Magnetic Resonance Symmetric Spectrum Non-Uniform Sampling Method, Reconstruction Method and Device

Abstract

The present invention discloses a method, a reconstruction method and a device for non-uniform sampling of magnetic resonance symmetric spectra. By constructing symmetric pairs of magnetic resonance free induction decay signals with uniform intervals and obtaining a first symmetric pair sequence; selecting a number of symmetric pairs from the first symmetric pair sequence at random Poisson intervals to obtain a second symmetric pair sequence; selecting symmetric pairs in the second symmetric pair sequence and randomly sampling one of the data points in the selected symmetric pairs to obtain a sampling result; in response to determining that the selected symmetric pair consists of two cross data points, filling the sampling result at the position of the other data point in the selected symmetric pair to obtain a non-uniformly sampled free induction decay signal, and performing fast reconstruction using the compressed sensing method. The obtained spectral cross peaks are more accurate, solving the problem of insufficient reconstruction accuracy of existing cross peaks, and having simple operation, wide applicability and excellent effects.

Description

Technical Field

[0001] The present invention relates to the field of magnetic resonance spectroscopy, and particularly to a non-uniform sampling method, a reconstruction method and a device for magnetic resonance symmetric spectra. Background Art

[0002] Magnetic resonance symmetric spectra are an important branch of multi-dimensional magnetic resonance spectra, which are a kind of multi-dimensional magnetic resonance spectra with a symmetric structure composed of diagonal peaks and cross peaks, such as Correlated SpectroscopY (COSY), Nuclear Overhauser Enhancement SpectroscopY (NOESY), solid-state carbon-13 correlation spectra based on Dipolar Assisted Rotational Resonance (DARR) or Proton-Driven Spin Diffusion (PDSD), etc., and other higher-dimensional NMR spectra containing symmetric modules. They provide a powerful tool for the structural analysis of biological macromolecules. Non-uniform sampling is an important strategy for accelerating the acquisition of multi-dimensional magnetic resonance spectrum data. By sampling a small number of data points and using algorithms to reconstruct the spectrum. However, existing non-uniform sampling methods for multi-dimensional magnetic resonance spectra (such as random sampling method, traditional Poisson interval sampling method, etc.) cannot efficiently extract the information of magnetic resonance symmetric spectra under non-uniform sampling at a low sampling rate, resulting in the disadvantage of insufficient reconstruction accuracy of cross peaks in the reconstructed spectrum. This affects the actual analysis efficiency of magnetic resonance symmetric spectra. Summary of the Invention

[0003] Aiming at the above-mentioned technical problems, the purpose of the embodiments of the present application is to propose a non-uniform sampling method, a reconstruction method and a device for magnetic resonance symmetric spectra to solve the technical problems mentioned in the above background art part, and is applicable to non-uniform sampling reconstruction of multi-dimensional magnetic resonance spectra with a symmetric structure.

[0004] In a first aspect, the present invention provides a non-uniform sampling method for magnetic resonance symmetric spectra, including the following steps:

[0005] S1, constructing symmetric pairs of magnetic resonance free induction decay signals with uniform intervals and obtaining a first symmetric pair sequence;

[0006] S2, selecting a plurality of symmetric pairs from the first symmetric pair sequence at random Poisson intervals to obtain a second symmetric pair sequence;

[0007] S3, selecting symmetric pairs in the second symmetric pair sequence and randomly sampling one of the data points in the selected symmetric pairs to obtain a sampling result;

[0008] S4. In response to determining that the selected symmetry pair consists of two cross data points, fill the sampling result at the position of the other data point in the selected symmetry pair to obtain a non-uniformly sampled free induction decay signal.

[0009] Preferably, the symmetry pair is composed of f(i,j) and f(j,i), denoted as sp(k), where f(i,j) represents the data point at the i-th row and j-th column in the magnetic resonance free induction decay signal f, and f(j,i) represents the data point at the j-th row and i-th column in the magnetic resonance free induction decay signal f. N is the signal length; the first symmetry pair sequence is {sp(k)} k＝1,2,…,l , l is the length of the first symmetry pair sequence, The second symmetry pair sequence is {sp(k t )} t＝1,…,q , where t represents the t-th selected symmetry pair, and k t represents the serial number of the t-th selected symmetry pair, where t = 1,..., q, and q is the length of the second symmetry pair sequence.

[0010] Preferably, step S2 specifically includes:

[0011] S21. Select the first symmetry pair, let t = 1, and k1 = 1;

[0012] S22. Select a symmetry pair from the first symmetry pair sequence and generate a non-negative random Poisson interval d t , and the formula is as follows:

[0013]

[0014] where α represents the adjustment constant of the sampling density;

[0015] S23. Select the next symmetry pair according to the non-negative random Poisson interval, and the formula is as follows:

[0016] k t+1 = k t + d t + 1;

[0017] S24. Let t = t + 1, and repeat steps S22 - S24 until the serial number of the selected symmetry pair is equal to the length of the first symmetry pair sequence, and output to obtain the second symmetry pair.

[0018] Preferably, step S22 further includes:

[0019] If t > q; then the adjustment constant α is adjusted to 2 times the adjustment constant in the previous iteration process;

[0020] If t < q, then the adjustment constant α is adjusted to 1 / 2 times the adjustment constant in the previous iteration process;

[0021] until t = q.

[0022] In a second aspect, the present invention provides a method for reconstructing a magnetic resonance symmetric spectrum, including the method for non-uniform sampling of a magnetic resonance symmetric spectrum in the first aspect, and further including:

[0023] S5. Reconstruct the magnetic resonance symmetric spectrum from the non-uniformly sampled free induction decay signal by using a compressive sensing soft threshold algorithm.

[0024] Preferably, step S5 specifically includes:

[0025] S51. Input the non-uniformly sampled free induction decay signal y, and let X m represent the output magnetic resonance symmetric spectrum, m represent the iteration number, and r m represent the difference between the non-uniformly sampled free induction decay signal y and the time-domain signal after performing the two-dimensional inverse Fourier transform on X m , S m represent the frequency-domain signal after performing the two-dimensional Fourier transform on the difference. Initialize the parameters, let m = 0, S 0 = F 2D P Ω H y, r 0 = y, X 0 = 0, where Ω is the index set established according to all data points in the first symmetry pair sequence, P Ω is the non-uniform sampling operator, and P Ω H is the adjoint operator of the non-uniform sampling operator;

[0026] S52. Update the threshold of the soft threshold operator during the iteration process: where maxiter is the maximum number of loops;

[0027] S53. Update the output magnetic resonance symmetric spectrum: X m+1 = X m + SHR μ (S m );

[0028] S54. Update the difference: r m+1 = y - P Ω F 2D H X m+1 ;

[0029] S55. Perform a two-dimensional Fourier transform on the difference: S m+1 = F 2D P Ω H r m+1 ;

[0030] S56, let m = m + 1, and repeat steps S52 - S56 until m > maxiter or ‖r m ‖2 < 10 -5 , and output the magnetic resonance symmetric spectrum of the last iteration.

[0031] In a third aspect, the present invention provides a magnetic resonance symmetric spectrum non - uniform sampling device, including:

[0032] A symmetric pair construction module, configured to construct symmetric pairs of uniformly - spaced magnetic resonance free induction decay signals and obtain a first symmetric pair sequence;

[0033] A symmetric pair selection module, configured to select a number of symmetric pairs from the first symmetric pair sequence at random Poisson intervals to obtain a second symmetric pair sequence;

[0034] A sampling module, configured to select symmetric pairs in the second symmetric pair sequence and randomly sample one of the data points in the selected symmetric pairs to obtain a sampling result;

[0035] A filling module, configured to, in response to determining that the selected symmetric pair consists of two cross data points, fill the sampling result at the position of the other data point in the selected symmetric pair to obtain a non - uniformly sampled free induction decay signal.

[0036] In a fourth aspect, the present invention provides a magnetic resonance symmetric spectrum reconstruction device, which is characterized by including the magnetic resonance symmetric spectrum non - uniform sampling device in the third aspect, and further including:

[0037] A spectrum reconstruction module, configured to reconstruct the magnetic resonance symmetric spectrum from the non - uniformly sampled free induction decay signal by using a compressive sensing soft - threshold algorithm.

[0038] In a fifth aspect, the present invention provides an electronic device, including one or more processors; a storage device for storing one or more programs, and when the one or more programs are executed by the one or more processors, enabling the one or more processors to implement the method described in any implementation manner in the first aspect.

[0039] In a sixth aspect, the present invention provides a computer - readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the method described in any implementation manner in the first aspect.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] (1) The present invention effectively combines the symmetry of data and the characteristics of the spectrum sampling template, and can achieve efficient non - uniform sampling of the magnetic resonance symmetric spectrum, thereby enhancing the reconstruction accuracy of cross - peaks.

[0042] (2) The present invention proposes a non-uniform sampling method for magnetic resonance symmetric spectra and uses the compressed sensing method for fast reconstruction. The resulting spectral cross-peaks are more accurate, solving the problem of insufficient reconstruction accuracy of existing cross-peaks.

[0043] (3) The operation of the present invention is simple, has wide applicability, and excellent effects, ultimately realizing fast and high-quality reconstruction of non-uniform sampling of magnetic resonance symmetric spectra. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0045] Figure 1 is an exemplary device architecture diagram to which an embodiment of the present application can be applied;

[0046] Figure 2 is a schematic flowchart of the non-uniform sampling method for magnetic resonance symmetric spectra in the embodiment of the present application;

[0047] Figure 3 is the non-uniform sampling operator P of the non-uniform sampling method for magnetic resonance symmetric spectra in the embodiment of the present application Ω and its adjoint operator P Ω H schematic diagram;

[0048] Figure 4 is the cytomegalovirus m04 protein in the embodiment 13 C- 13 C full-sampling reference spectrogram;

[0049] Figure 5 is the 13 C- 13 C reconstructed spectrogram of 5% non-uniform data of the cytomegalovirus m04 protein using the random sampling method in the embodiment;

[0050] Figure 6 is the 13 C- 13 C reconstructed spectrogram of 5% non-uniformly sampled data of the cytomegalovirus m04 protein using the traditional Poisson interval sampling method in the embodiment;

[0051] Figure 7 is the 13 C- 13 C reconstructed spectrogram of 5% non-uniformly sampled data of the cytomegalovirus m04 protein using the method of the present invention in the embodiment;

[0052] Figure 8 Schematic diagram of the magnetic resonance symmetric spectrum non-uniform sampling device according to an embodiment of the present application;

[0053] Figure 9 It is a schematic structural diagram of a computer device of an electronic device suitable for implementing the embodiments of the present application. Detailed implementation manners

[0054] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0055] Figure 1 An exemplary device architecture 100 is shown that can apply the magnetic resonance symmetric spectrum non-uniform sampling method or the magnetic resonance symmetric spectrum non-uniform sampling device according to the embodiments of the present application.

[0056] As Figure 1 shown, the device architecture 100 may include terminal devices 101, 102, 103, a network 104, and a server 105. The network 104 is used to provide a medium for communication links between the terminal devices 101, 102, 103 and the server 105. The network 104 may include various connection types, such as wired, wireless communication links, or fiber optic cables, etc.

[0057] Users can use the terminal devices 101, 102, 103 to interact with the server 105 through the network 104 to receive or send messages, etc. Various applications, such as data processing applications, file processing applications, etc., may be installed on the terminal devices 101, 102, 103.

[0058] The terminal devices 101, 102, 103 may be hardware or software. When the terminal devices 101, 102, 103 are hardware, they may be various electronic devices, including but not limited to smart phones, tablet computers, laptop portable computers, and desktop computers, etc. When the terminal devices 101, 102, 103 are software, they may be installed in the above-listed electronic devices. It may be implemented as multiple software or software modules (such as software or software modules for providing distributed services), or may be implemented as a single software or software module. No specific limitation is made here.

[0059] The server 105 may be a server that provides various services, such as a background data processing server that processes files or data uploaded by the terminal devices 101, 102, and 103. The background data processing server may process the obtained files or data to generate a processing result.

[0060] It should be noted that the method for non-uniform sampling of magnetic resonance symmetric spectra provided in the embodiments of the present application may be executed by the server 105 or by the terminal devices 101, 102, and 103. Correspondingly, the device for non-uniform sampling of magnetic resonance symmetric spectra may be provided in the server 105 or in the terminal devices 101, 102, and 103.

[0061] It should be understood that Figure 1 the numbers of the terminal devices, network, and server in

[0062] Figure 2 are merely illustrative. According to the implementation requirements, there may be any number of terminal devices, network, and server. In the case where the data to be processed does not need to be obtained remotely, the above device architecture may not include a network, but only a server or a terminal device.

[0063] S1. Construct a symmetric pair of magnetic resonance free induction decay signals with uniform intervals and obtain a first symmetric pair sequence.

[0064] In a specific embodiment, the symmetric pair is composed of f(i,j) and f(j,i), denoted by sp(k), where f(i,j) represents the data point at the i-th row and j-th column in the magnetic resonance free induction decay signal f, and f(j,i) represents the data point at the j-th row and i-th column in the magnetic resonance free induction decay signal f. N is the signal length; the first symmetric pair sequence is {sp(k)} k＝1,2,…,l , l is the length of the first symmetric pair sequence, The second symmetric pair sequence is {sp(k t )} t＝1,…,q , where t represents the t-th selected symmetric pair, and k t represents the serial number of the t-th selected symmetric pair, where t = 1,..., q, and q is the length of the second symmetric pair sequence.

[0065] Specifically, for a uniformly spaced magnetic resonance free induction decay signal f with a signal length of N in both dimensions, sp(k) represents a symmetric pair composed of f(i,j) and f(j,i), where Thus, an ordered first symmetric pair sequence {sp(k)} with a length of is obtained.k＝1,2,…,l 。

[0066] S2. Select several symmetric pairs from the first symmetric pair sequence at random Poisson intervals to obtain a second symmetric pair sequence.

[0067] In a specific embodiment, step S2 specifically includes:

[0068] S21. Select the first symmetric pair, let t = 1, and k1 = 1;

[0069] S22. Select a symmetric pair from the first symmetric pair sequence and generate a non - negative random Poisson interval d t , and the formula is as follows:

[0070]

[0071] where α represents the adjustment constant of the sampling density;

[0072] S23. Select the next symmetric pair according to the non - negative random Poisson interval, and the formula is as follows:

[0073] k t+1 = k t + d t + 1;

[0074] S24. Let t = t + 1, and repeat steps S22 - S24 until the serial number of the selected symmetric pair is equal to the length of the first symmetric pair sequence, and output to obtain the second symmetric pair.

[0075] Specifically, use k t to represent the serial number of the t - th selected symmetric pair, where t = 1, …, q; d t represents the serial number interval between the (t + 1) - th selected symmetric pair and the t - th selected symmetric pair, defined as d t = k t+1 - k t - 1 (if two points are adjacent, the interval is defined as 0); α represents the adjustment constant of the sampling density; let χ be a non - negative integer random variable. If the probability that d t = n, (n = 0, 1, 2, …) satisfies then it is said that χ satisfies the Poisson distribution with parameter β, denoted as χ ~ Poi(β), where,

[0076] In a specific embodiment, step S22 also includes:

[0077] If t > q; then the adjustment constant α is adjusted to 2 times the adjustment constant in the previous iteration process;

[0078] If t < q, then the adjustment constant α is adjusted to 1 / 2 times the adjustment constant in the previous iteration process;

[0079] until \(t = q\).

[0080] Specifically, in each iteration, if \(t>q\), the selected symmetric pairs are relatively dense, so the adjustment constant \(\alpha\) is adjusted to twice the adjustment constant in the previous iteration; if \(t<q\), the selected symmetric pairs are relatively sparse, so the adjustment constant \(\alpha\) is adjusted to 1 / 2 of the adjustment constant in the previous iteration.

[0081] S3. Select symmetric pairs in the second symmetric pair sequence and randomly sample one of the data points in the selected symmetric pairs to obtain a sampling result.

[0082] S4. In response to determining that the selected symmetric pair consists of two cross data points, fill the sampling result at the position of the other data point in the selected symmetric pair to obtain a non-uniformly sampled free induction decay signal.

[0083] Specifically, randomly sample one of the data points in each group of symmetric pairs in \(\{sp(k t )\}\) t＝1,…,q to obtain a sampling result. If the selected symmetric pair consists of two cross data points, fill the sampling result of the sampled data point at the other unsampled data point to obtain an augmented non-uniformly sampled free induction decay signal \(y\). If it is on the diagonal, the selected symmetric pair has only one data point, so it is necessary to determine whether the selected symmetric pair consists of two cross data points.

[0084] The embodiment of the present application also provides a method for reconstructing a magnetic resonance symmetric spectrum, including the above-mentioned non-uniform sampling method for magnetic resonance symmetric spectrum, and further including:

[0085] S5. Reconstruct the magnetic resonance symmetric spectrum from the non-uniformly sampled free induction decay signal by using a compressed sensing soft threshold algorithm.

[0086] In a specific embodiment, step S5 specifically includes:

[0087] S51. Input the non-uniformly sampled free induction decay signal \(y\), let \(X\) m represent the output magnetic resonance symmetric spectrum, \(m\) represent the iteration number, \(r\) m represent the difference between the non-uniformly sampled free induction decay signal \(y\) and the time-domain signal after the inverse two-dimensional Fourier transform of \(X\) m , \(S\) m represent the frequency-domain signal after the two-dimensional Fourier transform of the difference. Initialize the parameters, let \(m = 0\), \(S\) 0 = \(F\) 2D \(P\) Ω H \(y\), \(r\) 0 = \(y\), \(X\) 0= 0, where Ω is the index set established based on all data points in the first symmetry pair sequence, and P Ω is a non-uniform sampling operator, and P Ω H is the adjoint operator of the non-uniform sampling operator;

[0088] S52, update the threshold of the soft threshold operator during the iteration process: where maxiter is the maximum number of loops;

[0089] S53, update the output magnetic resonance symmetry spectrum: X m+1 = X m + SHR μ (S m );

[0090] S54, update the difference: r m+1 = y - P Ω F 2D H X m+1 ;

[0091] S55, perform a two-dimensional Fourier transform on the difference: S m+1 = F 2D P Ω H r m+1 ;

[0092] S56, let m = m + 1, and repeat steps S52 - S56 until m > maxiter or ‖r m ‖2 < 10 -5 , and output the magnetic resonance symmetry spectrum of the last iteration.

[0093] Specifically, the soft threshold operator is:

[0094]

[0095] where sing(.) is the sign function, abs(.) is the absolute value function; μ is the threshold.

[0096] Specifically, in the compressive sensing soft threshold algorithm, P Ω represents a non-uniform sampling operator, where Ω is the index set of all data points in the first symmetry pair sequence, that is, the data points are extracted according to the index set Ω, and after obtaining the data, it is vectorized and output, where the indices in the index set Ω are symmetric structures. For example, in a two-dimensional matrix, if (i, j) belongs to the index, then (j, i) also belongs to the index. P Ω H is the adjoint operator of P Ω , and to clearly illustrate its meaning, take Figure 3 as an example for the non-uniform sampling operator PΩ and its adjoint operator P Ω H is described, where the white squares represent the sampling positions (i.e., the positions indexed by Ω), the gray squares represent the non-sampled positions, and when P Ω acts on the matrix x, it obtains the data points (elements) of x according to the Ω index: x 11 , x 41 , x 32 , x 13 , x 33 , x 44 , and then the output is vectorized to obtain P Ω x, P Ω H P Ω x outputs a matrix of the same size as x, where, among the elements of this matrix, the data points indexed by Ω are the same as the corresponding data points of x, and the remaining elements are 0; represents the soft threshold operator with a threshold of μ > 0, sign(.) is the sign function, and abs(.) is the absolute value function; F 2D and F 2D H respectively represent the two-dimensional Fourier transform operator and the two-dimensional inverse Fourier transform operator. When the object of action is a matrix, the non-uniform sampling operator P Ω is used, and when the object of action is a vector, the adjoint operator P Ω of P Ω H is used.

[0097] Embodiment

[0098] The following takes a non-uniform sampling embodiment of the C- 13 C magnetic resonance symmetry spectrum of a cytomegalovirus m04 protein as an example, and further illustrates the present invention in conjunction with the accompanying drawings. The full sampling length of this data is 512 × 512. The data is non-uniformly sampled at 5% respectively by the random sampling method, the traditional Poisson interval sampling method, and the method of the present invention, and the C- 13 C spectrum is reconstructed from the non-uniformly sampled free induction decay signal using the compressed sensing soft threshold method. The specific steps are as follows: 13 C- 13 C spectrum, and the specific steps are as follows:

[0099] 1) Construct a symmetric pair of uniformly spaced magnetic resonance free induction decay signals:

[0100] In this embodiment, the two-dimensional lengths of the uniformly spaced magnetic resonance free induction decay signals are both 512, and sp(k) represents a symmetric pair composed of f(i, j) and f(j, i), where Thus, an ordered first symmetric pair sequence {sp(k)} with a length of 131328 can be constructed. k＝1,2,…,131328 .

[0101] 2) Select approximately 131328×5% ≈ 6566 "symmetric pairs" from the ordered first symmetric pair sequence using random Poisson intervals:

[0102] Let k t represent the serial number of the t-th selected symmetric pair, where t = 1, 2, …, 6566; d t represent the serial number interval between the (t + 1)-th selected symmetric pair and the t-th selected symmetric pair, defined as d t = k t+1 - k t - 1. And perform the following steps to select 6566 symmetric pairs to form the second symmetric pair sequence:

[0103] (1) Select the first symmetric pair and let t = 1; k1 = 1;

[0104] (2) Generate a non - negative random Poisson interval:

[0105] (3) Select the next symmetric pair according to the non - negative random Poisson interval, let k t+1 = k t + d t + 1; t = t + 1; until k t > 131328;

[0106] (4) If t > 6566 and the selected symmetric pairs are relatively dense, adjust the adjustment constant α to 2 times the adjustment constant in the previous iteration process;

[0107] (5) If t < 6566 and the selected symmetric pairs are relatively sparse, adjust the adjustment constant α to 1 / 2 times the adjustment constant in the previous iteration process; until t = 6566

[0108] (6) Output the selected symmetric pairs to obtain the second symmetric pair sequence {sp(k t )} t＝1,…,6566 .

[0109] 3) Randomly sample one data point from each symmetric pair in {sp(k t )} t＝1,…,6566 to obtain sampled point data. If the selected symmetric pair consists of two cross - data points, fill the sampled point data at the position of the other unsampled point to obtain the augmented non - uniform sampled data y.

[0110] 4) Reconstruct the symmetric spectrum from the augmented non - uniform sampled data y using the compressive sensing soft - threshold algorithm.

[0111] From Figures 4 - 7 it can be seen that, when comparing with the fully sampled reference spectrum, the reconstructed spectrum of the sampling data based on the method of the present invention has higher quality than the reconstructed spectra of the randomly sampled data and the traditionally Poisson interval sampled data. In the region of the red dashed box, all the cross peaks of the reconstructed spectrum of the randomly sampled data are missing, and some cross peaks of the reconstructed spectrum of the traditionally Poisson interval sampled data are still missing, while the method of the present invention can reconstruct the cross peaks more completely.

[0112] Further referring to Figure 8 , as an implementation of the methods shown in the above figures, the present application provides an embodiment of a magnetic resonance symmetric spectrum non-uniform sampling device. This device embodiment corresponds to the method embodiment shown in Figure 2 , and this device can be specifically applied to various electronic devices.

[0113] The embodiment of the present application provides a magnetic resonance symmetric spectrum non-uniform sampling device, including:

[0114] A symmetric pair construction module 1, configured to construct symmetric pairs of magnetic resonance free induction decay signals with uniform intervals and obtain a first symmetric pair sequence;

[0115] A symmetric pair selection module 2, configured to select several symmetric pairs from the first symmetric pair sequence at random Poisson intervals to obtain a second symmetric pair sequence;

[0116] A sampling module 3, configured to select symmetric pairs in the second symmetric pair sequence and randomly extract one data point from the selected symmetric pairs for sampling to obtain a sampling result;

[0117] A filling module 4, configured to, in response to determining that the selected symmetric pair consists of two cross data points, fill the sampling result at the position of the other data point in the selected symmetric pair to obtain a non-uniformly sampled free induction decay signal.

[0118] The embodiment of the present application also provides a magnetic resonance symmetric spectrum reconstruction device, including the above magnetic resonance symmetric spectrum non-uniform sampling device, and further including:

[0119] A spectrum reconstruction module, configured to reconstruct a magnetic resonance symmetric spectrum from the non-uniformly sampled free induction decay signal by using a compressed sensing soft threshold algorithm.

[0120] Next, referring to Figure 9 , which shows a schematic structural diagram of a computer device 900 of an electronic device (such as the server or terminal device shown in Figure 1 ) suitable for implementing the embodiments of the present application. Figure 9 The electronic device shown is only an example and should not bring any limitation to the functions and usage scopes of the embodiments of the present application.

[0121] As Figure 9 shown, the computer device 900 includes a central processing unit (CPU) 901 and a graphics processing unit (GPU) 902, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 903 or a program loaded from a storage section 909 into a random access memory (RAM) 904. In the RAM 904, various programs and data required for the operation of the device 900 are also stored. The CPU 901, GPU 902, ROM 903, and RAM 904 are connected to each other via a bus 905. An input / output (I / O) interface 906 is also connected to the bus 905.

[0122] The following components are connected to the I / O interface 906: an input section 907 including a keyboard, a mouse, etc.; an output section 908 including, for example, a liquid crystal display (LCD), etc. and a speaker, etc.; a storage section 909 including a hard disk, etc.; and a communication section 910 including a network interface card such as a LAN card, a modem, etc. The communication section 910 performs communication processing via a network such as the Internet. A drive 911 may also be connected to the I / O interface 906 as needed. A removable medium 912, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 911 as needed so that a computer program read from it can be installed into the storage section 909 as needed.

[0123] Specifically, according to an embodiment of the present disclosure, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present disclosure includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program includes program codes for performing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network via the communication section 910, and / or installed from the removable medium 912. When the computer program is executed by the central processing unit (CPU) 901 and the graphics processing unit (GPU) 902, the above functions defined in the method of the present application are executed.

[0124] It should be noted that the computer-readable medium described in this application can be a computer-readable signal medium, a computer-readable medium, or any combination of the two. The computer-readable medium can be, for example, but not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor devices, apparatuses, or components, or any combination of the above. More specific examples of the computer-readable medium can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this application, the computer-readable medium can be any tangible medium that contains or stores a program, which can be used by or in conjunction with an instruction execution device, apparatus, or component. And in this application, the computer-readable signal medium can include a data signal propagated in a baseband or as part of a carrier wave, which carries the computer-readable program code. Such a propagated data signal can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The computer-readable signal medium can also be any computer-readable medium other than the computer-readable medium, which can send, propagate, or transmit a program for use by or in conjunction with an instruction execution device, apparatus, or component. The program code contained on the computer-readable medium can be transmitted using any appropriate medium, including but not limited to: wireless, wire, optical fiber, RF, etc., or any suitable combination of the above.

[0125] The computer program code for performing the operations of this application can be written in one or more programming languages or combinations thereof. The programming languages include object-oriented programming languages - such as Java, Smalltalk, C++, and also include conventional procedural programming languages - such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, executed as an independent software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer through any type of network - including a local area network (LAN) or a wide area network (WAN) - or, alternatively, can be connected to an external computer (for example, by using an Internet service provider to connect through the Internet).

[0126] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of devices, methods, and computer program products according to various embodiments of the present application. In this regard, each block in the flowchart or block diagram may represent a module, a segment of a program, or a part of code that contains one or more executable instructions for implementing a specified logical function. It should also be noted that, in some alternative implementations, the functions noted in the blocks may occur in a different order than that noted in the accompanying drawings. For example, two consecutive blocks shown may actually be executed substantially in parallel, and they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and combinations of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based device that performs the specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

[0127] The modules described in the embodiments of the present application can be implemented in software or in hardware. The described modules can also be provided in a processor.

[0128] As another aspect, the present application also provides a computer-readable medium, which may be included in the electronic device described in the above embodiments; or may exist separately without being assembled into the electronic device. The above computer-readable medium carries one or more programs, and when the one or more programs are executed by the electronic device, the electronic device is caused to: construct a symmetric pair of uniformly spaced nuclear magnetic resonance free induction decay signals and obtain a first symmetric pair sequence; select a plurality of symmetric pairs from the first symmetric pair sequence at random Poisson intervals to obtain a second symmetric pair sequence; select symmetric pairs in the second symmetric pair sequence and randomly sample one of the data points in the selected symmetric pairs to obtain a sampling result; in response to determining that the selected symmetric pair consists of two cross data points, fill the sampling result in the position of the other data point in the selected symmetric pair to obtain a non-uniformly sampled free induction decay signal.

[0129] The above description is only the preferred embodiments of the present application and an explanation of the applied technical principles. Those skilled in the art should understand that the scope of the invention involved in the present application is not limited to the technical solutions formed by the specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above inventive concept. For example, technical solutions formed by mutually replacing the above features with (but not limited to) technical features having similar functions disclosed in the present application.

Claims

1. A method for non-uniform sampling of magnetic resonance symmetric spectra, characterized in that, Including the following steps: S1. Construct symmetric pairs of uniformly spaced nuclear magnetic resonance free induction decay signals and obtain a first symmetric pair sequence; S2. Select a number of symmetric pairs from the first symmetric pair sequence using random Poisson intervals to obtain a second symmetric pair sequence; S3. Select symmetric pairs in the second symmetric pair sequence and randomly sample one of the data points in the selected symmetric pairs to obtain a sampling result; S4. In response to determining that the selected symmetric pair consists of two cross data points, fill the sampling result in the position of the other data point in the selected symmetric pair to obtain a non-uniformly sampled free induction decay signal.

2. The non-uniform sampling method for magnetic resonance symmetric spectrum according to claim 1, characterized in that The symmetric pair is composed of f(i,j) and f(j,i), denoted as sp(k), where f(i,j) represents the data point at the i-th row and j-th column in the free induction decay signal f of magnetic resonance, and f(j,i) represents the data point at the j-th row and i-th column in the free induction decay signal f of magnetic resonance. N is the signal length; the first symmetric pair sequence is {sp(k)} k＝1,2,…,l , l is the length of the first symmetric pair sequence, The second symmetric pair sequence is {sp(k t )} t＝1,…,q , where t represents the t-th selected symmetric pair, and k t represents the serial number of the t-th selected symmetric pair, where t = 1, …, q, and q is the length of the second symmetric pair sequence.

3. The non-uniform sampling method of magnetic resonance symmetric spectrum according to claim 2, characterized in that The step S2 specifically includes: S21. Select the first symmetric pair, let t = 1, and k1 = 1; S22, select a symmetry pair from the first symmetry pair sequence and generate a non-negative random Poisson interval d t , the formula is as follows: where α represents an adjustment constant for the sampling density; S23. Select the next symmetric pair according to the non-negative random Poisson interval, and the formula is as follows: k t+1 = k t + d t + 1; S24. Let t = t + 1, and repeat steps S22 - S24 until the serial number of the selected symmetric pair is equal to the length of the first symmetric pair sequence, and output to obtain the second symmetric pair.

4. The method for asymmetric sampling of magnetic resonance symmetric spectrum according to claim 3, wherein The step S22 further includes: If t > q, the adjustment constant α is adjusted to twice the adjustment constant in the previous iteration process; If t < q, the adjustment constant α is adjusted to 1 / 2 times the adjustment constant in the previous iteration process; until t = q.

5. A magnetic resonance symmetric spectrum reconstruction method, characterized in that, Including the non-uniform sampling method for nuclear magnetic resonance symmetric spectrum according to any one of claims 1 - 4, further including: S5. Reconstruct the nuclear magnetic resonance symmetric spectrum from the non-uniformly sampled free induction decay signal using a compressed sensing soft threshold algorithm.

6. The magnetic resonance symmetric spectrum reconstruction method according to claim 5, wherein The step S5 specifically includes: S51. Input the non-uniformly sampled free induction decay signal y, and let X m represent the output magnetic resonance symmetric spectrum, m represent the iteration number, and r m represent the difference between the non-uniformly sampled free induction decay signal y and the time-domain signal after performing inverse two-dimensional Fourier transform on X m ; S m represent the frequency-domain signal after performing two-dimensional Fourier transform on the difference. Initialize the parameters, let m = 0, S 0 = F 2D P Ω H y, r 0 = y, X 0 = 0, where Ω is the index set established based on all data points in the first symmetric pair sequence, and P Ω is the non-uniform sampling operator, and P Ω H is the adjoint operator of the non-uniform sampling operator; S52, updating the threshold of the soft threshold operator during the iteration process: where maxiter is the maximum number of loops; S53, update the output nuclear magnetic resonance symmetric spectrum: X m+1 = X m + SHR μ (S m ) S54, Update difference: r m+1 = y - P Ω F 2D H X m+1 ; S55, perform a two-dimensional Fourier transform on the difference: S m+1 = F 2D P Ω H r m+1 ; S56. Let \(m = m + 1\), and repeat steps S52 - S56 until \(m>\text{maxiter}\) or \(\|r\) m \|^2<10 -5 , and output the magnetic resonance symmetry spectrum of the last iteration.

7. A magnetic resonance symmetric spectrum non-uniform sampling device, characterized in that, Including: A symmetric pair construction module configured to construct symmetric pairs of uniformly spaced nuclear magnetic resonance free induction decay signals and obtain a first symmetric pair sequence; A symmetric pair selection module configured to select a number of symmetric pairs from the first symmetric pair sequence using random Poisson intervals to obtain a second symmetric pair sequence; A sampling module configured to select symmetric pairs in the second symmetric pair sequence and randomly sample one of the data points in the selected symmetric pairs to obtain a sampling result; A filling module configured to, in response to determining that the selected symmetric pair consists of two cross data points, fill the sampling result in the position of the other data point in the selected symmetric pair to obtain a non-uniformly sampled free induction decay signal.

8. A magnetic resonance symmetric spectrum reconstruction device, characterized in that, Including the non-uniform sampling device for nuclear magnetic resonance symmetric spectrum according to claim 7, further including: A spectrum reconstruction module configured to reconstruct the nuclear magnetic resonance symmetric spectrum from the non-uniformly sampled free induction decay signal using a compressed sensing soft threshold algorithm.

9. An electronic device, including: One or more processors; A storage device for storing one or more programs, When the one or more programs are executed by the one or more processors, enabling the one or more processors to implement the method according to any one of claims 1 - 4.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method according to any one of claims 1 - 4.

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