Ground magnetic resonance signal sparse denoising method based on combined dictionary

Abstract

The invention belongs to the field of magnetic resonance measurement signal noise filtering, and particularly relates to a ground magnetic resonance signal sparse denoising method of a combined dictionary, which comprises the following steps: reconstructing a power frequency harmonic component of a magnetic resonance signal according to frequency bands, and eliminating power frequency harmonics from the magnetic resonance signal to obtain a power frequency-removed signal; constructing a track matrix Z by adopting a Gaussian random matrix, constructing a track matrix Y by adopting a power frequency-removed signal, taking first K columns of the track matrix Z and normalizing to obtain an initial dictionary D, and using the track matrix Y as an original sample for constructing a sparse coefficient matrix X; updating the initial dictionary D and the sparse coefficient matrix X through K-SVD dictionary learning, and reconstructing a track matrix by adopting the updated dictionary # imgabs0 # and the sparse coefficient matrix # imgabs1 # to obtain a track matrix W; and obtaining a pure magnetic resonance signal by taking the first row of the track matrix W, and realizing effective removal of MRS signal noise in a complex electromagnetic interference scene under the condition of single signal acquisition.

Description

Technical Field

[0001] This application belongs to the field of Magnetic Resonance Sounding (MRS) signal noise filtering, and specifically relates to a sparse denoising method for ground magnetic resonance signals using a combined dictionary. Background Art

[0002] As a core means of non-invasive groundwater exploration, the ground magnetic resonance sounding technology obtains key parameters such as the relaxation time, initial amplitude, initial phase, and Larmor frequency of the aquifer by exciting the nuclear magnetic resonance effect of hydrogen protons in the underground aquifer, so as to quantitatively characterize the occurrence state of groundwater. Compared with traditional geophysical exploration methods, this technology has significant advantages such as high detection efficiency, rich information dimensions, and quantitative result interpretation, and has become a key technical support in the fields of underground water resource census, geological disaster warning, and major project hydrogeological assessment.

[0003] Due to the restriction of the natural field source characteristics of the geomagnetic field on the engineering application of this technology, the intensity of the MRS signal collected after excitation is extremely weak, usually at the nanovolt level, and a high-gain acquisition system is required to capture the signal. More seriously, in an open-field operating environment, the broadband environmental noise (including power frequency harmonic interference, random white noise, and spike pulses) mixed in the signal transmission path strongly couples with the effective signal, resulting in the degradation of the quality of the detected MRS signal, a very low signal-to-noise ratio of the original data, and thus affecting the extraction of MRS signal characteristic parameters, reducing the accuracy of the inversion results, and greatly affecting the effective assessment of the groundwater resource content in the signal acquisition area.

[0004] The current noise suppression technology system has limitations. Although the active cancellation algorithm based on the power frequency harmonic characteristics can attenuate the interference in specific frequency bands, its random noise suppression efficiency is insufficient; the Empirical Mode Decomposition (EMD) method can extract the signal attenuation trend under medium signal-to-noise ratio conditions, but it faces the problem of low-frequency noise residue caused by the mixing of intrinsic mode functions; although the time-frequency joint analysis method (such as improved STFT) improves the adaptability to non-stationary noise, it is prone to cause distortion of the effective signal when separating the noise in the main frequency band of the signal. Existing methods mostly focus on suppressing different types of noise by different means, lacking a systematic solution for complex noise coupling scenarios, and it is difficult to meet the engineering requirements of synchronous elimination of multi-source interference in field exploration.

[0005] This technical defect directly restricts the detection depth and resolution of the ground magnetic resonance sounding technology in a strong interference environment, especially the application effect in severely electromagnetic polluted areas such as urban pipe network areas and industrial agglomeration areas has decreased significantly. Therefore, developing a composite noise suppression method with strong robustness has become a key issue in improving the engineering applicability of the ground magnetic resonance sounding technology. Summary of the Invention

[0006] An embodiment of the present application provides a sparse denoising method for ground magnetic resonance signals based on a combined dictionary, which solves the problem that MRS signals are easily interfered by random noise and power frequency harmonic noise during the measurement process.

[0007] The present application is implemented as follows. A sparse denoising method for ground magnetic resonance signals based on a combined dictionary, the method comprising the following steps: Reconstruct the power frequency harmonic components of the magnetic resonance signal in frequency bands, and eliminate the power frequency harmonics from the magnetic resonance signal to obtain a power frequency-removed signal; Construct a trajectory matrix using a Gaussian random matrix and construct a trajectory matrix using the power frequency-removed signal , the trajectory matrix Take the first columns and normalize them to obtain an initial dictionary , the trajectory matrix is used as the original sample to construct a sparse coefficient matrix ; Complete the update of the initial dictionary and the sparse coefficient matrix through K-SVD dictionary learning, and use the updated dictionary and the sparse coefficient matrix to reconstruct the trajectory matrix to obtain the trajectory matrix ; Take the first row of the trajectory matrix to obtain the pure magnetic resonance signal.

[0008] Further, reconstructing the power frequency harmonic components of the magnetic resonance signal in frequency bands includes: reconstructing the power frequency harmonic components in sequence according to the harmonic order using a cosine function.

[0009] Further, reconstructing the power frequency harmonic components in sequence according to the harmonic order using a cosine function includes: Set the fundamental frequency of the power frequency harmonics, and obtain the th harmonic frequency according to the fundamental frequency of the power frequency harmonics; Construct an objective function in the form of a cosine function with the th harmonic frequency, and use the amplitude, harmonic frequency, and phase in the objective function as a parameter combination; Randomly set a first parameter combination, generate an objective function corresponding to the first parameter combination, and calculate the first goodness-of-fit between the objective function corresponding to the first parameter combination and the preprocessed signal, where the preprocessed signal is the signal after removing the spike noise from the magnetic resonance signal; Add perturbations to generate a second parameter combination, and generate an objective function corresponding to the second parameter combination, and calculate the second goodness between the objective function corresponding to the second parameter combination and the preprocessed signal; Calculate the difference between the second goodness and the first goodness, and determine whether the second parameter combination replaces the first parameter combination according to the difference; Iterate multiple times. After the iteration ends, obtain the optimal parameter combination corresponding to the th harmonic frequency, and perform reconstruction according to the optimal parameter combination to obtain the power frequency harmonic component in the form of a cosine function; Traverse all harmonic frequencies to obtain the power frequency harmonic components corresponding to all harmonic frequencies.

[0010] Furthermore, the simulated annealing algorithm is used to control the randomness of the iteration process during the iteration.

[0011] Furthermore, the magnetic resonance signal is a single-shot signal collected under single-shot signal acquisition conditions.

[0012] Furthermore, determining whether the second parameter combination replaces the first parameter combination according to the difference includes: If the difference is greater than 0, or the difference is less than 0 and , where is the difference, is the temperature in the simulated annealing algorithm, is a random number uniformly distributed in (0, 1), then the second parameter combination replaces the first parameter combination; otherwise the first parameter combination is equal to the first parameter combination.

[0013] Furthermore, the trajectory matrix is used as the original sample to construct the sparse coefficient matrix , including: S21 extracts the th column in the trajectory matrix and records it as , , is the total number of columns, calculate the inner product of each column in the initial dictionary and , select the atoms with the first absolute values, and record them as , , is the preset sparsity, calculate the Jaccard coefficient between and , select the atoms with the first Jaccard coefficient values, and add them to the index set ; S22 repeats S21 until the length of the index set is equal to the maximum number of selected atoms , solve the sparse coefficients using the least squares method , and complete the solution of the sparse coefficients of, and calculate according to the sparse coefficients residual ; S23 Backtracking optimization index set , calculate the initial dictionary the inner product of each column in and the residual , select the atom with the largest absolute value of the inner product, and record the index of the atom with the largest absolute value as , and judge whether it exists in the index set ; if not, replace the position in the index set in turn; solve the new sparse coefficient and calculate the energy of the residual , , if the minimum value in the energy of the residual is less than the energy of the residual , then replace the index at the corresponding position with , and retain the new sparse coefficient ; S24 Repeat S21 - S23 until the solution of the sparse coefficients of each column in the trajectory matrix is completed, and the sparse coefficients of all columns are used to construct the sparse coefficient matrix .

[0014] Further, the calculation method of the Jaccard coefficient is: , is and the Jaccard coefficient between.

[0015] Further, update the initial dictionary and the sparse coefficient matrix through K - SVD dictionary learning, including: establishing the optimization problem , and expanding to obtain: , where, is the total number of columns of the initial dictionary , is the -th column of the initial dictionary , is the -th row of the sparse coefficient matrix ; is the -th column of the initial dictionary , is a sparse coefficient matrix of the row, representing the residual matrix; Performing singular value decomposition on the residual matrix to obtain , where is the left singular matrix, is the singular value matrix, is the right singular matrix, represents transpose, and the eigenvalues in the diagonal matrix obtained by singular value decomposition are arranged from large to small. Take the first column of the left singular matrix as 's updated value, extract the product of the largest singular value and the first row of the right singular matrix , and replace the corresponding non-zero positions in ; Repeat the operation until the initial dictionary is completely updated to obtain the updated dictionary and the updated sparse coefficient matrix .

[0016] Compared with the prior art, the beneficial effects of this application are as follows: For MRS signals containing both random noise and power frequency harmonics, this application constructs a dictionary based on cosine functions, optimizes parameters in combination with the simulated annealing algorithm, and reconstructs and eliminates power frequency harmonic components; it can effectively remove the noise of MRS signals in complex electromagnetic interference scenarios under single signal acquisition conditions, solving the efficiency bottleneck problem caused by the traditional technology relying on repeated acquisitions. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a flowchart of the ground magnetic resonance signal sparse denoising method based on a combined dictionary provided by an embodiment of this application; Figure 2 is the noisy signal, ideal signal and spectrum provided by an embodiment of this application. (A) is the time-amplitude diagram of the noisy signal and ideal signal, and (B) is the corresponding frequency-amplitude diagram; Figure 3 is the noisy signal, the noisy signal after eliminating harmonics, i.e., the power frequency removal signal , ideal signal and spectrum provided by an embodiment of this application. (A) is the time-amplitude diagram, and (B) is the frequency-amplitude diagram; Figure 4 is the noisy signal, ideal signal, reconstructed signal and spectrum provided by an embodiment of this application. (A) is the time-amplitude diagram, and (B) is the frequency-amplitude diagram;​ Figure 5 The measured noisy signal and spectrum provided by the embodiments of the present application, (A) is a time-amplitude diagram, and (B) is a frequency-amplitude diagram; Figure 6 The measured noisy signal, the power-frequency signal after eliminating harmonic noise, and the spectrum provided by the embodiments of the present application, (A) is a time-amplitude diagram, and (B) is the corresponding frequency-amplitude diagram.

[0018] Figure 7 The measured noisy signal, the reconstructed signal, and the spectrum provided by the embodiments of the present application, (A) is a time-amplitude diagram, and (B) is the corresponding frequency-amplitude diagram. Specific implementation manners

[0019] In order to make the objectives, technical solutions, and advantages of the present application clearer and more intuitive, the present application will be further described in detail below in conjunction with embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0020] Regarding the effective removal of the noise of the MRS signal in a complex electromagnetic interference scenario, the existing processing methods rely on repeatedly collecting signals, resulting in a large amount of data to be processed during the denoising process and a reduction in efficiency due to multiple collections.

[0021] The embodiments of the present application address the above problems. For the MRS signal containing both random noise and power-frequency harmonics, a dictionary is constructed based on the cosine function, the parameters are optimized by combining the simulated annealing algorithm, and then K-SVD dictionary learning is adopted and combined with the Jaccard algorithm. By using the Jaccard coefficient as the atom selection criterion and integrating the residual backtracking mechanism, the efficient separation of the signal and noise is realized, and the effective removal of the noise of the MRS signal in a complex electromagnetic interference scenario can be achieved under the condition of single signal acquisition.

[0022] See Figure 1 As shown, a sparse denoising method for ground magnetic resonance signals based on a combined dictionary, the method includes the following steps: S11 Reconstruct the power-frequency harmonic components of the magnetic resonance signal in frequency bands, and eliminate the power-frequency harmonics from the magnetic resonance signal to obtain a power-frequency removed signal; The magnetic resonance signal here can be a single signal collected under the condition of single signal acquisition or a single signal collected under the condition of multiple signal acquisitions. The single signal acquisition condition refers to quickly collecting complete signal data after a single excitation pulse sequence, which greatly shortens the imaging time. However, there are problems such as low signal-to-noise ratio (SNR), low resolution, and sensitivity to magnetic field inhomogeneity. Here, the single time does not only refer to one time, but can also refer to a small number of acquisitions. The present application is not limited to single time and can also be multiple times.

[0023] Magnetic resonance signals usually contain multiple frequency components, among which power frequency harmonic components may mask useful signal information. Through band - segmented reconstruction, the magnetic resonance signal can be decomposed into different frequency bands, and the power frequency harmonic components and other useful signal components can be processed separately, so as to more effectively remove noise and improve signal quality.

[0024] A set of original noisy magnetic resonance signals can be collected by a magnetic resonance sounding water detector for magnetic resonance signals , with a Larmor frequency of , a signal length of . The original noisy magnetic resonance signal is pre - processed by removing spike noise to obtain the pre - processed signal , where represents the time series; The cosine function , as shown in formula (1), is used to construct a dictionary and combined with the simulated annealing algorithm for band - segmented reconstruction and elimination of power frequency harmonics in the pre - processed signal . The reconstructed power frequency harmonics are sequentially recorded as , ; represents the total number of reconstructions. The signal after removing power frequency is calculated by formula (2) and denoted as ; (1), (2), S12 uses a Gaussian random matrix to construct a trajectory matrix , and uses the signal after removing power frequency to construct a trajectory matrix . The trajectory matrix takes the first columns and normalizes them to obtain the initial dictionary . The trajectory matrix is used as the original sample to construct the sparse coefficient matrix ; The Gaussian random matrix is used to generate random measurements or random samplings, and its elements are randomly drawn from a Gaussian distribution (normal distribution). The trajectory matrix is a structured matrix used to represent certain characteristics of the signal. The process of constructing the trajectory matrix using the Gaussian random matrix is to obtain the trajectory matrix through matrix multiplication of the Gaussian random matrix.

[0025] The signal after removing power frequency is the signal that has been segmented by S11. By arranging the signals of each segment in matrix form, a trajectory matrix is formed.

[0026] S13 completes the update of the initial dictionary and the sparse coefficient matrix using K-SVD dictionary learning, and reconstructs the trajectory matrix using the updated dictionary and the sparse coefficient matrix to obtain the trajectory matrix ; K-SVD dictionary learning (K-Singular Value Decomposition) is to find a dictionary such that a signal can be sparsely represented as a linear combination of atoms in the dictionary.

[0027] The trajectory matrix is expressed as: .

[0028] S14 takes the first row of the trajectory matrix to obtain the pure magnetic resonance signal.

[0029] In one embodiment, in S11, the power frequency harmonic components are reconstructed in sequence using the cosine function, including: Setting the power frequency harmonic fundamental frequency, and obtaining the th harmonic frequency according to the power frequency harmonic fundamental frequency; Constructing an objective function in the form of a cosine function for the th harmonic frequency , where the amplitude, harmonic frequency, and phase in the objective function are used as parameter combinations; among them, is the parameter to be optimized, the maximum value of the parameter , the minimum value ; is the th harmonic frequency, is the power frequency harmonic fundamental frequency.

[0030] Randomly set the first parameter combination, generate the objective function corresponding to the first parameter combination, and calculate the first goodness-of-fit between the objective function corresponding to the first parameter combination and the preprocessed signal; the first parameter combination is an initialization parameter randomly set under the conditions of the simulated annealing algorithm, and the conditions of the simulated annealing algorithm refer to the initial temperature and the cooling rate. For example, in one embodiment, the initial temperature , the cooling rate . The first parameter combination is represented by , the generated objective function corresponding to the first parameter combination , and calculate the first goodness-of-fit , the goodness-of-fit is calculated by the formula; , represents the preprocessed signal Length.

[0031] The preprocessed signal is the signal after removing the spike noise from the magnetic resonance signal.

[0032] Adding perturbations to generate a second parameter combination, generating an objective function corresponding to the second parameter combination, and calculating a second goodness-of-fit between the objective function corresponding to the second parameter combination and the preprocessed signal; the second parameter combination is used to represent, the perturbation formula: , generating the objective function corresponding to the objective function corresponding to the second parameter combination .

[0033] Calculating the difference between the second goodness-of-fit and the first goodness-of-fit, and determining whether the second parameter combination replaces the first parameter combination according to the difference; according to the difference , determining whether to accept the second parameter combination as the initial value for the next iteration, if or and , is a random number uniformly distributed in (0, 1), is the temperature in the simulated annealing algorithm, then accept the second parameter combination ; otherwise , where the difference calculation formula , the temperature reduction calculation method in the iteration process: , represents the updated temperature; Performing multiple iterations, and obtaining the optimal parameter combination corresponding to the th harmonic frequency after the iteration ends , and reconstructing according to the optimal parameter combination to obtain the power frequency harmonic component in the form of a cosine function ; is the optimal amplitude corresponding to the th harmonic frequency, is the optimal frequency corresponding to the th harmonic frequency, is the optimal phase corresponding to the th harmonic frequency, Traversing all harmonic frequencies to obtain the power frequency harmonic components corresponding to all harmonic frequencies.

[0034] In one embodiment, the trajectory matrix is used as the original sample to construct the sparse coefficient matrix , including: S21 extracts the th column in the trajectory matrix and records it as , is the total number of columns. Calculate the inner product of each column in the initial dictionary D with and select the atoms with the top absolute values, denoted as , , is the preset sparsity. Calculate the Jaccard coefficient between and , and select the atoms with the top Jaccard coefficient values and add them to the index set ; Calculate the Jaccard coefficient between and : , is and the Jaccard coefficient between them.

[0035] S22 repeats S21 until the length of the index set is equal to the maximum number of selected atoms . Use the least squares method to solve the sparse coefficient , complete the solution of the sparse coefficient of , and calculate the residual of ; ; represents the atoms corresponding to the first columns in the selected index set in the dictionary. Here, the in the first columns is the same as the maximum number of selected atoms .

[0036] S23 backtracks and optimizes the index set , calculates the inner product of each column of the initial dictionary with the residual , selects the atom with the largest absolute value of the inner product, and the index of the atom with the largest absolute value is denoted as . Determine whether exists in the index set ; if not, replace the position in the index set in turn; solve the new sparse coefficient and calculate the energy of the residual , . If the minimum value in the energy of the residual is less than the energy of the residual , replace the index at the corresponding position with , and retain the new sparse coefficient ; the energy of the residual is the sum of the squares of each point in the residual sequence.

[0037] S24 repeats S21 - S23 until the solution of the sparse coefficients for each column in the trajectory matrix is completed, and all column sparse coefficients are used to construct a sparse coefficient matrix .

[0038] In one embodiment, the initial dictionary and the sparse coefficient matrix are updated through K - SVD dictionary learning, including: establishing an optimization problem , which expands to obtain: , where is the total number of columns of the initial dictionary , is the -th column of the initial dictionary , is the -th row of the sparse coefficient matrix ; is the element at the -th row and -th column of the initial dictionary , is the -th row of the sparse coefficient matrix , and represents the residual matrix; The residual matrix is subjected to singular value decomposition to obtain , where is the left singular matrix, is the singular value matrix, is the right singular matrix, is the first column of the left singular matrix and is used as 's update value. The product of the largest singular value and the first row of the right singular matrix is extracted and replaces the corresponding non - zero positions in ; Repeat the operation until the initial dictionary is completely updated to obtain the updated dictionary and the updated sparse coefficient matrix .

[0039] The method of this application adopts a novel noise suppression mechanism that combines two dictionaries, innovatively introducing a residual ratio dynamic criterion and a Jaccard coefficient optimization strategy. It can effectively remove signal noise in complex electromagnetic interference scenarios under single signal acquisition conditions, solving the efficiency bottleneck problem caused by the traditional technology's reliance on repeated acquisitions. Its technical advantages are not only reflected in the significant improvement of the quality of the original data, but also in reconstructing the signal processing flow, removing different types of noise step by step according to their characteristics, greatly reducing the field exploration operation intensity, and opening up a new technical path for the theoretical deepening and engineering application of magnetic resonance detection technology.

[0040] The following is a simulation experiment of the method of this application carried out in the MATLAB, R2023a programming environment.

[0041] According to the mathematical formula Construct a pure magnetic resonance signal with a Larmor frequency of 2325 Hz, an amplitude of 200 nV, a relaxation time of 0.2 s, and an initial phase of . The signal sampling frequency , the sampling time interval length , and the number of data points . Add random noise with an amplitude ranging from 0 to 50 nV; then add power frequency harmonic noise with 100 harmonic orders, and its amplitude is a random number between 0 and 200 nV. The fundamental frequency of the power frequency harmonic varies in the range of 49.98 - 50.02 Hz. After mixing the noise and the signal, a raw noisy magnetic resonance signal with a signal-to-noise ratio of -25.45 dB is obtained . As Figure 2 shown, where Figure 2 in (A) is the time-amplitude diagram of the noisy signal (raw noisy magnetic resonance signal) and the ideal signal, Figure 2 in (B) is the corresponding frequency-amplitude diagram, including the noisy signal (raw noisy magnetic resonance signal) and the ideal signal.

[0042] The de-power frequency signal is obtained after processing. As Figure 3 shown, where Figure 3 in (A) is the time-amplitude diagram of the noisy signal (raw noisy magnetic resonance signal), the noisy signal after eliminating harmonics, i.e., the de-power frequency signal , and the ideal signal, Figure 3 in (B) is the corresponding frequency-amplitude diagram.

[0043] Create a Gaussian random matrix with the same length as the de-power frequency signal , and use the power frequency signal Construct a trajectory matrix with a Gaussian random matrix to convert a one-dimensional signal into a two-dimensional image. Among them, the trajectory matrix constructed by the Gaussian random matrix is used as the initial value of the dictionary, that is, the initial dictionary, and the K-SVD dictionary learning is combined with the JBGOMP algorithm to reconstruct and remove the power frequency signal. To eliminate random noise, take the first row of the reconstructed trajectory matrix to obtain the reconstructed signal, that is, the pure magnetic resonance signal.

[0044] To verify the effect of the method of this application, as Figure 4 shown, the noisy signal (original noisy magnetic resonance signal), the ideal signal, and the reconstructed signal (reconstructed pure magnetic resonance signal) are subjected to comparative analysis in the time domain and the frequency domain, where Figure 4 (A) in is the time-amplitude diagram of the three signals, Figure 4 (B) in is the corresponding frequency-amplitude diagram. After calculation, the initial amplitude error is -0.47%, the relaxation time error is 0.94%, its SNR = 28.98 dB, and the SNR is increased by 54.43 dB compared with that before processing. The obtained key parameter errors all meet the application requirements.

[0045] In the embodiment of this application, the magnetic resonance signal collected on the spot in the Cultural Square of Changchun City is used as the processing object of the method of this application. The original noisy magnetic resonance signal is generated by an Agilent-35670A signal source, and the Larmor frequency is set to , relaxation time , signal sampling frequency , transmission frequency is 2326 Hz, and the sampling time length . The analog signal is transmitted through the transmitting coil, and a certain distance is maintained between the transmitting coil and the receiving coil. The original noisy magnetic resonance signal is attenuated to the nanovolt level through space coupling, and a large amount of environmental noise will also be introduced. Due to the attenuation of the amplitude of the signal during the coupling process, the coupled by the receiving coil is different from the amplitude set by the initial signal source, and this value is uncertain. As Figure 5 shown, Figure 5 (A) in is the measured noisy signal (measured magnetic resonance signal), Figure 5 (B) in is the corresponding spectrogram, and its signal-to-noise ratio is calculated to be -17.08 dB.

[0046] After the harmonic noise in the original noisy magnetic resonance signal is completely reconstructed and eliminated through the cosine function combined with the simulated annealing algorithm, the power frequency removal signal is obtained. As Figure 6 shown, where Figure 6 (A) in is the time-amplitude diagram of the noisy signal (original noisy magnetic resonance signal) and the signal after eliminating harmonics, that is, the power frequency removal signal .Figure 6 In (B), it is the corresponding frequency-amplitude diagram.

[0047] Create a Gaussian random matrix with the same length as the power-frequency removed signal Use the power-frequency removed signal and the Gaussian random matrix to construct a trajectory matrix, converting the one-dimensional signal into a two-dimensional image. Among them, the trajectory matrix constructed by the Gaussian random matrix is used as the initial value of the dictionary, and the K-SVD dictionary learning combined with the JBGOMP algorithm is used to reconstruct the power-frequency removed signal to eliminate random noise. Take the first row of the reconstructed trajectory matrix to obtain the reconstructed signal, that is, the pure magnetic resonance signal.

[0048] To verify the effect of the method of this application, as Figure 7 shown, perform a comparative analysis of the measured noisy signal (measured magnetic resonance signal) and the reconstructed signal (reconstructed pure magnetic resonance signal) in the time domain and frequency domain, where Figure 7 in (A) is the time-amplitude diagram of the two signals, Figure 7 and in (B) is the corresponding frequency-amplitude diagram. Through calculation, the relaxation time error is -0.96%, its SNR = 22.40 dB, which is 39.48 dB higher than the SNR before processing, and the errors of the obtained key parameters all meet the application requirements.

[0049] The above are only the preferred embodiments of this application, and are not intended to limit this application. Any modifications, equivalent replacements, and improvements made within the spirit and principle of this application shall be included within the protection scope of this application.

Claims

1. A sparse denoising method for ground magnetic resonance signals based on a combined dictionary, characterized in that, The method includes the following steps: Reconstruct the power frequency harmonic components of the magnetic resonance signal in frequency bands, and eliminate the power frequency harmonics from the magnetic resonance signal to obtain a de-power frequency signal; Construct the trajectory matrix using a Gaussian random matrix , construct the trajectory matrix using the power frequency removal signal , the trajectory matrix Take the first columns and obtain the initial dictionary after normalization , the trajectory matrix is used as the original sample to construct the sparse coefficient matrix ; Complete the update of the initial dictionary through K-SVD dictionary learning and the sparse coefficient matrix Then, use the updated dictionary and the sparse coefficient matrix to reconstruct the trajectory matrix to obtain the trajectory matrix ; Obtain the trajectory matrix and take the first row to obtain a pure magnetic resonance signal.

2. The method for sparse denoising of ground magnetic resonance signals based on a combined dictionary according to claim 1, characterized in that Reconstructing the power frequency harmonic components of the magnetic resonance signal in frequency bands includes: reconstructing the power frequency harmonic components in sequence according to the harmonic order using a cosine function.

3. The method for sparse denoising of ground magnetic resonance signals based on a combined dictionary according to claim 2, wherein, Reconstructing the power frequency harmonic components in sequence according to the harmonic order using a cosine function includes: Set the fundamental frequency of power frequency harmonics, and obtain the harmonic frequency of the nth order according to the fundamental frequency of power frequency harmonics; Construct a target function in the form of a cosine function for the sub-harmonic frequency, where the amplitude, harmonic frequency, and phase in the target function are used as parameter combinations; Randomly set a first parameter combination, generate an objective function corresponding to the first parameter combination, and calculate a first goodness between the objective function corresponding to the first parameter combination and the preprocessed signal, where the preprocessed signal is the magnetic resonance signal after removing spike noise; Add perturbations to generate a second parameter combination, generate an objective function corresponding to the second parameter combination, and calculate a second goodness between the objective function corresponding to the second parameter combination and the preprocessed signal; Calculate the difference between the second goodness and the first goodness, and determine whether the second parameter combination replaces the first parameter combination according to the difference; After multiple iterations, the optimal parameter combination corresponding to the th harmonic frequency is obtained. Reconstruction is performed according to the optimal parameter combination to obtain the power frequency harmonic component in the form of a cosine function; Iterate through all harmonic frequencies to obtain the power frequency harmonic components corresponding to all harmonic frequencies.

4. The method for sparse denoising of ground magnetic resonance signals based on a combined dictionary according to claim 3, wherein, During the iteration process, the simulated annealing algorithm is used to control the randomness of the iteration process.

5. The method for sparse denoising of ground magnetic resonance signals based on a combined dictionary according to claim 1, wherein The magnetic resonance signal is a single-shot signal collected under single-shot signal acquisition conditions.

6. The method for sparse denoising of ground magnetic resonance signals based on a combined dictionary according to claim 3, wherein Determining whether the second parameter combination replaces the first parameter combination according to the difference includes: If the difference is greater than 0, or the difference is less than 0 and , where is the difference, is the temperature in the simulated annealing algorithm, is a random number uniformly distributed in (0, 1), then the second parameter combination replaces the first parameter combination; otherwise the first parameter combination equals the first parameter combination.

7. The method for sparse denoising of ground magnetic resonance signals based on a combined dictionary according to claim 1, wherein Trajectory matrix Construct a sparse coefficient matrix as the original sample , including: S21 Extract the trajectory matrix The th column is denoted as , , is the total number of columns. Calculate the inner product of each column in the initial dictionary and . Select the atoms with the top absolute values and denote them as , , is the preset sparsity. Calculate the Jaccard coefficient between and . Select the atoms with the top Jaccard coefficient values and add them to the index set ; Repeat S21 in S22 until the index set has a length equal to the maximum number of selected atoms , and solve for the sparse coefficients using the least squares method , completing the solution for the sparse coefficients of, and calculating the residuals of ; S23 Backtracking Optimization Index Set , calculate the initial dictionary Calculate the inner product of each column in with the residual , select the atom with the largest absolute value of the inner product, and record the index of the atom with the largest absolute value as , and judge whether it exists in the index set ; if not, replace the positions in the index set in turn; solve the new sparse coefficient and calculate the energy of the residual . If the minimum value in the energy of the residual is less than the energy of the residual , then replace the index at the corresponding position with and retain the new sparse coefficient S24 repeats S21 - S23 until the solution of the sparse coefficients for each column in the trajectory matrix is completed, and the sparse coefficients of all columns construct a sparse coefficient matrix .

8. The method for sparse denoising of ground magnetic resonance signals based on a combined dictionary according to claim 7, characterized in that The calculation method of the Jaccard coefficient is as follows: , is the Jaccard coefficient between and 9. The method for sparse denoising of ground magnetic resonance signals based on a combined dictionary according to claim 7 or 8, characterized in that Complete the update of the initial dictionary and the sparse coefficient matrix through K-SVD dictionary learning, including: establishing an optimization problem and which, after expanding , gives : ， Among them, is the total number of columns of the initial dictionary . is the th column of the initial dictionary . is the th row of the sparse coefficient matrix . is the th column of the initial dictionary . is the th row of the sparse coefficient matrix , represents the residual matrix; For the residual matrix perform singular value decomposition to obtain , where is the left singular matrix, is the singular value matrix, is the right singular matrix, represents transpose. The eigenvalues in the diagonal matrix obtained by singular value decomposition are arranged from largest to smallest. Take the first column of the left singular matrix as 's updated value, extract the product of the largest singular value and the first row of the right singular matrix , and replace the corresponding non-zero positions in ; Repeat the operation until the initial dictionary is completely updated to obtain the updated dictionary and the updated sparse coefficient matrix .

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