Nuclear magnetic resonance one-dimensional hydrogen spectrum virtual decoupling method based on deep learning

Abstract

The invention provides a nuclear magnetic resonance one-dimensional hydrogen spectrum virtual decoupling method based on deep learning. The method mainly relates to virtual decoupling of a one-dimensional nuclear magnetic resonance hydrogen spectrum through a deep learning model. Firstly, a training sample required by a deep learning model is generated; secondly, designing the structure of a deep learning model; then, training a deep learning model by adopting the training sample to obtain a trained deep learning model; and finally, performing virtual decoupling on the nuclear magnetic resonance one-dimensional hydrogen spectrum by adopting the trained deep learning model. The method has the main effects that a pulse sequence does not need to be designed, and decoupling of the one-dimensional hydrogen spectrum can be realized only through the deep learning model.

Description

Technical Field

[0001] The present invention belongs to a nuclear magnetic resonance (NMR) spectroscopy signal processing method, which is a one-dimensional nuclear magnetic resonance hydrogen spectrum virtual decoupling method based on deep learning. Background Art

[0002] Nuclear magnetic resonance spectroscopy is a powerful analytical technique that is often used for molecular structure, dynamics and environmental analysis. 1 H and 13 C) Under the action of an external magnetic field, nuclear spins are arranged, absorbing and emitting electromagnetic radiation of a specific frequency, thereby forming a nuclear magnetic resonance spectrum, which provides structural information about the molecule. Coupling peak splitting is a common phenomenon in nuclear magnetic resonance spectroscopy, which is a phenomenon caused by the interaction between adjacent spins. It will cause the spectrum peaks to be crowded and the resolution to decrease, which brings a lot of inconvenience to the analysis of the spectrum. In order to remove the negative effects brought by coupling peak splitting and restore the pure chemical shift spectrum, the traditional method mainly uses pulse sequences including: BIRD, ZS and PSYCHE three pulse sequences for decoupling. However, the traditional decoupling method has a long spectrum acquisition time and great experimental difficulty, and the pure chemical shift spectrum obtained by it has problems such as pseudo peaks and reduced resolution, which greatly limits the application of pure chemical shift spectrum. Summary of the invention

[0003] The main technical problem to be solved by the present invention is to provide a virtual decoupling method for one-dimensional nuclear magnetic resonance hydrogen spectrum based on deep learning, which can decouple the one-dimensional nuclear magnetic resonance hydrogen spectrum to obtain a clean pure chemical shift spectrum.

[0004] In order to solve the technical problems of long pulse sequence decoupling experiment time and great difficulty, the present invention adopts the following technical solution:

[0005] A virtual decoupling method for one-dimensional hydrogen spectrum of nuclear magnetic resonance based on deep learning, comprising the following steps:

[0006] S1: Generate the training set and test set required for the deep learning model;

[0007] S2: Design deep learning model architecture and build the model;

[0008] S3: Using the training set and the test set to train the deep learning model to obtain a converged and trained deep learning model;

[0009] S4: Use the test set and the one-dimensional hydrogen spectrum collected in the experiment to test the trained deep learning model.

[0010] In a preferred embodiment, step S1 specifically includes:

[0011] S11: Based on the characteristic that the free induction decay signal is composed of the superposition of complex exponential signals, a mathematical model is used to generate a simulated one-dimensional nuclear magnetic resonance hydrogen spectrum with a Vo i gt peak shape, noise and distortion;

[0012] The parameters of the simulated one-dimensional nuclear magnetic resonance hydrogen spectrum include: the number of coupled systems, the number of coupled system spins, spectrum width, line width, spectrum peak position, coupling constant, noise intensity and distortion degree;

[0013] S12: generating a pure chemical shift spectrum without coupling split peaks, noise and distortion corresponding to the one-dimensional nuclear magnetic resonance hydrogen spectrum described in S11;

[0014] S13: Generate the peak position and intensity in the pure chemical shift spectrum according to S12, and generate two-channel label data, each peak occupies the position of three data points; the data size of the first channel is 0 or 1, representing whether the point is a peak; the data of the second channel is the peak intensity;

[0015] S14: Logarithmically scale the label spectrum peak intensity to control it at the same order of magnitude;

[0016] S15: Repeat S11-S14 to generate a set amount of training sets and test sets.

[0017] In a preferred embodiment, the step S2 specifically includes:

[0018] S21: Design and build encoder modules: Each level of the encoder module consists of a multi-scale feature extraction module and three CBR modules; the CBR module consists of a convolutional layer with a convolution kernel of 3 and a stride of 1; each convolutional layer is followed by a batch normalization layer and a nonlinear layer ReLU; each level is followed by a maximum pooling layer with a size of 2 and a stride of 2 for downsampling;

[0019] S22: Design and build a decoder module: Each level of the decoder module includes an upsampling convolution module, an attention gate module, a multi-scale feature extraction module and three CBR modules;

[0020] The upsampling convolution module consists of a deconvolution layer with a convolution kernel of 4 and a stride of 2 and a CBR module; the output of the decoder module of the previous layer is dimensionally expanded through the upsampling convolution module and input into the attention gate module together with the encoder output of the same layer, and the output of the attention gate module is concatenated with the output of the upsampling convolution module in the channel dimension, followed by a multi-scale feature extraction module and three CBR modules;

[0021] S23: Design and build a multi-scale feature extraction module: The multi-scale feature extraction module consists of four convolution channels, namely: (1) a convolution layer with a convolution kernel of 1 and a stride of 1; (2) a convolution layer with a convolution kernel of 1 and a stride of 1 is stacked with a convolution layer with a convolution kernel of 8 and a stride of 1; (3) a convolution layer with a convolution kernel of 1 and a stride of 1 is stacked with a convolution layer with a convolution kernel of 32 and a stride of 1; (4) a convolution layer with a convolution kernel of 1 and a stride of 1 is stacked with a convolution layer with a convolution kernel of 64 and a stride of 1; each convolution layer is followed by a batch normalization layer and the first nonlinear layer ReLU;

[0022] S24: The encoder and decoder modules perform feature extraction and feature recovery respectively;

[0023] S25: Design and build an attention gate module: The attention gate module includes two independent convolution layers with a convolution kernel of 1 and a step size of 1. The outputs of the two are added and then passed through the second nonlinear layer ReLU, a convolution layer with a convolution kernel of 1 and a step size of 1, and the first nonlinear layer S i gmo id; the encoder output of the same layer and the output of the upsampling convolution module in the decoder pass through the attention gate module, and the output of the first nonlinear layer S i gmo id is multiplied by the encoder output as the output of the attention gate module;

[0024] S26: Design and build an output module: The output module consists of two convolutional layers with a convolution kernel of 3 and a stride of 1; the first convolutional layer is followed by a third nonlinear layer ReLU and a batch normalization layer; the output of the second convolutional layer, the first channel is followed by the second nonlinear layer S i gmo id, and the second channel is followed by the fourth nonlinear layer ReLU.

[0025] In a preferred embodiment, step S3 specifically includes:

[0026] S31: Design loss function: The loss function consists of two parts. The first part is the loss function of the peak position information, which is composed of the binary cross entropy loss function; the second part is the loss function of the peak intensity information, which is composed of the mean square error loss function; the total loss function is composed of the weighted sum of the two.

[0027] S32: Single network training: Input the one-dimensional hydrogen spectrum in the training set into the model, use the output and label of the model to calculate the loss function described in S31, and use the Adam optimizer to update the parameters in the model based on this loss function; at the same time, use the test set to calculate the loss function after each training to select the best model;

[0028] S33: Repeat the training steps described in S32 multiple times until the number of training times reaches a preset maximum number, or the training is stopped when the loss function decreases to convergence, to obtain a trained deep learning model.

[0029] In a preferred embodiment, step S4 specifically includes:

[0030] S41: Design evaluation indicators: evaluate the accuracy of the peak position information by calculating the true positive (TP), false positive (FP), true negative (TN), false negative (FN), precision, recall and F1 score of the peak position; evaluate the accuracy of the peak intensity information by calculating the normalized mean square error of the spectrum; the meaning of the evaluation indicators is:

[0031] TP: The point is judged as a spectrum peak, and the corresponding position of the label is the spectrum peak;

[0032] FP: The point is judged as a peak, but the corresponding position of the label is the baseline;

[0033] TN: The point is judged as the baseline, and the corresponding position of the label is the baseline;

[0034] FN: The point is judged as the baseline, but the corresponding position of the label is the spectrum peak;

[0035] Accuracy:

[0036]

[0037] Recall:

[0038]

[0039] F1 score:

[0040]

[0041] Normalized mean square error:

[0042]

[0043] In formula (4), x is the one-dimensional data obtained by the model output, y is the corresponding reference pure chemical shift spectrum data, and N is the spectrum data length;

[0044] Formulas (1), (2), and (3) can be used to quantitatively determine the accuracy of the peak position information. The closer the precision and recall are to 100%, and the closer the F1 score is to 1, the more accurate the peak position is. Formula (4) can be used to quantitatively determine the regression error and accuracy of the peak intensity information. The closer the normalized mean square error is to 0, the closer the model output spectrum is to the reference spectrum.

[0045] S42: Input the test set samples or the one-dimensional hydrogen spectrum samples obtained from the experiment into the model, and the model outputs data containing the peak position information and intensity information; based on the obtained data and the peak model, construct the peak at a specific position of the spectrum, thereby obtaining a pure chemical shift spectrum. Quantitatively evaluate the obtained spectrum and data.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] The method proposed in the present invention can process the one-dimensional hydrogen spectrum of nuclear magnetic resonance based on the characteristics of the deep learning model and the nuclear magnetic resonance coupling splitting peak, so as to obtain a pure chemical shift spectrum, which greatly improves the interpretability of the one-dimensional hydrogen spectrum of nuclear magnetic resonance. At the same time, compared with the pure chemical shift spectrum obtained by traditional pulse sequence decoupling, the spectrum after decoupling by this method has been improved in signal-to-noise ratio, distortion reduction and line width. In addition, the method has wide applicability for different spectral widths and coupling systems, and also has good robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is the deep learning model structure.

[0049] Figure 2 This is a comparison of the simulated spectrum before and after decoupling.

[0050] Figure 3 This is a comparison chart before and after decoupling the experimental spectrum. DETAILED DESCRIPTION

[0051] The various steps in the specific implementation process of the present invention are as follows:

[0052] Step 1: Generate the training set and test set required for the deep learning model.

[0053] According to the characteristic that the free induction decay signal is composed of the superposition of complex exponential signals, a mathematical model is used to generate a simulated one-dimensional nuclear magnetic resonance hydrogen spectrum with a Voigt peak type, noise and distortion; the parameters of the simulated one-dimensional nuclear magnetic resonance hydrogen spectrum include: the number of coupled systems is [2,12], the number of coupled system spins is [1,5], the spectrum width is [2048,4096] Hz, the line width is [5,12] Hz, the peak position, the coupling constant is [5,20] Hz, the signal-to-noise ratio SNR is [20.97, 35.74] dB, and the degree of distortion includes phase distortion and baseline distortion; the above signal-to-noise ratio calculation formula is: The above parameters are all randomly generated; the final data of size 2×8192 is generated, which are the real and imaginary parts of the one-dimensional hydrogen spectrum;

[0054] Generate a pure chemical shift spectrum without coupling split peaks, noise and distortion corresponding to the one-dimensional nuclear magnetic resonance hydrogen spectrum; generate two-channel label data according to the peak position and intensity in the pure chemical shift spectrum, and each peak occupies the position of three data points; the data size of the first channel is 0 or 1, representing whether the point is a peak; the data of the second channel is the peak intensity; perform logarithmic scaling on the peak intensity in the label to control it to the same order of magnitude;

[0055] Repeat the above steps to generate a 140,000 training set and a 20,000 test set.

[0056] Step 2: Design the deep learning model architecture and build the model.

[0057] Deep learning models such as Figure 1 As shown in the figure, the model consists of four parts, namely encoder, decoder, attention gate module and output module.

[0058] Each level of the encoder module consists of a multi-scale feature extraction module and three CBR (Conv, BatchNorm, ReLU) modules; the CBR module consists of a convolution layer with a kernel of 3 and a stride of 1; each convolution layer is followed by a batch normalization layer and a nonlinear layer ReLU; each level is followed by a maximum pooling layer of size 2 and a stride of 2 for downsampling;

[0059] Each level of the decoder module includes an upsampling convolution module, an attention gate module, a multi-scale feature extraction module and three CBR modules; the upsampling convolution module consists of a deconvolution layer with a convolution kernel of 4 and a step size of 2 and a CBR module; the output of the decoder module of the previous level is dimensionally expanded through the upsampling convolution module, and is input into the attention gate module together with the encoder output of the same level, and the output of the attention gate module is spliced ​​with the output of the upsampling convolution module in the channel dimension, followed by a multi-scale feature extraction module and three CBR modules.

[0060] The multi-scale feature extraction module consists of four convolution channels, namely: (1) a convolution layer with a convolution kernel of 1 and a stride of 1; (2) a convolution layer with a convolution kernel of 1 and a stride of 1 superimposed on a convolution layer with a convolution kernel of 8 and a stride of 1; (3) a convolution layer with a convolution kernel of 1 and a stride of 1 superimposed on a convolution layer with a convolution kernel of 32 and a stride of 1; (4) a convolution layer with a convolution kernel of 1 and a stride of 1 superimposed on a convolution layer with a convolution kernel of 64 and a stride of 1; each convolution layer is followed by a batch normalization layer and a nonlinear layer ReLU.

[0061] The encoder and decoder modules perform feature extraction and feature recovery respectively. The skip connection between the two modules ensures that the details lost due to downsampling are restored, and these losses are also weighted by the attention gate module to make the restored features more representative.

[0062] The attention gate module includes: two independent convolution layers with a kernel of 1 and a stride of 1, the outputs of which are added and then passed through a nonlinear layer ReLU, a convolution layer with a kernel of 1 and a stride of 1, and a nonlinear layer Sigma id; the encoder output of the same layer and the output of the upsampling convolution module in the decoder pass through the attention gate module, and the output of the Sigma d layer is multiplied by the encoder output as the output of the attention gate module;

[0063] The output module consists of two convolutional layers with a kernel of 3 and a stride of 1; the first convolutional layer is followed by a nonlinear layer ReLU and a batch normalization layer; the output of the second convolutional layer, the first channel is followed by a nonlinear layer Sigmoid, and the second channel is followed by a nonlinear layer ReLU.

[0064] Step 3: Use the training set and the test set to train the deep learning model to obtain a converged and trained deep learning model.

[0065] The loss function consists of two parts. The first part is the loss function of the spectral peak position information, which is composed of the binary cross entropy loss function; the second part is the loss function of the spectral peak intensity information, which is composed of the mean square error loss function; the total loss function is composed of the weighted sum of the two.

[0066] A single network training is to input the one-dimensional hydrogen spectrum in the training set into the model, use the model output and label to calculate the above loss function, and use the Adam optimizer to update the parameters in the model based on this loss function; at the same time, after each training, use the test set to calculate the loss function and select the best model;

[0067] The training steps are repeated multiple times until the number of training times reaches the preset maximum number, or the training is stopped when the loss function drops to convergence, and a trained deep learning model is obtained.

[0068] Step 4: Use the test set and the one-dimensional hydrogen spectrum collected in the experiment to test the trained deep learning model.

[0069] Design evaluation indicators: evaluate the accuracy of the peak position information by calculating the true positive (TP), false positive (FP), true negative (TN), false negative (FN), precision, recall and F1 score of the peak position; evaluate the accuracy of the peak intensity information by calculating the normalized mean square error of the spectrum; the meaning of the evaluation indicators is:

[0070] TP: The point is judged as a spectrum peak, and the corresponding position of the label is the spectrum peak;

[0071] FP: The point is judged as a peak, but the corresponding position of the label is the baseline;

[0072] TN: The point is judged as the baseline, and the corresponding position of the label is the baseline;

[0073] FN: The point is judged as the baseline, but the corresponding position of the label is the spectrum peak;

[0074] Accuracy:

[0075]

[0076] Recall:

[0077]

[0078] F1 score:

[0079]

[0080] Normalized mean square error:

[0081]

[0082] In formula (4), x is the one-dimensional data obtained by the model output, y is the corresponding reference pure chemical shift spectrum data, and N is the spectrum data length;

[0083] Formulas (1), (2), and (3) can be used to quantitatively determine the accuracy of the peak position information. The closer the precision and recall are to 100%, and the closer the F1 score is to 1, the more accurate the peak position is. Formula (4) can be used to quantitatively determine the regression error and accuracy of the peak intensity information. The closer the normalized mean square error is to 0, the closer the model output spectrum is to the reference spectrum.

[0084] The samples in the test set or the one-dimensional hydrogen spectrum samples collected in the experiment are input into the model, and the model outputs data containing the peak position information and intensity information; based on the obtained data and the peak model, the peak is constructed at a specific position of the spectrum, thereby obtaining a pure chemical shift spectrum. The obtained spectrum and data are quantitatively evaluated.

[0085] The following is a detailed description of the accompanying drawings:

[0086] Figure 1 : Deep learning model structure;

[0087] Figure 2: The output spectrum obtained by inputting the simulated one-dimensional nuclear magnetic resonance hydrogen spectrum into the model and the pure chemical shift spectrum as a label; even if some peaks are very close to each other, the model can still restore the peaks at all positions of the spectrum;

[0088] Figure 3 :The output spectrum obtained by inputting the one-dimensional nuclear magnetic resonance hydrogen spectrum of estradiol sample into the model is compared with the pure chemical shift spectrum obtained by decoupling with the PSYCHE pulse sequence; compared with the pure chemical shift spectrum obtained by experiment, the model can restore the peaks at all positions of the spectrum, reduce the line width of the peaks, and improve the resolution of the peaks;

[0089] The above embodiments are only used to further illustrate the one-dimensional nuclear magnetic resonance hydrogen spectrum virtual decoupling method of the present invention, but the present invention is not limited to the embodiments. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention fall within the protection scope of the technical solution of the present invention.

Claims

1. A virtual decoupling method for one-dimensional hydrogen spectrum of nuclear magnetic resonance based on deep learning, characterized in that: The steps include: S1: Generate the training set and test set required for the deep learning model; S2: Design deep learning model architecture and build the model; S3: Using the training set and the test set to train the deep learning model to obtain a converged and trained deep learning model; S4: Use the test set and the one-dimensional hydrogen spectrum collected in the experiment to test the trained deep learning model.

2. The method for virtual decoupling of one-dimensional hydrogen nuclear magnetic resonance spectrum based on deep learning according to claim 1, characterized in that: Step S1 specifically includes: S11: Based on the characteristic that the free induction decay signal is composed of the superposition of complex exponential signals, a mathematical model is used to generate a simulated one-dimensional nuclear magnetic resonance hydrogen spectrum with Voigt peak shape, noise and distortion; The parameters of the simulated one-dimensional nuclear magnetic resonance hydrogen spectrum include: the number of coupled systems, the number of coupled system spins, spectrum width, line width, spectrum peak position, coupling constant, noise intensity and distortion degree; S12: generating a pure chemical shift spectrum without coupling split peaks, noise and distortion corresponding to the one-dimensional nuclear magnetic resonance hydrogen spectrum described in S11; S13: Generate the peak position and intensity in the pure chemical shift spectrum according to S12, and generate two-channel label data, each peak occupies the position of three data points; the data size of the first channel is 0 or 1, representing whether the point is a peak; the data of the second channel is the peak intensity; S14: Logarithmically scale the label spectrum peak intensity to control it at the same order of magnitude; S15: Repeat S11-S14 to generate a set amount of training sets and test sets.

3. The method for virtual decoupling of one-dimensional hydrogen nuclear magnetic resonance spectrum based on deep learning according to claim 1, characterized in that: The step S2 specifically includes: S21: Design and build encoder modules: Each level of the encoder module consists of a multi-scale feature extraction module and three CBR modules; the CBR module consists of a convolutional layer with a convolution kernel of 3 and a stride of 1; each convolutional layer is followed by a batch normalization layer and a nonlinear layer ReLU; each level is followed by a maximum pooling layer with a size of 2 and a stride of 2 for downsampling; S22: Design and build a decoder module: Each level of the decoder module includes an upsampling convolution module, an attention gate module, a multi-scale feature extraction module and three CBR modules; The upsampling convolution module consists of a deconvolution layer with a convolution kernel of 4 and a stride of 2 and a CBR module; the output of the decoder module of the previous layer is dimensionally expanded through the upsampling convolution module and input into the attention gate module together with the encoder output of the same layer, and the output of the attention gate module is concatenated with the output of the upsampling convolution module in the channel dimension, followed by a multi-scale feature extraction module and three CBR modules; S23: Design and build a multi-scale feature extraction module: The multi-scale feature extraction module consists of four convolution channels, namely: (1) a convolution layer with a convolution kernel of 1 and a stride of 1; (2) a convolution layer with a convolution kernel of 1 and a stride of 1 is stacked with a convolution layer with a convolution kernel of 8 and a stride of 1; (3) a convolution layer with a convolution kernel of 1 and a stride of 1 is stacked with a convolution layer with a convolution kernel of 32 and a stride of 1; (4) a convolution layer with a convolution kernel of 1 and a stride of 1 is stacked with a convolution layer with a convolution kernel of 64 and a stride of 1; each convolution layer is followed by a batch normalization layer and the first nonlinear layer ReLU; S24: The encoder and decoder modules perform feature extraction and feature recovery respectively; S25: Design and build an attention gate module: The attention gate module includes two independent convolution layers with a convolution kernel of 1 and a step size of 1. The outputs of the two are added and then passed through the second nonlinear layer ReLU, a convolution layer with a convolution kernel of 1 and a step size of 1, and the first nonlinear layer Sigmoid; the encoder output of the same layer and the output of the upsampling convolution module in the decoder pass through the attention gate module, and the output of the first nonlinear layer Sigmoid is multiplied by the encoder output as the output of the attention gate module; S26: Design and build an output module: The output module consists of two convolutional layers with a convolution kernel of 3 and a stride of 1; the first convolutional layer is followed by a third nonlinear layer ReLU and a batch normalization layer; the output of the second convolutional layer, the first channel is followed by a second nonlinear layer Sigmoid, and the second channel is followed by a fourth nonlinear layer ReLU.

4. The method for virtual decoupling of one-dimensional hydrogen nuclear magnetic resonance spectrum based on deep learning according to claim 1, characterized in that: Step S3 specifically includes: S31: Design loss function: The loss function consists of two parts. The first part is the loss function of the peak position information, which is composed of the binary cross entropy loss function; the second part is the loss function of the peak intensity information, which is composed of the mean square error loss function; the total loss function is composed of the weighted sum of the two. S32: Single network training: Input the one-dimensional hydrogen spectrum in the training set into the model, use the output and label of the model to calculate the loss function described in S31, and use the Adam optimizer to update the parameters in the model based on this loss function; at the same time, use the test set to calculate the loss function after each training to select the best model; S33: Repeat the training steps described in S32 multiple times until the number of training times reaches a preset maximum number, or the training is stopped when the loss function decreases to convergence, to obtain a trained deep learning model.

5. The method for virtual decoupling of one-dimensional hydrogen nuclear magnetic resonance spectrum based on deep learning according to claim 1, characterized in that: Step S4 specifically includes: S41: Design evaluation indicators: evaluate the accuracy of the peak position information by calculating the true positive (TP), false positive (FP), true negative (TN), false negative (FN), precision, recall and F1 score of the peak position; evaluate the accuracy of the peak intensity information by calculating the normalized mean square error of the spectrum; the meaning of the evaluation indicators is: TP: The point is judged as a spectrum peak, and the corresponding position of the label is the spectrum peak; FP: The point is judged as a peak, but the corresponding position of the label is the baseline; TN: The point is judged as the baseline, and the corresponding position of the label is the baseline; FN: The point is judged as the baseline, but the corresponding position of the label is the spectrum peak; Accuracy: Recall: F1 score: Normalized mean square error: In formula (4), x is the one-dimensional data obtained by the model output, y is the corresponding reference pure chemical shift spectrum data, and N is the spectrum data length; Formulas (1), (2), and (3) can be used to quantitatively determine the accuracy of the peak position information. The closer the precision and recall are to 100%, and the closer the F1 score is to 1, the more accurate the peak position is. Formula (4) can be used to quantitatively determine the regression error and accuracy of the peak intensity information. The closer the normalized mean square error is to 0, the closer the model output spectrum is to the reference spectrum. S42: Input the test set samples or the one-dimensional hydrogen spectrum samples obtained from the experiment into the model, and the model outputs data containing the peak position information and intensity information; based on the obtained data and the peak model, construct the peak at a specific position of the spectrum, thereby obtaining a pure chemical shift spectrum. Quantitatively evaluate the obtained spectrum and data.

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