An artificial intelligence hypercomplex spectrum reconstruction method

Abstract

An artificial intelligence hypercomplex spectrum reconstruction method involves the reconstruction of magnetic resonance spectrum sampling signals. 1) Obtain a full sampling signal of an N-dimensional magnetic resonance spectrum in a hypercomplex form; 2) Fill the uncollected data positions with zeros according to the actual undersampling template to generate an undersampling signal of the N-dimensional magnetic resonance spectrum; 3) Use the full sampling signal of the N-dimensional magnetic resonance spectrum in step 1) as the output of a deep learning network, and use the undersampling signal and undersampling template of the N-dimensional magnetic resonance spectrum in step 2) as network input to form a training set; 4) Design a deep learning network model, loss function and feedback function of the network based on rank-one approximate decomposition; 5) Use the training set to train the parameters of the deep learning network based on rank-one approximate decomposition; 6) Input the undersampling signal of the N-dimensional magnetic resonance spectrum to be reconstructed into the trained network to obtain a reconstructed signal of the N-dimensional magnetic resonance spectrum. Through the deep learning network and the rank-one approximate decomposition characteristics, the reconstruction error is effectively reduced.

Description

Technical Field

[0001] The present invention relates to a method for reconstructing a magnetic resonance spectroscopy sampling signal, and in particular to an artificial intelligence hypercomplex spectrum reconstruction method for a magnetic resonance spectroscopy sampling signal based on a deep learning network model of rank-one approximate decomposition. Background Art

[0002] Magnetic resonance technology is a non-invasive and radiation-free imaging and analysis technology, which mainly includes magnetic resonance imaging and magnetic resonance spectroscopy. Magnetic resonance imaging generates high-resolution anatomical images through strong magnetic fields and radio frequency waves, and is widely used in medical imaging. Magnetic resonance spectroscopy is used to analyze the structure and concentration of chemical substances in the body, helping to diagnose and study metabolic diseases, etc. Hypercomplex numbers are mathematical structures that extend the concept of complex numbers and are usually used to represent multidimensional data. In magnetic resonance spectroscopy, hypercomplex numbers are used to process complex multi-peak signals. By encoding multi-dimensional information into hypercomplex form, the structure and concentration changes of chemical substances can be more effectively analyzed and interpreted, improving the accuracy and efficiency of spectral analysis.

[0003] Magnetic resonance signal acquisition takes a long time. In order to shorten the time, many optimization-based fast reconstruction methods for magnetic resonance undersampled signals have been proposed, including sparse constraint-based methods and hypercomplex low-rank-based methods. However, the former has poor reconstruction performance for broad spectral peaks and requires phase modulation of the undersampled signals before reconstruction. The latter can only reconstruct three-dimensional NMR spectra, and a single reconstruction takes about 3 hours.

[0004] Recently, deep learning methods have been introduced to the field of rapid reconstruction of magnetic resonance undersampled signals, such as DLNMR and DHMF. However, the former has poor reconstruction performance for low-intensity spectral peaks, while the latter can only support the reconstruction of 2D spectra. In addition, the training process of deep learning networks is highly dependent on the distribution of data, and has disadvantages in generalization performance.

[0005] In the field of fast reconstruction of magnetic resonance under-sampling signals, the generalization performance of existing methods needs to be improved. There is no intelligent reconstruction method based on the rank-one characteristics of single-exponential signals to build a deep learning network based on rank-one approximate decomposition to reduce reconstruction errors. Summary of the invention

[0006] The purpose of the present invention is to provide an artificial intelligence hypercomplex spectrum reconstruction method for magnetic resonance spectrum sampling signals that is fast, high-fidelity and has good generalization performance, in order to address the problems of poor reconstruction performance, long reconstruction time, dependence on data distribution, and poor generalization performance in the prior art.

[0007] The present invention comprises the following steps:

[0008] 1) Obtain the full sampling signal of the N-dimensional magnetic resonance spectrum in the form of hypercomplex numbers;

[0009] 2) Performing zero-filling operation on the uncollected data positions according to the actual under-sampling template to generate an under-sampling signal of the N-dimensional magnetic resonance spectrum;

[0010] 3) using the full sampling signal of the N-dimensional magnetic resonance spectrum in step 1) as the output of the deep learning network, and using the under-sampled signal and under-sampled template of the N-dimensional magnetic resonance spectrum in step 2) as the network input to form a training set;

[0011] 4) Design a deep learning network model based on rank-one approximate decomposition and the network loss function And the feedback function of the network; K iteration blocks are superimposed in series as the entire network structure, and each iteration block is composed of several sub-blocks, including a peak retrieval module, a low-rank approximation module, a data consistency module, and a deep learning module;

[0012] 5) Using the training set obtained in step 3), the set of learnable parameters of the deep learning network model based on rank-one approximate decomposition is Perform training to obtain a trained network model;

[0013] 6) Inputting the undersampled signal of the N-dimensional magnetic resonance spectrum to be reconstructed into the trained network model in step 5) to obtain the reconstructed signal of the N-dimensional magnetic resonance spectrum.

[0014] In step 1), the specific steps of obtaining the full sampling signal of the N-dimensional magnetic resonance spectrum in the form of a hypercomplex number are as follows: all hypercomplex signals are represented by symbols with superscripts, and the full sampling signal of the N-dimensional magnetic resonance spectrum is It is expressed as the sum of R N-dimensional hypercomplex exponentials; each hypercomplex signal consists of N complex exponential signals constitute:

[0015] (1)

[0016] in, represents the full sampling signal of N-dimensional magnetic resonance spectrum; represents the number of dimensions, , l1, l n , l N Respectively represent the size of the 1st, nth, and Nth dimensions; represents the summation operation, the entire N-dimensional hypercomplex exponent is assumed to be the sum of R rank-one N-dimensional hypercomplex exponents; r represents the number of hypercomplex exponents; represents the magnitude of the rth hypercomplex exponent; e represents the base of the natural logarithm; , , They represent the phase, attenuation factor, and normalized frequency of the rth hypercomplex and nth complex exponential signals, respectively. , , ; is the nth imaginary unit, for any , , ,have .

[0017] In step 2), the process of performing zero-filling operation on the uncollected data positions according to the actual under-sampling template is expressed as:

[0018] (2)

[0019] in, is the undersampled signal of the obtained N-dimensional magnetic resonance spectrum, represents the undersampling operation, is the full sampling signal of N-dimensional magnetic resonance spectroscopy; is additive noise that satisfies Gaussian distribution.

[0020] In step 3), the training set consists of the full sampling signal of N-dimensional magnetic resonance spectroscopy , undersampling operation and undersampled signals of N-dimensional magnetic resonance spectroscopy composition.

[0021] In step 4), the deep learning network model based on rank-one approximate decomposition is composed of iterative blocks, and several iterative blocks are stacked in series as the entire network structure, and each iterative block is composed of 6 sub-blocks.

[0022] The six sub-blocks are sub-block 1, sub-block 2, sub-block 3, sub-block 4, sub-block 5, and sub-block 6, and the variables are updated in sequence , , , , , ; Sub-block 1 is the peak retrieval module, sub-block 2 and sub-block 4 are low-rank approximation modules, sub-block 3 and sub-block 6 are data consistency modules, and sub-block 5 is a deep learning module; the internal structure of each iteration block is as follows:

[0023] (1) Sub-block 1 is a peak retrieval module, which is used to obtain the undersampled signal of N-dimensional magnetic resonance spectrum. and the reconstructed signal of the N-dimensional magnetic resonance spectrum obtained in the previous iteration Retrieve the currently lost spectral peaks in the search, the specific operations are as follows;

[0024] Time domain undersampled signal with missing spectral peaks It is expressed as:

[0025] (3)

[0026] in, represents an undersampling operation; is the signal containing the missing peak; is the undersampled signal of N-dimensional magnetic resonance spectroscopy; represents an undersampling operation; Represents the reconstructed signal obtained in the previous iteration;

[0027] Then the time domain undersampled signal with lost spectrum peak is Divide by the sampling rate Get the normalized signal through the virtual echo operation Get the complex conjugate signal, and then go through Fourier transform After that, the real spectrum is obtained, and the peak with the highest intensity in the real spectrum is extracted as the missing peak; this process is expressed as:

[0028] (4)

[0029] in, represents the missing N-dimensional peak; For extraction operations; is Fourier transform; For virtual echo operation; represents an undersampling operation; is the signal containing the missing peak; the sampling rate , is the number of sampling points of the fully sampled signal, is the number of sampling points of the under-sampled signal;

[0030] Obtain the maximum intensity of the real spectrum except the nth dimension, and obtain the frequency information of the nth dimension of the missing peak. This process is defined as the operation , then this process can be expressed as:

[0031] (5)

[0032] in, represents the number of dimensions, ; The factor vector representing the n-th dimension projection; It means to obtain the maximum intensity of the real spectrum except the nth dimension, and obtain the frequency information of the nth dimension of the missing peak; represents the missing N-dimensional peak;

[0033] Get the n-th dimension factor matrix containing the missing peak frequency information The process is expressed as:

[0034] (6)

[0035] in, and denote the virtual echo operation and the inverse Fourier transform, respectively; Indicates the build size is The value of the rth column of the matrix is , the values ​​of other columns are 0, and the rth column is the first one in all R columns. Lower than One thousandth of a column;

[0036] (2) Sub-block 2 and sub-block 4 are low-rank approximation modules, which are used to update and ;

[0037] In the nth dimension, the low-rank matrix Solved by the following formula:

[0038] (7)

[0039] in, represents the number of iterations, , For the matrix The low-rank approximation operation of is the regularization parameter, is the rank-one singular value threshold operator, defined as ;vector and vector are the corresponding left and right singular vectors, scalars is equal to the first singular value; , Respectively represent the selected p-th column and q-th row, a total of P columns and Q rows are selected;

[0040] Finally, the result of the n-th dimensional low-rank approximation module is obtained :

[0041] (8)

[0042] in, For the matrix is the inverse operation of the low-rank approximation operation, r represents the number of hypercomplex exponents, represents the number of dimensions, is the result of the n-th dimension low-rank approximation module;

[0043] (3) Sub-block 3 and sub-block 6 are data consistency modules, which are used to update and ;

[0044] To solve the factor matrix , first fix the variables and other factor matrices ( ); Its solution model is as follows:

[0045] (9)

[0046] in, is a modulo n matrix operation, represents the undersampling operation, is a factor matrix, and is the regularization parameter, represents the Frobenius norm; represents the result of the n-th dimensional low-rank approximation module, ; represents the Khatri-Rao product of matrices;

[0047] (4) Sub-block 5 is a deep learning module that uses a densely connected network with a residual module to update variables ; The densely connected network includes a one-dimensional convolution layer and a linear rectifier activation function; In the kth round of iteration, the relevant variables of the k-1th round and the kth round are As input; one-dimensional Fourier transform and its inverse transform Applied to each matrix separately; the real and imaginary parts of all input matrices are concatenated together as the output of the densely connected network.

[0048] In step 4), the loss function of the network is The reconstructed signal obtained by a total of K iteration blocks through the data consistency module With full sampling signal The mean square error of is summed up, which is specifically expressed as:

[0049] (10)

[0050] in, represents the sum operation, represents the number of iterations, ; represents all learnable parameters, including and learnable weights in densely connected networks; represents the Frobenius norm; Represents the reconstruction signal obtained by the data consistency module, , is the full sampling signal of N-dimensional magnetic resonance spectroscopy.

[0051] In step 4), in the process of constructing a deep learning network model based on rank-one approximate decomposition, according to the loss function of the network , the reconstructed signal of the N-dimensional magnetic resonance spectrum output by the network model Fully sampled signal with N-dimensional magnetic resonance spectroscopy Comparison is made and the gradient is fed back to update all parameters of the iterative block, so that the output value of the network model gradually approaches the full sampling signal of the N-dimensional magnetic resonance spectrum.

[0052] In step 5), the training set obtained in step 3) is used to calculate the learnable parameter set of the deep learning network model based on rank-one approximate decomposition. Training; using the Adam optimizer that performs well in deep learning, the network is trained using the training set obtained in step 3) by minimizing the loss function obtained in step 4) The optimal set of learnable parameters is obtained, that is, the trained network model is obtained.

[0053] In step 6), the undersampled signal of the N-dimensional magnetic resonance spectrum to be reconstructed is input into the trained network model in step 5) to obtain the reconstructed signal of the N-dimensional magnetic resonance spectrum, and the specific method is as follows:

[0054] (1) The sizes of the direct dimension and the indirect dimension are and Undersampled signals of N-dimensional magnetic resonance spectroscopy , perform Fourier transform along the direct dimension, and separate along the direct dimension into The size is Undersampled signals of N-1 dimensional magnetic resonance spectroscopy ;

[0055] (2) Each undersampled signal of the N-1 dimensional magnetic resonance spectrum to be reconstructed Input the deep learning network model based on rank-one approximate decomposition that has been trained in step 5) , and use the set of learnable parameters obtained in step 5) , output the reconstructed signal of N-1 dimensional magnetic resonance spectrum , the process is expressed as:

[0056] (11)

[0057] in, represents the reconstructed signal of the N-1 dimensional magnetic resonance spectrum, represents the undersampled signal of the N-1 dimensional magnetic resonance spectrum, represents the deep learning network model based on rank-one approximate decomposition that has been trained in step 5), represents the set of learnable parameters obtained in step 5);

[0058] (3) Reconstruct the signal of each N-1-dimensional magnetic resonance spectrum The time domain reconstruction signal of a complete N-dimensional magnetic resonance spectrum is spliced ​​along the direct dimension, and then a Fourier transform is performed along each indirect dimension to obtain a frequency domain reconstruction signal of a complete N-dimensional magnetic resonance spectrum.

[0059] Compared with the prior art, the outstanding technical effects and advantages of the present invention are: first, by utilizing rank-one approximate decomposition, the magnetic resonance signal can be reconstructed more accurately and the reconstruction error can be reduced. Secondly, the method can effectively improve the reconstruction speed without the need for phase modulation of the undersampled signal. In addition, the deep learning network has excellent generalization performance and can adapt to different types of data distribution, solving the shortcomings of the existing deep learning methods in generalization performance. Finally, the method is not only suitable for the reconstruction of two-dimensional spectra, but can also be extended to the reconstruction of multi-dimensional spectra, overcoming the limitations of the existing methods in spectral dimensions. Therefore, the present invention has important application value and broad prospects in the field of rapid reconstruction of magnetic resonance undersampled signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 This is a block diagram of the deep learning network structure based on rank-one approximate decomposition.

[0061] Figure 2 It is the structural block diagram of the peak retrieval module.

[0062] Figure 3 It is the structural block diagram of the deep learning module.

[0063] Figure 4 It is the three-dimensional magnetic resonance full sampling label spectrum and its reconstructed spectrum at 5% sampling rate. DETAILED DESCRIPTION

[0064] The following embodiments will further illustrate the present invention in conjunction with the accompanying drawings.

[0065] The embodiment of the present invention utilizes the full sampling signal of the two-dimensional magnetic resonance spectrum , undersampling operation and undersampled signals of N-dimensional magnetic resonance spectroscopy A training set is constructed, and the optimal network parameter set is obtained through several iterative trainings. Finally, the undersampled signal of the three-dimensional magnetic resonance spectroscopy is input into the trained deep learning network model to obtain the reconstructed signal of the three-dimensional magnetic resonance spectroscopy.

[0066] An embodiment of the reconstruction of undersampled signals for three-dimensional magnetic resonance spectroscopy comprises the following steps:

[0067] Step 1: Acquire the full sampling signal of 2D MR spectroscopy As a training set;

[0068] The full sampling signal of the two-dimensional magnetic resonance spectrum in this embodiment It can be expressed as the sum of R two-dimensional hypercomplex exponentials:

[0069] (1)

[0070] In this embodiment, for each full sampling signal of the two-dimensional magnetic resonance spectrum , , Indicates the size of the nth dimension. The specific parameters are: the full sampling signal of the two-dimensional magnetic resonance spectrum The size is 89×43, the amplitude of the rth hypercomplex exponent , the phase of the rth hypercomplex nth complex exponential signal , the attenuation factor of the rth hypercomplex nth complex exponential signal and the normalized frequency of the rth hypercomplex nth complex exponential signal .

[0071] Step 2: Perform zero-filling operation on the uncollected data positions according to the actual under-sampling template and add noise to generate an under-sampling signal of the zero-filled N-dimensional magnetic resonance spectrum;

[0072] Generates undersampling operations based on a 2D Poisson distribution , the time domain data of the undersampled two-dimensional magnetic resonance spectrum is obtained .

[0073] Then add noise, the process can be expressed as:

[0074] (2)

[0075] in, is the undersampled signal of the obtained N-dimensional magnetic resonance spectrum, represents the undersampling operation, is additive noise that satisfies Gaussian distribution.

[0076] Step 3: Use the time domain data of the fully sampled magnetic resonance spectrum in the first step as the output of the deep learning network, and use the time domain data of the undersampled magnetic resonance spectrum and the undersampled template in the second step as the network input to form a training set:

[0077] The fully sampled signal from 40,000 two-dimensional magnetic resonance spectra , the corresponding undersampling operation and undersampled signals from two-dimensional magnetic resonance spectroscopy Form a training set.

[0078] Step 4: Design a deep learning network model, loss function, and network feedback function based on rank-one approximate decomposition.

[0079] The deep learning network model based on rank-one approximate decomposition is as follows Figure 1 As shown, it is composed of iteration blocks. By stacking several iteration blocks in series as the entire network structure, each iteration block is composed of sub-block 1, sub-block 2, sub-block 3, sub-block 4, sub-block 5, and sub-block 6, and the variables are updated in sequence. , , , , , ; Wherein sub-block 1 is called the peak retrieval module, sub-block 2 and sub-block 4 are low-rank approximation modules, sub-block 3 and sub-block 6 are data consistency modules, and sub-block 5 is a deep learning module. Take the kth iteration block as an example:

[0080] (1) Sub-block 1 is a peak retrieval module. The structural block diagram of the peak retrieval module is as follows: Figure 2 As shown, for the undersampled signal from N-dimensional magnetic resonance spectroscopy and the reconstructed signal of the N-dimensional magnetic resonance spectrum obtained in the previous iteration Search for the currently missing peaks in the spectrum. The specific operations are as follows:

[0081] Time domain undersampled signal with missing spectral peaks It is expressed as:

[0082] (3)

[0083] in, represents an undersampling operation; is the signal containing the missing peak; is the undersampled signal of N-dimensional magnetic resonance spectroscopy; Represents the reconstructed signal obtained in the previous iteration;

[0084] Then the signal Divide by the sampling rate Get the normalized signal through the virtual echo operation Get the complex conjugate signal, and then go through Fourier transform After that, the real spectrum is obtained, and the peak with the highest intensity in the real spectrum is extracted as the missing peak; this process is expressed as:

[0085] (4)

[0086] in, represents the missing N-dimensional peak; For extraction operations; is Fourier transform; For virtual echo operation; represents an undersampling operation; is the signal containing the missing peak; the sampling rate , is the number of sampling points of the fully sampled signal, is the number of sampling points of the undersampled signal.

[0087] Obtain the maximum intensity of the real spectrum except the nth dimension, and obtain the frequency information of the nth dimension of the missing peak. This process is defined as the operation , then this process can be expressed as:

[0088] (5)

[0089] in, ; The factor vector representing the n-th dimension projection; It means to obtain the maximum intensity of the real spectrum except the nth dimension, and obtain the frequency information of the nth dimension of the missing peak; Indicates the missing N-dimensional peak.

[0090] Get the n-th dimension factor matrix containing the missing peak frequency information The process is expressed as:

[0091] (6)

[0092] in, and denote the virtual echo operation and the inverse Fourier transform, respectively; Indicates the build size is The value of the rth column of the matrix is , the values ​​of other columns are 0, and the rth column is the first one in all R columns. Lower than One thousandth of a column.

[0093] (2) Sub-block 2 and sub-block 4 are low-rank approximation modules, which are used to update and ;

[0094] In the nth dimension, the low-rank matrix It can be solved by the following formula:

[0095] (7)

[0096] in, represents the number of iterations, , For the matrix The low-rank approximation operation of is the regularization parameter, is the rank-one singular value threshold operator, defined as ;vector and vector are the corresponding left and right singular vectors, scalars is equal to the first singular value; , Respectively represent the selected p-th column and q-th row, a total of P columns and Q rows are selected;

[0097] Finally, the result of the n-th dimensional low-rank approximation module is:

[0098] (8)

[0099] in, For the matrix is the inverse operation of the low-rank approximation operation, r represents the number of hypercomplex exponents, represents the number of dimensions, is the result of the n-th dimensional low-rank approximation module.

[0100] (3) Sub-block 3 and sub-block 6 are data consistency modules, which are used to update and ;

[0101] To solve the factor matrix , first fix the variables and other factor matrices ( ); Its solution model is as follows:

[0102] (9)

[0103] in, is a modulo n matrix operation, represents the undersampling operation, is a factor matrix, and is the regularization parameter, represents the Frobenius norm; represents the result of the n-th dimensional low-rank approximation module, ; Represents the Khatri-Rao product of matrices.

[0104] (4) Sub-block 5 is a deep learning module (such as Figure 3 ), using a densely connected network with a residual module to update the variables ; The densely connected network includes a one-dimensional convolution layer and a linear rectifier activation function; In the kth round of iteration, the relevant variables of the k-1th round and the kth round are As input; one-dimensional Fourier transform and its inverse transform Applied to each matrix separately; the real and imaginary parts of all input matrices are concatenated together as the output of the densely connected network.

[0105] The loss function of the network is The reconstructed signal obtained by a total of K iteration blocks through the data consistency module With full sampling signal The mean square error of is summed up, which is specifically expressed as:

[0106] (10)

[0107] in, represents the sum operation, represents the number of iterations, ; represents all learnable parameters, including regularization parameters and learnable weights in densely connected networks; represents the Frobenius norm. Represents the reconstruction signal obtained by the data consistency module, , is the full sampling signal of N-dimensional magnetic resonance spectroscopy.

[0108] In the process of constructing a deep learning network model based on rank-one approximate decomposition, according to the loss function of the network, the reconstructed signal of the reconstructed two-dimensional magnetic resonance spectrum output by the network model is converted into Fully sampled signal with two-dimensional magnetic resonance spectroscopy The comparison is made and the gradient is fed back to update all the parameters of the iterative block, so that the output value of the network model gradually approaches the full sampling signal of the two-dimensional magnetic resonance spectrum.

[0109] Step 5: Use the training set obtained in step 3 to train the parameters of the deep learning network model based on rank-one approximate decomposition. Adopt the Adam optimizer (Diederik Kingma and Jimmy Ba, “Adam: A method for stochastic optimization,” arXiv:1412.6980, 2014.), which has performed well in deep learning, and use the training set obtained in step 3 to train the network. By minimizing the loss function obtained in step 4, By obtaining the optimal set of learnable parameters, a trained network model can be obtained.

[0110] Step 6: Input the undersampled signal of the three-dimensional magnetic resonance to be reconstructed into the trained network model to obtain the reconstructed signal of the three-dimensional magnetic resonance spectrum, which specifically includes:

[0111] (1) For the undersampled signal of 3D MR spectroscopy, the lengths of the direct and indirect dimensions are 879 and 90×44 respectively. , Fourier transform is performed along the direct dimension to obtain the mixed spatial data of magnetic resonance spectroscopy, and then separated into 879 undersampled two-dimensional magnetic resonance spectroscopy time domain data along the direct dimension. .

[0112] (2) Each undersampled signal of the two-dimensional magnetic resonance spectrum to be reconstructed Input the trained network model in step 5) and use the set of learnable parameters obtained in step 5) Output of 2D MRI reconstructed signal , the process is expressed as:

[0113] (11)

[0114] in, is the reconstructed signal of the two-dimensional magnetic resonance spectrum, is the deep learning network model based on rank-one approximate decomposition that has been trained in step 5), is the undersampled signal of the two-dimensional magnetic resonance spectroscopy, is the set of learnable parameters obtained in step 5).

[0115] (3) Reconstructing each 2D MR spectrum signal The signals are spliced ​​together into a complete magnetic resonance spectrum reconstruction signal, and Fourier transform is performed along each indirect dimension to obtain a complete magnetic resonance spectrum reconstruction signal.

[0116] In an embodiment, the input of the network is an undersampled signal of a three-dimensional magnetic resonance spectrum with a sampling rate of 5%. The fully sampled signal of the three-dimensional magnetic resonance spectrum and the reconstructed signal of the three-dimensional magnetic resonance spectrum of the present invention at a sampling rate of 5% are respectively as follows: Figure 4 The first column and Figure 4 The third column in . Figure 4 The second column in is the spectrum reconstructed at a sampling rate of 5% using the cutting-edge hypercomplex low-rank spectral reconstruction algorithm HLRF (Yi Guo, Jiaying Zhan, Zhangren Tu, Yirong Zhou, Jianfan Wu, QingHong, Yuqi Huang, Vladislav Orekhov, Xiaobo Qu and Di Guo,"Hypercomplex lowrank reconstruction for nmr spectroscopy", Signal Processing, 2023, 203:108809.). Figure 4It can be seen that the artificial intelligence hypercomplex spectrum reconstruction method of the present invention can quickly reconstruct high-quality magnetic resonance spectra, and the reconstructed spectrum is better than the cutting-edge hypercomplex low-rank spectrum reconstruction algorithm HLRF. The method of the present invention performs better in maintaining spectral details and accuracy, especially under low sampling rate conditions. Experiments show that the method of the present invention is superior and effective in the field of magnetic resonance spectrum reconstruction. Figure 4 The artificial intelligence hypercomplex spectrum reconstruction method of the present invention shown in the third column can avoid Figure 4 The arrow in the second column of the figure shows the pseudo peak problem in the reconstruction results of the frontier hypercomplex low-rank spectral reconstruction algorithm HLRF. Pseudo peaks are a common error in spectral reconstruction, which can lead to misunderstanding of spectral analysis results. The method of the present invention can significantly reduce such errors, thereby improving the accuracy and reliability of magnetic resonance spectroscopy reconstruction.

[0117] The above embodiments are only preferred embodiments of the present invention and cannot be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the present invention.

Claims

1. An artificial intelligence hypercomplex spectrum reconstruction method, characterized in that The following steps are involved: 1) Obtaining the full sampling signal of the N-dimensional magnetic resonance spectrum in the form of a hypercomplex number, the specific steps are as follows: All hypercomplex signals are represented by symbols with superscripts, and the full sampling signal of the N-dimensional magnetic resonance spectrum It is expressed as the sum of R N-dimensional hypercomplex exponentials; each hypercomplex signal consists of N complex exponential signals constitute: in, represents the full sampling signal of N-dimensional magnetic resonance spectrum; n represents the number of dimensions, n = 1, 2, ..., N, l1, l n , l N Respectively represent the size of the first, nth, and Nth dimensions; ∑ represents the summation operation, and the entire N-dimensional hypercomplex exponent is assumed to be the sum of R rank-one N-dimensional hypercomplex exponents; r represents the number of hypercomplex exponents; a r ≥0 indicates the amplitude of the rth hypercomplex exponent; e indicates the base of the natural logarithm; φ r，n , τ r，n 、f r，n Respectively represent the phase, attenuation factor, and normalized frequency of the rth hypercomplex and nth complex exponential signals, φ r，n ∈[0,2π),τ r，n ≥0, f r，n ∈[0,1); i n is the nth imaginary unit. For any n1=1,2,...,N,n2=1,2,...,N,n1≠n2,there is 2) performing zero-filling operation on the uncollected data positions according to the actual under-sampling template to generate an under-sampling signal of the N-dimensional magnetic resonance spectrum; 3) using the full sampling signal of the N-dimensional magnetic resonance spectrum in step 1) as the output of the deep learning network, and using the under-sampled signal and under-sampled template of the N-dimensional magnetic resonance spectrum in step 2) as the network input to form a training set; 4) Design a deep learning network model based on rank-one approximate decomposition and the network loss function And the feedback function of the network; K iteration blocks are superimposed in series as the entire network structure, and each iteration block is composed of several sub-blocks, including a peak retrieval module, a low-rank approximation module, a data consistency module, and a deep learning module; The deep learning network model based on rank-one approximate decomposition is composed of iterative blocks, and a plurality of iterative blocks are superimposed in series as the entire network structure, and each iterative block is composed of 6 sub-blocks; The six sub-blocks are sub-block 1, sub-block 2, sub-block 3, sub-block 4, sub-block 5, and sub-block 6, and the variables are updated in sequence Sub-block 1 is the peak retrieval module, sub-block 2 and sub-block 4 are low-rank approximation modules, sub-block 3 and sub-block 6 are data consistency modules, and sub-block 5 is a deep learning module. The internal structure of each iteration block is as follows: (1) Sub-block 1 is a peak retrieval module for obtaining the undersampled signal of the N-dimensional magnetic resonance spectrum. and the reconstructed signal of the N-dimensional magnetic resonance spectrum obtained in the previous iteration Retrieve the currently lost spectral peaks in the search, the specific operations are as follows; Time domain undersampled signal with missing spectral peaks It is expressed as: in, represents an undersampling operation; is the signal containing the missing peak; is the undersampled signal of N-dimensional magnetic resonance spectroscopy; represents an undersampling operation; Represents the reconstructed signal obtained in the previous iteration; Then the time domain undersampled signal with lost spectrum peak is Divide by the sampling rate u to get the normalized signal, through the virtual echo operation Get the complex conjugate signal, and then go through Fourier transform After that, the real spectrum is obtained, and the peak with the highest intensity in the real spectrum is extracted as the missing peak; this process is expressed as: in, represents the missing N-dimensional peak; For extraction operations; is Fourier transform; For virtual echo operation; represents an undersampling operation; is a signal containing missing peaks; sampling rate u=A / B, A is the number of sampling points of the fully sampled signal, and B is the number of sampling points of the under-sampled signal; Obtain the maximum intensity of the real spectrum except the nth dimension, and obtain the frequency information of the nth dimension of the missing peak. This process is defined as the operation This process can be expressed as: Where n represents the number of dimensions, n=1, 2, ..., N; The factor vector representing the n-th dimension projection; It means to obtain the maximum intensity of the real spectrum except the nth dimension, and obtain the frequency information of the nth dimension of the missing peak; represents the missing N-dimensional peak; Get the n-th dimension factor matrix containing the missing peak frequency information The process is expressed as: in, and denote the virtual echo operation and the inverse Fourier transform, respectively; Indicates the build size is L n ×R matrix, the value of the rth column of the matrix is The values ​​of other columns are 0, and the rth column is the first one in all R columns. Lower than One thousandth of a column; (2) Sub-block 2 and sub-block 4 are low-rank approximation modules, which are used to update and In the nth dimension, the low-rank matrix Solved by the following formula: Where k represents the number of iterations, k = 1, 2, ..., K, For the matrix The low-rank approximation operation of , β is the regularization parameter, is the rank-one singular value threshold operator, defined as vector and vector are the corresponding left and right singular vectors, scalars is equal to the first singular value; p=1, ..., P, q=1, ..., Q represent the selected p-th column and q-th row respectively, and a total of P columns and Q rows are selected; Finally, the result of the n-th dimensional low-rank approximation module is obtained in, For the matrix is the inverse operation of the low-rank approximation operation, r represents the number of hypercomplex exponents, n represents the number of dimensions, is the result of the n-th dimension low-rank approximation module; (3) Sub-block 3 and sub-block 6 are data consistency modules, which are used to update and To solve the factor matrix Fix the variables first and other factor matrices The solution model is as follows: in, is a modulo n matrix operation, represents the undersampling operation, is the factor matrix, λ and β are regularization parameters, represents the Frobenius norm; represents the result of the n-th dimensional low-rank approximation module, ⊙ represents the Khatri-Rao product of the matrix; (4) Sub-block 5 is a deep learning module that uses a densely connected network with a residual module to update variables The densely connected network includes a one-dimensional convolution layer and a linear rectifier activation function; in the kth iteration, the relevant variables of the k-1th and kth rounds are As input; one-dimensional Fourier transform and its inverse transform Apply to each matrix separately; concatenate the real and imaginary parts of all input matrices together as the output of the densely connected network; 5) Using the training set obtained in step 3), the learnable parameter set of the deep learning network model based on rank-one approximate decomposition Perform training to obtain a trained network model; 6) Inputting the undersampled signal of the N-dimensional magnetic resonance spectrum to be reconstructed into the trained network model in step 5) to obtain the reconstructed signal of the N-dimensional magnetic resonance spectrum.

2. An artificial intelligence hypercomplex spectrum reconstruction method as claimed in claim 1, characterized in that In step 2), the process of performing zero-filling operation on the uncollected data positions according to the actual under-sampling template is expressed as: in, is the undersampled signal of the obtained N-dimensional magnetic resonance spectrum, represents the undersampling operation, is the full sampling signal of N-dimensional magnetic resonance spectroscopy; is additive noise that satisfies Gaussian distribution.

3. An artificial intelligence hypercomplex spectrum reconstruction method as claimed in claim 1, characterized in that In step 3), the training set consists of the full sampling signal of N-dimensional magnetic resonance spectroscopy Undersampling Operation and undersampled signals of N-dimensional magnetic resonance spectroscopy composition.

4. The artificial intelligence hypercomplex spectrum reconstruction method as claimed in claim 1, characterized in that In step 4), the loss function of the network is The reconstructed signal obtained by a total of K iteration blocks through the data consistency module With full sampling signal The mean square error of is summed up, which is specifically expressed as: Where ∑ represents a summation operation, k represents the number of iterations, k = 1, 2, ..., K; Θ represents all learnable parameters, including λ, β, and learnable weights in densely connected networks; represents the Frobenius norm; represents the reconstructed signal obtained by the data consistency module, n=1, 2, ..., N, is the full sampling signal of N-dimensional magnetic resonance spectroscopy.

5. The artificial intelligence hypercomplex spectrum reconstruction method as claimed in claim 1, characterized in that In step 4), in the process of constructing a deep learning network model based on rank-one approximate decomposition, according to the loss function of the network The reconstructed signal of the N-dimensional magnetic resonance spectrum output by the network model Fully sampled signal with N-dimensional magnetic resonance spectroscopy Comparison is made and the gradient is fed back to update all parameters of the iterative block, so that the output value of the network model gradually approaches the full sampling signal of the N-dimensional magnetic resonance spectrum.

6. An artificial intelligence hypercomplex spectrum reconstruction method as claimed in claim 1, characterized in that In step 5), the training set obtained in step 3) is used to calculate the learnable parameter set of the deep learning network model based on rank-one approximate decomposition. Training: Use the Adam optimizer, which performs well in deep learning, to train the network using the training set obtained in step 3), and minimize the loss function obtained in step 4). The optimal set of learnable parameters is obtained, that is, the trained network model is obtained.

7. The artificial intelligence hypercomplex spectrum reconstruction method as claimed in claim 1, characterized in that In step 6), the undersampled signal of the N-dimensional magnetic resonance spectrum to be reconstructed is input into the trained network model in step 5) to obtain the reconstructed signal of the N-dimensional magnetic resonance spectrum, and the specific method is as follows: (1) The sizes of the direct and indirect dimensions are L1 and L2×…×L respectively. N Undersampled signals of N-dimensional magnetic resonance spectroscopy Perform Fourier transform along the direct dimension and separate into L1 pieces of size L2×…×L along the direct dimension N Undersampled signals of N-1 dimensional magnetic resonance spectroscopy (2) Each undersampled signal of the N-1 dimensional magnetic resonance spectrum to be reconstructed Input the deep learning network model F(·) based on rank-one approximate decomposition trained in step 5) and use the learnable parameter set obtained in step 5) Output N-1 dimensional magnetic resonance spectrum reconstruction signal The process is expressed as: in, represents the reconstructed signal of the N-1 dimensional magnetic resonance spectrum, represents the undersampled signal of N-1 dimensional magnetic resonance spectrum, F(·) represents the deep learning network model based on rank-one approximate decomposition trained in step 5), represents the set of learnable parameters obtained in step 5); (3) Reconstructing each N-1-dimensional magnetic resonance spectrum The time domain reconstruction signal of a complete N-dimensional magnetic resonance spectrum is spliced ​​along the direct dimension, and then a Fourier transform is performed along each indirect dimension to obtain a frequency domain reconstruction signal of a complete N-dimensional magnetic resonance spectrum.

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