performing magnetic resonance scanning on the imaging target, magnetic resonance signals of each channel are collected by means of under-sampling, and the collected magnetic resonance signals of each channel are respectively put into K spaces of each channel; For any under-sampling point in the K space of each channel of the imaging target, the under-sampling point is recovered by means of high-order interpolation on surrounding data points of the under-sampling point.

2. The method of claim 1, wherein, The under-sampling point is recovered by means of high-order interpolation on surrounding data points of the under-sampling point, comprising: Second-order interpolation is performed on all reference data points of the under-sampling point to obtain a recovered signal value of the under-sampling point. The reference data point is a data point located in a preset interpolation range.

3. The method of claim 2, wherein, The under-sampling point is recovered by means of high-order interpolation on surrounding data points of the under-sampling point, comprising: A quadratic function with any reference data point of the under-sampling point as an independent variable and a constant term of 0 is constructed; The signal value of each reference data point of the under-sampling point is respectively substituted into the quadratic function as an independent variable value of the quadratic function to obtain quadratic function values, and the obtained quadratic function values are added to obtain a recovered signal value of the under-sampling point; wherein the preset interpolation range is a preset neighborhood of the under-sampling point in the K space of each channel.

4. The method of claim 3, wherein, In the process of performing magnetic resonance scanning on the imaging target, magnetic resonance signals of each channel are collected by means of under-sampling, and the collected magnetic resonance signals of each channel are respectively put into K spaces of each channel, further comprising: In the process of performing magnetic resonance scanning on the imaging target, automatic calibration signals ACS of each channel are collected by means of full sampling, and the collected ACS of each channel are put into K spaces of each channel; The quadratic term coefficient and the linear term coefficient of the quadratic function are obtained by the following method: In the K space of each channel, a plurality of ACS are selected, for each selected ACS, a quadratic equation is constructed; all the constructed quadratic equations form a quadratic equation set; the quadratic equation set is solved to obtain the quadratic term coefficient and the linear term coefficient of the quadratic function.

5. The method of claim 4, wherein, The quadratic equation is constructed by the following method: Each ACS in a preset neighborhood of the selected ACS is respectively substituted into the quadratic function as an independent variable value of the quadratic function to obtain quadratic function values, and the obtained quadratic function values are added to be equal to the selected ACS.

6. The method of claim 2, wherein, The under-sampling point is recovered by means of high-order interpolation on surrounding data points of the under-sampling point, comprising: A function is constructed, which includes: a linear term with any first-type reference data point of the under-sampling point as an independent variable; a linear term with any second-type reference data point of the under-sampling point as an independent variable; and a quadratic term with a product of any first-type reference data point and any second-type reference data point of the under-sampling point as an independent variable; The above two linear terms and one quadratic term are added to obtain the function; combining all the first-type reference data points and all the second-type reference data points of the undersampling point two by two, substituting the signal values of the first-type reference data points and the signal values of the second-type reference data points of each combination into the above function respectively, obtaining function values of each combination, and adding the function values to obtain the recovered signal value of the undersampling point; The preset interpolation range includes a preset first interpolation range and a preset second interpolation range, the first-type reference data points are data points located in the preset first interpolation range, the preset first interpolation range is a preset neighborhood of the undersampling point in the K-space of each channel, and the second-type reference data points are data points located in the preset second interpolation range, and the preset second interpolation range is a region other than the preset neighborhood in the K-space of each channel.

7. The method of claim 6, wherein, In the process of performing the magnetic resonance scan on the imaging target, the magnetic resonance signals of the channels are collected in an undersampling manner, and the collected magnetic resonance signals of the channels are respectively placed in the K-space of the channels. In the process of performing the magnetic resonance scan on the imaging target, the automatic calibration signals ACS of the channels are collected in a full sampling manner, and the collected ACS of the channels are placed in the K-space of the channels. The coefficients of the two first-order terms and the coefficient of the second-order term of the function are obtained in the following manner: For each selected ACS, a quadratic equation is constructed, all the constructed quadratic equations are combined to form a quadratic equation group, and the quadratic equation group is solved to obtain the coefficients of the two first-order terms and the coefficient of the second-order term of the function.

8. The method of claim 7, wherein, The quadratic equation is constructed in the following manner: All the ACS in the preset first interpolation range and all the ACS in the preset second interpolation range of the selected ACS are combined two by two, the two ACS of each combination are respectively substituted into the above function to obtain function values, and the function values are added to make the sum equal to the selected ACS.

9. An apparatus for undersampled point restoration in magnetic resonance imaging, characterized by The device comprises: In the process of performing the magnetic resonance scan on the imaging target, the magnetic resonance signals of the channels are collected in an undersampling manner, and the collected magnetic resonance signals of the channels are respectively placed in the K-space of the channels. The recovery module is configured to recover the undersampling point by performing high-order interpolation on the surrounding data points of the undersampling point.

10. The apparatus of claim 9, wherein, The recovery module recovers the undersampling point by performing high-order interpolation on the surrounding data points of the undersampling point, including: performing second-order interpolation on all the reference data points of the undersampling point to obtain the recovered signal value of the undersampling point; The reference data points are data points located in a preset interpolation range.

11. The apparatus of claim 10, wherein, The recovery module performs second-order interpolation on all the reference data points of the undersampling point to obtain the recovered signal value of the undersampling point, including: a quadratic function with any reference data point of the undersampling point as an independent variable and a constant term of 0 is constructed; The signal value of each reference data point of the undersampling point is respectively substituted into the quadratic function as an independent variable value of the quadratic function, to obtain a quadratic function value, and the obtained quadratic function values are added to obtain a recovered signal value of the undersampling point; wherein, the preset interpolation range is: a preset neighborhood of the undersampling point in the K-space of each channel.

12. The apparatus of claim 11, wherein, The acquisition module is further configured to: In the process of performing the magnetic resonance scan on the imaging target, the automatic calibration signals ACS of each channel are acquired by using a full sampling mode, and the acquired ACS of each channel is placed in the K-space of each channel; The quadratic term coefficient and the linear term coefficient of the quadratic function in the recovery module are obtained by the following method: In the K-space of each channel, a plurality of ACS are selected, for each selected ACS, a quadratic equation is constructed; all the constructed quadratic equations form a quadratic equation group; the quadratic equation group is solved to obtain the quadratic term coefficient and the linear term coefficient of the quadratic function.

13. The apparatus of claim 12, wherein, The recovery module, for each selected ACS, constructs a quadratic equation, including: Each ACS in a preset neighborhood of the selected ACS is respectively substituted into the quadratic function as an independent variable value of the quadratic function, to obtain a quadratic function value, and the obtained quadratic function values are added to obtain the selected ACS.

14. The apparatus of claim 10, wherein, The recovery module performs second-order interpolation on all the reference data points of the undersampling point to obtain a recovered signal value of the undersampling point, including: A function is constructed, which includes: a linear term with any first-type reference data point of the undersampling point as an independent variable; a linear term with any second-type reference data point of the undersampling point as an independent variable; and a quadratic term with the product of any first-type reference data point and any second-type reference data point of the undersampling point as an independent variable; The above two linear terms and one quadratic term are added to obtain the function; All the first-type reference data points and all the second-type reference data points of the undersampling point are combined in pairs, the signal value of the first-type reference data point and the signal value of the second-type reference data point of each combination are respectively substituted into the above function to obtain a function value, and the obtained function values are added to obtain a recovered signal value of the undersampling point; Wherein, the preset interpolation range includes: a preset first interpolation range and a preset second interpolation range, the first-type reference data point is a data point located in the preset first interpolation range, the preset first interpolation range is: a preset neighborhood of the undersampling point in the K-space of each channel, the second-type reference data point is a data point located in the preset second interpolation range, and the preset second interpolation range is: a region in the K-space of each channel except the preset domain.

15. The apparatus of claim 14, wherein, The acquisition module is further configured to: In the process of performing the magnetic resonance scan on the imaging target, the automatic calibration signals ACS of each channel are acquired by using a full sampling mode, and the acquired ACS of each channel is placed in the K-space of each channel; The coefficients of the two linear terms and the coefficient of the quadratic term of the function in the recovery module are obtained by the following method: In the K-space of each channel, a plurality of ACS are selected, for each selected ACS, a quadratic equation is constructed; all the constructed quadratic equations form a quadratic equation group; the quadratic equation group is solved to obtain the quadratic term coefficient and the linear term coefficient of the quadratic function. selecting a plurality of ACSs in the K-space of each channel, constructing a quadratic equation for each selected ACS, forming a quadratic equation group with all the constructed quadratic equations, and solving the quadratic equation group to obtain the coefficients of the two linear terms and the coefficient of the quadratic term of the function.

16. The apparatus of claim 15, wherein, The recovery module, for each selected ACS, constructs a quadratic equation, including: combining all ACSs in a preset first interpolation range and all ACSs in a preset second interpolation range of the selected ACSs in pairs, substituting the two ACSs of each combination into the function respectively to obtain function values, adding the obtained function values, and letting the sum equal the selected ACS, thereby obtaining a quadratic equation.

17. A magnetic resonance imaging system, characterized by The system includes the under-sampling point recovery device in magnetic resonance imaging as claimed in any one of claims 9 to 16.

Images