A sparse denoising method for ground magnetic resonance signals based on combined dictionary

Abstract

The present application belongs to the field of magnetic resonance signal noise filtering, specifically a sparse denoising method for ground magnetic resonance signals using a combined dictionary, which divides the magnetic resonance signal into frequency bands to reconstruct the power frequency harmonic components, and eliminates the power frequency harmonics from the magnetic resonance signal to obtain a power frequency-free signal; a trajectory matrix is ​​constructed using a Gaussian random matrix. Z , using the power frequency signal to construct the trajectory matrix Y , trajectory matrix Z Take the front K After column normalization, the initial dictionary is obtained D , trajectory matrix Y As original samples used to construct sparse coefficient matrix X ; Complete the initial dictionary through K-SVD dictionary learning D and the sparse coefficient matrix X The updated dictionary and sparse coefficient matrix are used to reconstruct the trajectory matrix to obtain the trajectory matrix W ; Take the trajectory matrix W The first row of is used to obtain a pure magnetic resonance signal, which can effectively remove the MRS signal noise in complex electromagnetic interference scenarios under the condition of a single signal acquisition.

Description

Technical Field

[0001] The present application relates to the field of noise filtering of magnetic resonance sounding (MRS) signals, and specifically to a sparse denoising method for ground magnetic resonance signals using a combined dictionary. Background Art

[0002] As a core method for non-invasive groundwater exploration, ground magnetic resonance sounding technology stimulates the nuclear magnetic resonance effect of hydrogen protons in underground aquifers to obtain key parameters such as the aquifer's relaxation time, initial amplitude, initial phase, and Larmor frequency, thereby quantitatively characterizing the groundwater's occurrence state. Compared to traditional geophysical exploration methods, this technology offers significant advantages, including high detection efficiency, rich information dimensionality, and quantitative interpretation of results. It has become a key technical support for groundwater resource surveys, geological disaster warnings, and hydrogeological assessments of major projects.

[0003] Because the engineering application of this technology is constrained by the natural field source characteristics of the Earth's magnetic field, the intensity of the MRS signal collected after excitation is extremely weak, usually at the nanovolt level, and requires a high-gain acquisition system to achieve signal capture. Even more serious is that in open field operating environments, the mixed broadband environmental noise (including power frequency harmonic interference, random white noise and spike pulses) in the signal transmission path is strongly coupled with the effective signal, resulting in the quality of the detected MRS signal being affected and the original data signal-to-noise ratio being extremely low. This in turn affects the extraction of MRS signal characteristic parameters, reduces the accuracy of the inversion results, and greatly affects the effective assessment of the groundwater resource content in the signal collection area.

[0004] Current noise suppression technology systems have limitations. Active cancellation algorithms based on power frequency harmonic characteristics can attenuate interference in specific frequency bands, but are ineffective against random noise. Empirical mode decomposition (EMD) methods can extract signal attenuation trends under moderate signal-to-noise ratio conditions, but face the problem of residual low-frequency noise caused by aliasing of intrinsic mode functions. Joint time-frequency analysis methods (such as the improved STFT) improve adaptability to non-stationary noise but are prone to distortion of the effective signal when separating noise from the main frequency band. Existing methods primarily focus on suppressing different types of noise using different means, lacking systematic solutions for complex noise coupling scenarios and struggling to meet the engineering requirements for simultaneous elimination of multi-source interference during field exploration.

[0005] This technical shortcoming directly restricts the detection depth and resolution of ground-based magnetic resonance sounding technology in strong interference environments, significantly reducing its effectiveness in areas with severe electromagnetic pollution, such as urban pipeline networks and industrial clusters. Therefore, developing a highly robust composite noise suppression method has become a key issue in improving the engineering applicability of ground-based magnetic resonance sounding technology. Summary of the Invention

[0006] The 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 with by random noise and power frequency harmonic noise during the measurement process.

[0007] This application is implemented in this way.

[0008] A sparse denoising method for ground magnetic resonance signals based on a combined dictionary, the method comprising the following steps:

[0009] Reconstructing the power frequency harmonic components by dividing the magnetic resonance signal into frequency segments, and eliminating the power frequency harmonic components from the magnetic resonance signal to obtain a power frequency-free signal;

[0010] Use Gaussian random matrix to construct trajectory matrix , using the power frequency signal to construct the trajectory matrix , trajectory matrix Take the front After column normalization, the initial dictionary is obtained , trajectory matrix As original samples used to construct sparse coefficient matrix ;

[0011] The initial dictionary is completed through K-SVD dictionary learning and the sparse coefficient matrix Update, using the updated dictionary and the sparse coefficient matrix Reconstruct the trajectory matrix to obtain the trajectory matrix ;

[0012] Get the trajectory matrix The first row of is used to obtain a pure magnetic resonance signal.

[0013] Furthermore, the magnetic resonance signal is divided into frequency segments to reconstruct the power frequency harmonic components, including: using a cosine function to sequentially reconstruct the power frequency harmonic components according to the harmonic order.

[0014] Furthermore, the cosine function is used to reconstruct the power frequency harmonic components in sequence according to the harmonic order, including:

[0015] Set the power frequency harmonic fundamental frequency, and get the first Subharmonic frequencies;

[0016] The first The subharmonic frequency constructs a target function in the form of a cosine function, wherein the amplitude, harmonic frequency and phase of the target function are combined as parameters;

[0017] randomly setting a first parameter combination, generating an objective function corresponding to the first parameter combination, and calculating a first goodness of fit between the objective function corresponding to the first parameter combination and a preprocessed signal, wherein the preprocessed signal is a signal of the magnetic resonance signal after spike noise is removed;

[0018] Adding disturbance 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;

[0019] Calculating the difference between the second optimality and the first optimality, and determining whether the second parameter combination replaces the first parameter combination according to the difference;

[0020] After multiple iterations, the The optimal parameter combination corresponding to the subharmonic frequency is reconstructed according to the optimal parameter combination to obtain the power frequency harmonic component in the form of a cosine function;

[0021] Traverse all harmonic frequencies and obtain the power frequency harmonic components corresponding to all harmonic frequencies.

[0022] Furthermore, a simulated annealing algorithm is used in the iterative process to control the randomness of the iterative process.

[0023] Furthermore, the magnetic resonance signal is a single signal acquired under a single signal acquisition condition.

[0024] Furthermore, judging whether the second parameter combination replaces the first parameter combination according to the difference includes:

[0025] If the difference is greater than 0, or the difference is less than 0 and ,in is the difference, is the temperature in the simulated annealing algorithm, is a random number uniformly distributed in (0, 1), the second parameter combination replaces the first parameter combination; otherwise, the first parameter combination is equal to the first parameter combination.

[0026] Furthermore, the trajectory matrix Construct a sparse coefficient matrix as the original sample ,include:

[0027] S21 Extraction Trajectory Matrix Middle Column record , , For the total number of columns, calculate the initial dictionary Each column in The inner product of the absolute value is selected first. atoms, denoted as , , is the preset sparsity, calculation and Jaccard coefficient between the two, select the Jaccard coefficient value before Named atom, added to the index set ;

[0028] S22 repeats S21 until the index set Length equal to the maximum number of selected atoms , using the least squares method to solve the sparse coefficients , complete the The solution of the sparse coefficient and the calculation based on the sparse coefficient The residual ;

[0029] S23 Backtracking Optimization Index Collection , calculate the initial dictionary Each column in The inner product of the atom with the largest absolute value of the inner product is selected, and the index of the atom with the largest absolute value is recorded as ,judge Whether it exists in the index collection If it does not exist, replace the index collection in sequence Position in; solve the new sparse coefficient And calculate the energy of the residual , , if the residual energy The minimum value in is less than the residual , then replace the index of the corresponding position with , and retain the new sparse coefficients ;

[0030] S24 repeats S21-S23 until the trajectory matrix is ​​completed Solve the sparse coefficients of each column in the sparse coefficients of all columns to construct a sparse coefficient matrix .

[0031] Furthermore, the Jaccard coefficient is calculated as follows: , for and The Jaccard coefficient between .

[0032] Furthermore, the initial dictionary is learned through K-SVD dictionary learning. and the sparse coefficient matrix Updates include: Setting up optimization problems ,Will After expansion, we get:

[0033] ,

[0034] in, For the initial dictionary The total number of columns, For the initial dictionary No. List, is a sparse coefficient matrix No. OK; For the initial dictionary No. List, is a sparse coefficient matrix No. OK, represents the residual matrix;

[0035] Residual matrix Perform singular value decomposition to obtain ,in is a left singular matrix, is the singular value matrix, is a right singular matrix, Represents the diagonal matrix obtained by transposing and decomposing the singular value Arrange the eigenvalues ​​from large to small and take the left singular matrix The first column As Update value of , extract the maximum singular value and the first row of the right singular matrix The product of ,replace The corresponding non-zero position;

[0036] Repeat the operation until the initial dictionary Completely update to get the updated dictionary and the updated sparse coefficient matrix .

[0037] Compared with the prior art, the present application has the following advantages:

[0038] This application targets MRS signals that contain both random noise and power frequency harmonics. It constructs a dictionary based on the cosine function, optimizes parameters using the simulated annealing algorithm, and reconstructs and eliminates the power frequency harmonic components. Effective removal of MRS signal noise in complex electromagnetic interference scenarios can be achieved under single signal acquisition conditions, solving the efficiency bottleneck problem caused by traditional technologies relying on repeated acquisition. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1A flowchart of a method for sparse denoising of ground magnetic resonance signals based on a combined dictionary provided in an embodiment of the present application; Figure 2 The noisy signal, ideal signal, and spectrum provided in the embodiments of the present application. (A) is a time-amplitude diagram of the noisy signal and the ideal signal, and (B) is a corresponding frequency-amplitude diagram.

[0040] Figure 3 The noisy signal provided in the embodiment of the present application, the noisy signal after eliminating harmonics, that is, the power frequency-removed signal , ideal signal and spectrum, (A) is the time-amplitude diagram, (B) is the frequency-amplitude diagram;

[0041] Figure 4 The noisy signal, ideal signal, reconstructed signal and spectrum provided in the embodiments of the present application, (A) is a time-amplitude diagram, (B) is a frequency-amplitude diagram;

[0042] Figure 5 The measured noisy signal and spectrum provided in the embodiments of the present application, (A) is a time-amplitude diagram, (B) is a frequency-amplitude diagram;

[0043] Figure 6 The measured noisy signal, the power frequency signal after harmonic noise elimination, and the spectrum provided in the embodiments of the present application. (A) is a time-amplitude diagram, and (B) is the corresponding frequency-amplitude diagram.

[0044] Figure 7 The measured noisy signal, reconstructed signal and spectrum provided in the embodiments of the present application, (A) is a time-amplitude diagram, and (B) is the corresponding frequency-amplitude diagram. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solutions and advantages of this application clearer and more intuitive, the following further describes this application in detail with reference to the embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0046] To effectively remove MRS signal noise in complex electromagnetic interference scenarios, existing processing methods rely on repeated signal acquisition, resulting in a large amount of data to be processed during the denoising process and reduced efficiency due to multiple acquisitions.

[0047] In response to the above-mentioned problems, the embodiments of the present application construct a dictionary based on the cosine function for MRS signals containing both random noise and power frequency harmonics, optimize the parameters in combination with the simulated annealing algorithm, then adopt K-SVD dictionary learning and combine it with the Jaccard algorithm. The Jaccard coefficient is used as the atom selection criterion to integrate the residual backtracking mechanism to achieve efficient separation of signal and noise. Effective removal of MRS signal noise in complex electromagnetic interference scenarios can be achieved under the condition of a single signal acquisition.

[0048] See also Figure 1 As shown, a sparse denoising method for ground magnetic resonance signals based on a combined dictionary comprises the following steps:

[0049] S11 divides the magnetic resonance signal into frequency segments to reconstruct the power frequency harmonic components, and eliminates the power frequency harmonics from the magnetic resonance signal to obtain a power frequency-free signal;

[0050] The magnetic resonance signal here can be a single signal acquired under single-shot signal acquisition conditions or a single signal acquired under multiple-shot signal acquisition conditions. Single-shot signal acquisition conditions refer to the rapid acquisition of 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 inhomogeneities. The single here can refer to more than just one acquisition; it can also refer to a small number of acquisitions. This application is not limited to a single acquisition; multiple acquisitions are also possible.

[0051] Magnetic resonance signals typically contain multiple frequency components, among which power frequency harmonics can mask useful signal information. Frequency segment reconstruction can decompose the MRI signal into different frequency segments, processing the power frequency harmonics and other useful signal components separately, thereby more effectively removing noise and improving signal quality.

[0052] Magnetic resonance signals can be acquired by using a magnetic resonance sounder to collect a set of original noisy magnetic resonance signals. , the Larmor frequency is , the signal length is , by removing the spike noise from the original noisy magnetic resonance signal Perform preprocessing to obtain the preprocessed signal ,in represents a time series;

[0053] Using the cosine function As shown in formula (1), a dictionary is constructed and combined with the simulated annealing algorithm to reconstruct and eliminate the preprocessed signal in frequency bands. The power frequency harmonics in the reconstructed power frequency harmonics are recorded in ascending order of frequency as , ; Represents the total number of reconstructions. The power frequency signal is calculated by formula (2) and is recorded as ;

[0054] (1),

[0055] (2),

[0056] S12 uses Gaussian random matrix to construct trajectory matrix , using the power frequency signal to construct the trajectory matrix , trajectory matrix Take the front After column normalization, the initial dictionary is obtained , trajectory matrix As original samples used to construct sparse coefficient matrix ;

[0057] The Gaussian random matrix is ​​used to generate random measurements or random samples. Its elements are randomly drawn from the Gaussian distribution (normal distribution). The trajectory matrix is ​​a structured matrix used to represent certain characteristics of the signal. The process is to obtain the trajectory matrix by matrix multiplication of the Gaussian random matrix .

[0058] The power frequency-removed signal is a signal that has been segmented by S11. By arranging each segmented signal into a matrix, a trajectory matrix is ​​formed. .

[0059] S13 completes the initial dictionary through K-SVD dictionary learning and the sparse coefficient matrix Update, using the updated dictionary and the sparse coefficient matrix Reconstruct the trajectory matrix to obtain the trajectory matrix ;

[0060] K-SVD dictionary learning (K-Singular Value Decomposition) is to find a dictionary so that the signal can be sparsely represented as a linear combination of atoms in the dictionary.

[0061] Trajectory Matrix Expressed as: .

[0062] S14 takes the trajectory matrix The first row of is used to obtain a pure magnetic resonance signal.

[0063] In one embodiment, in S11, reconstructing the power frequency harmonic components in sequence according to the harmonic order using a cosine function includes:

[0064] Set the power frequency harmonic fundamental frequency, and get the first Subharmonic frequencies;

[0065] The first Subharmonic frequencies construct the objective function in the form of cosine function , the amplitude, harmonic frequency and phase in the objective function are combined as parameters; wherein, is the parameter to be optimized, the maximum value of the parameter , minimum ; For the Subharmonic frequencies, It is the fundamental frequency of power frequency harmonic.

[0066] A first parameter combination is randomly set, and an objective function corresponding to the first parameter combination is generated, and a first goodness of fit between the objective function corresponding to the first parameter combination and the preprocessed signal is calculated; the set 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 , cooling rate The first parameter combination is used Indicates that the objective function corresponding to the first parameter combination generated , and calculate the first goodness , goodness The calculation formula is;

[0067] ,

[0068] Represents the preprocessed signal length.

[0069] The preprocessed signal is the signal after the spike noise of the magnetic resonance signal is removed.

[0070] Add disturbance to generate the second parameter combination, generate the 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; the second parameter combination adopts Expressed as, the perturbation formula: , generate the objective function corresponding to the second parameter combination .

[0071] Calculate the difference between the second optimality and the first optimality, and judge whether the second parameter combination replaces the first parameter combination according to the difference; , determine whether to accept the second parameter combination as the initial value of the next iteration, if or and , is a random number uniformly distributed in (0, 1), For the temperature in the simulated annealing algorithm, the second parameter combination is accepted ;otherwise , where the difference Calculation formula , iterative process cooling calculation method: , Indicates the updated temperature;

[0072] After multiple iterations, the Optimal parameter combination corresponding to subharmonic frequency , reconstructed according to the optimal parameter combination, and the power frequency harmonic component in the form of cosine function is obtained ; For the The optimal amplitude corresponding to the subharmonic frequency, For the The optimal frequency corresponding to the subharmonic frequency, For the The optimal phase corresponding to the subharmonic frequency,

[0073] Traverse all harmonic frequencies and obtain the power frequency harmonic components corresponding to all harmonic frequencies.

[0074] In one embodiment, the trajectory matrix Construct a sparse coefficient matrix as the original sample ,include:

[0075] S21 Extraction Trajectory Matrix Middle Column record , , is the total number of columns, calculate the difference between each column in the initial dictionary D and The inner product of the absolute value is selected first. atoms, denoted as , , is the preset sparsity, calculation and Jaccard coefficient between the two, select the Jaccard coefficient value before Named atom, added to the index set ;

[0076] calculate and Jaccard coefficient between: , for and The Jaccard coefficient between .

[0077] S22 repeats S21 until the index set Length equal to the maximum number of selected atoms , using the least squares method to solve the sparse coefficients , complete the The solution of the sparse coefficient and the calculation based on the sparse coefficient The residual ; ; Indicates the selection of index sets in the dictionary The front The atoms corresponding to the columns are In the column and the maximum number of selected atoms same.

[0078] S23 Backtracking Optimization Index Collection , calculate the initial dictionary Each column and residual The inner product of the atom with the largest absolute value of the inner product is selected, and the index of the atom with the largest absolute value is recorded as ,judge Whether it exists in the index collection If it does not exist, replace the index collection in sequence Position in; solve the new sparse coefficient And calculate the energy of the residual , , if the residual energy The minimum value in is less than the residual , then replace the index of the corresponding position with , and retain the new sparse coefficients ; The energy of the residual is the sum of the squares of each point in the residual sequence.

[0079] S24 repeats S21-S23 until the trajectory matrix is ​​completed Solve the sparse coefficients of each column in the sparse coefficient matrix, and construct a sparse coefficient matrix for all columns of sparse coefficients .

[0080] In one embodiment, the initial dictionary is learned by K-SVD dictionary learning. and the sparse coefficient matrix Updates include: Setting up optimization problems ,Will After expansion, we get:

[0081] ,

[0082] in, For the initial dictionary The total number of columns, For the initial dictionary No. List, is a sparse coefficient matrix No. OK; For the initial dictionary No. ranks, is a sparse coefficient matrix No. OK, represents the residual matrix;

[0083] Residual matrix Perform singular value decomposition to obtain ,in is a left singular matrix, is the singular value matrix, is a right singular matrix, Represents the diagonal matrix obtained by transposing and decomposing the singular value Arrange the eigenvalues ​​from large to small and take the left singular matrix The first column As Update value of , extract the maximum singular value and the first row of the right singular matrix The product of ,replace The corresponding non-zero position;

[0084] Repeat the operation until the initial dictionary Completely update to get the updated dictionary and the updated sparse coefficient matrix .

[0085] This application method utilizes a novel noise suppression mechanism combining two dictionaries, innovatively introducing a dynamic residual ratio criterion and a Jaccard coefficient optimization strategy. This method effectively removes signal noise in complex electromagnetic interference scenarios with a single signal acquisition, resolving the efficiency bottleneck caused by traditional techniques relying on repeated acquisitions. Its technical advantages lie not only in significantly improving the quality of raw data but also in reconstructing the signal processing flow to remove different types of noise step by step based on their characteristics, significantly reducing the workload of field exploration and opening up new technical paths for the theoretical advancement and engineering application of magnetic resonance detection technology.

[0086] The following simulation experiment of the present application method is carried out in the MATLAB, R2023a programming environment.

[0087] According to mathematical formula Constructing a pure magnetic resonance signal, Larmor frequency is 2325Hz, amplitude 200nV, relaxation time 0.2s, initial phase for . Signal sampling frequency , the length of the sampling time interval , number of data points Add random noise, set its amplitude to 0-50nV; then add power frequency harmonic noise, with the harmonic order of 100 and its amplitude set to a random number between 0-200nV. The fundamental frequency of the power frequency harmonic varies from 49.98 to 50.02Hz. After mixing the noise with the signal, the original noisy magnetic resonance signal with a signal-to-noise ratio of -25.45dB is obtained. .like Figure 2 As shown, Figure 2 Middle (A) is the time-amplitude diagram of the noisy signal (original noisy magnetic resonance signal) and the ideal signal. Figure 2 Middle (B) is the corresponding frequency-amplitude diagram, including the noisy signal (original noisy magnetic resonance signal) and the ideal signal.

[0088] After processing, the power frequency signal is removed .like Figure 3 As shown, Figure 3 (A) is the noisy signal (original noisy magnetic resonance signal), the noisy signal after harmonic elimination, that is, the power frequency-removed signal , ideal signal time-amplitude diagram, Figure 3 Middle (B) is the corresponding frequency-amplitude diagram.

[0089] Creating and removing power frequency signals Gaussian random matrices of the same length, using power frequency signals The trajectory matrix is ​​constructed with the Gaussian random matrix to convert the one-dimensional signal into a two-dimensional image. The trajectory matrix constructed by the Gaussian random matrix is ​​used as the initial value of the dictionary, that is, the initial dictionary. K-SVD dictionary learning is combined with the JBGOMP algorithm to reconstruct the power frequency-removed signal. In order to eliminate random noise, the first row of the reconstructed trajectory matrix is ​​taken to obtain the reconstructed signal, that is, the pure magnetic resonance signal.

[0090] In order to verify the effect of this application method, Figure 4 As shown in the figure, the noisy signal (original noisy magnetic resonance signal), the ideal signal, and the reconstructed signal (the reconstructed pure magnetic resonance signal) are compared and analyzed in the time domain and frequency domain. Figure 4 (A) in the figure shows the time-amplitude diagrams of three signals. Figure 4(B) in the figure shows the corresponding frequency-amplitude plot. Calculations show an initial amplitude error of -0.47%, a relaxation time error of 0.94%, and an SNR of 28.98 dB, a 54.43 dB improvement over the pre-processing SNR. The key parameter errors meet application requirements.

[0091] The present embodiment uses the magnetic resonance signal collected on-site at the Changchun Cultural Square as the processing object of the present method. 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 The sampling time is 2326Hz. 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 spatial coupling, and a large amount of environmental noise is also introduced. Due to the attenuation of the signal amplitude during the coupling process, the receiving coil coupled The amplitude is different from the initial signal source setting and the value is uncertain. Figure 5 As shown, Figure 5 (A) The measured noisy signal (measured magnetic resonance signal), Figure 5 (B) in the figure is the corresponding spectrum diagram, and its signal-to-noise ratio is calculated to be -17.08dB.

[0092] The original noisy magnetic resonance signal is processed by combining the cosine function with the simulated annealing algorithm. After the harmonic noise in the signal is completely reconstructed and eliminated, the power frequency-free signal is obtained. .like Figure 6 As shown, Figure 6 (A) is the noisy signal (original noisy magnetic resonance signal) and the signal after harmonic elimination, that is, the power frequency-removed signal. The time-amplitude diagram of Figure 6 Middle (B) is the corresponding frequency-amplitude diagram.

[0093] Creating and removing power frequency signals Gaussian random matrices of the same length, using the power frequency signal The trajectory matrix is ​​constructed with the Gaussian random matrix to convert the one-dimensional signal into a two-dimensional image. The trajectory matrix constructed by the Gaussian random matrix is ​​used as the initial value of the dictionary. The K-SVD dictionary learning is combined with the JBGOMP algorithm to reconstruct the power frequency-removed signal. To eliminate random noise, the first row of the reconstructed trajectory matrix is ​​taken to obtain the reconstructed signal, that is, the pure magnetic resonance signal.

[0094] In order to verify the effect of this application method, Figure 7As shown in the figure, the measured noisy signal (measured magnetic resonance signal) and the reconstructed signal (reconstructed pure magnetic resonance signal) are compared and analyzed in the time domain and frequency domain, where Figure 7 (A) is the time-amplitude diagram of two signals. Figure 7 (B) in the figure shows the corresponding frequency-amplitude plot. Calculations show a relaxation time error of -0.96%, resulting in an SNR of 22.40 dB, a 39.48 dB improvement over the preprocessing SNR. The key parameter errors meet application requirements.

[0095] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A sparse denoising method for ground magnetic resonance signals based on a combined dictionary, characterized in that: The method comprises the following steps: Reconstructing the power frequency harmonic components by dividing the magnetic resonance signal into frequency segments, and eliminating the power frequency harmonic components from the magnetic resonance signal to obtain a power frequency-free signal; Use Gaussian random matrix to construct trajectory matrix , using the power frequency signal to construct the trajectory matrix , trajectory matrix Take the front After column normalization, the initial dictionary is obtained , trajectory matrix As original samples used to construct sparse coefficient matrix ; The initial dictionary is completed through K-SVD dictionary learning and the sparse coefficient matrix Update, using the updated dictionary and the sparse coefficient matrix Reconstruct the trajectory matrix to obtain the trajectory matrix ; Get the trajectory matrix The first row of is used 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: The magnetic resonance signal is divided into frequency segments to reconstruct the power frequency harmonic components, including: using a cosine function to sequentially reconstruct the power frequency harmonic components according to the harmonic order.

3. The method for sparse denoising of ground magnetic resonance signals based on a combined dictionary according to claim 2, characterized in that: Use the cosine function to reconstruct the power frequency harmonic components in sequence according to the harmonic order, including: Set the power frequency harmonic fundamental frequency, and get the first Subharmonic frequencies; The first The subharmonic frequency constructs a target function in the form of a cosine function, wherein the amplitude, harmonic frequency and phase of the target function are combined as parameters; randomly setting a first parameter combination, generating an objective function corresponding to the first parameter combination, and calculating a first goodness of fit between the objective function corresponding to the first parameter combination and a preprocessed signal, wherein the preprocessed signal is a signal of the magnetic resonance signal after spike noise is removed; Adding disturbance 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; Calculating the difference between the second optimality and the first optimality, and determining whether the second parameter combination replaces the first parameter combination according to the difference; After multiple iterations, the The optimal parameter combination corresponding to the subharmonic frequency is reconstructed according to the optimal parameter combination to obtain the power frequency harmonic component in the form of a cosine function; Traverse all harmonic frequencies and 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, characterized in that: In the iterative process, the simulated annealing algorithm is used to control the randomness of the iterative process.

5. The method for sparse denoising of ground magnetic resonance signals based on a combined dictionary according to claim 1, characterized in that: The magnetic resonance signal is a single signal acquired under a single signal acquisition condition.

6. The method for sparse denoising of ground magnetic resonance signals based on a combined dictionary according to claim 3, characterized in that: 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 ,in is the difference, is the temperature in the simulated annealing algorithm, is a random number uniformly distributed in (0, 1), the second parameter combination replaces the first parameter combination; otherwise, the first parameter combination is equal to the first parameter combination.

7. The method for sparse denoising of ground magnetic resonance signals based on a combined dictionary according to claim 1, characterized in that: Trajectory Matrix Construct a sparse coefficient matrix as the original sample ,include: S21 Extraction Trajectory Matrix Middle Column record , , For the total number of columns, calculate the initial dictionary Each column in The inner product of the absolute value is selected first. atoms, denoted as , , is the preset sparsity, calculation and Jaccard coefficient between the two, select the Jaccard coefficient value before Named atom, added to the index collection ; S22 repeats S21 until the index set Length equal to the maximum number of selected atoms , using the least squares method to solve the sparse coefficients , complete the The solution of the sparse coefficient and the calculation based on the sparse coefficient The residual ; S23 Backtracking Optimization Index Collection , calculate the initial dictionary Each column in The inner product of the atom with the largest absolute value of the inner product is selected, and the index of the atom with the largest absolute value is recorded as ,judge Whether it exists in the index collection If it does not exist, replace the index collection in sequence Position in; solve the new sparse coefficient , and calculate the new sparse coefficients The energy of the residual of the reconstructed signal , , if the residual energy The minimum value in is less than the residual , then replace the index of the corresponding position with , and retain the new sparse coefficients ; S24 repeats S21-S23 until the trajectory matrix is ​​completed Solve the sparse coefficients of each column in the sparse coefficients of all columns to 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 Jaccard coefficient is calculated as follows: , for and The Jaccard coefficient between .

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: The initial dictionary is completed through K-SVD dictionary learning and the sparse coefficient matrix Updates include: Setting up optimization problems ,Will After expansion, we get: ， in, For the initial dictionary The total number of columns, For the initial dictionary No. List, is a sparse coefficient matrix No. OK; For the initial dictionary No. List, is a sparse coefficient matrix No. OK, represents the residual matrix; Residual matrix Perform singular value decomposition to obtain ,in is a left singular matrix, is the singular value matrix, is a right singular matrix, Indicates transposition, the eigenvalues ​​in the diagonal matrix obtained by singular value decomposition are arranged from large to small, and the left singular matrix is ​​taken The first column As Update value of , extract the maximum singular value and the first row of the right singular matrix The product of ,replace The corresponding non-zero position; Repeat the operation until the initial dictionary Completely update to get the updated dictionary and the updated sparse coefficient matrix .

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