Magnetic resonance signal denoising method based on constructing Gabor atom library sparse coding

Abstract

The present invention belongs to the field of noise filtering of magnetic resonance sounding signals, and is specifically a method for denoising magnetic resonance signals based on sparse coding of a Gabor atom library, comprising: constructing a dictionary D using a Gabor function, sparsely representing a noisy MRS signal, multiplying the dictionary D to reconstruct the main information in the noisy MRS signal, obtaining a residual signal of the main information, sparsely coding the residual signal of the main information using the dictionary D, obtaining an iterative residual signal, obtaining a reconstructed signal after undergoing i-th iterative decomposition, selecting atoms in the reconstructed signal, and selecting atoms that meet frequency requirements. Noise is effectively removed from a noisy MRS signal, the signal-to-noise ratio of the signal is improved, and characteristic parameters of the signal are accurately extracted.

Description

Technical Field

[0001] The present invention belongs to the field of magnetic resonance sounding (MRS) signal noise filtering, and specifically is a magnetic resonance signal denoising method based on building a Gabor atom library sparse coding. Background Art

[0002] Ground magnetic resonance sounding is a type of geophysical method for directly detecting groundwater, mainly used to detect groundwater resources and hydrogeological information. This technology quantitatively analyzes the occurrence of groundwater bodies by measuring the changes in the relaxation characteristics of hydrogen protons in groundwater. MRS has the advantages of fast detection rate, rich detection content, and quantitative interpretation. It is widely used in important fields such as groundwater resource exploration, geological safety monitoring, prevention of water seepage accidents in mining areas, and control of tunnel water inrush risks.

[0003] When conducting ground magnetic resonance detection, since the detection relies on the naturally existing geomagnetic field, the generated MRS signal is extremely weak, usually only at the nanovolt level. Highly sensitive detection equipment must be used to capture and record these signals to ensure the accuracy and reliability of data acquisition. However, since the detection process cannot shield the external environment, it is easily disturbed by random noise, power frequency harmonic noise and spike noise in the environment, which affects the quality of the detected MRS signal, thereby affecting the extraction of MRS signal characteristic parameters, reducing the accuracy of the inversion results, and causing inaccurate assessment of regional water resources content. Domestic and foreign scholars have conducted research on how to filter out noise to accurately extract effective signals. The block cancellation method is used to eliminate power frequency harmonic noise, but there are limitations in processing random noise. The EMD method is used to extract the attenuation trend of MRS signals with a high signal-to-noise ratio, but this method has limited effect when processing low signal-to-noise ratio data. And through the improved short-time Fourier transform method, the suppression effect of random noise is improved, but this method may be challenging when processing noise close to the signal frequency.

[0004] Although existing noise suppression methods perform well under specific conditions, they each have limitations. Given the uncertainty of the noise contained in the MRS signal, it is difficult to use one method to simultaneously eliminate multiple complex noises in the MRS signal and effectively extract the MRS signal. Summary of the invention

[0005] The present invention provides a magnetic resonance signal denoising method based on constructing a Gabor atom library sparse coding, which solves the problem that the MRS signal is easily interfered by random noise, spike noise and power frequency harmonic noise during the measurement process. By constructing a Gabor atom library to achieve sparse representation of noisy MRS signals, and by adopting a frequency selection method, noise is effectively removed from the noisy MRS signals, the signal-to-noise ratio of the signal is improved, and the characteristic parameters of the signal are accurately extracted.

[0006] The present invention is achieved in this way.

[0007] A method for denoising a magnetic resonance signal based on constructing a Gabor atom library sparse coding, the method comprising the following steps:

[0008] S1: Using a magnetic resonance sounder to collect a set of original noisy MRS signals , the Larmor frequency is , for the original noisy MRS signal Perform 10-fold interval downsampling to obtain a noisy MRS signal , the signal length is N; where t represents the time series, and n represents the noisy MRS signal after downsampling The nth sample point;

[0009] S2: Use Gabor function to build dictionary D, Corresponding to a certain atomic combination in the dictionary D, the parameters contained therein include: is the scale factor, is the displacement factor, is the frequency factor, is the phase factor; discretize the scale factor, displacement factor, frequency factor and phase factor, change the value of each parameter, and obtain different atoms;

[0010] S3: Noisy MRS signal For sparse representation, use Algorithm to solve the sparse representation coefficient matrix Multiply with dictionary D to reconstruct the noisy MRS signal Key information in , represents the number of atoms, Indicates The coefficient of atoms, , find the main information through formula (1) The residual signal :

[0011] (1),

[0012] S4: Main information The residual signal Use dictionary D for sparse coding to obtain the residual signal Key information The calculation process is the same as step S3. The iteration number is calculated by formula (2) The residual signal :

[0013] (2)

[0014] Represents the main signal of the reconstructed i-1th residual signal, Represents the residual signal of the i-1th iteration;

[0015] S5: Residual ratio As a criterion, the iterative process is terminated. After i iterative decompositions, the signal is reconstructed. It is expressed by formula (3): , in each decomposition process, corresponding to for , ; Indicates the number of the last iteration,

[0016] (3),

[0017] S6: Reconstructing the signal The atoms in the are selected, and the frequency range is [ ] , , z means that a total of z atoms are set in the dictionary D, and the remaining atoms are set to zero. The noisy MRS signal is restored using the atoms in the selected frequency range. The target signal in the image, the target signal after denoising It is expressed by formula (4), where This means selecting atoms that meet the frequency requirements:

[0018] (4).

[0019] Further: The specific steps of constructing the dictionary D in step S2 are:

[0020] Combining atoms After discretization, we get the discrete atomic combination ,in , , , , , , , , change the parameter value in the atomic combination, substitute into the Gabor function to get different atoms, establish the dictionary D, and replace the first Atoms are denoted as , a total of h, then , Gabor function is formula (5):

[0021] (5),

[0022] A mathematical model that represents an atom.

[0023] Further: Step S3 specifically includes:

[0024] Noisy MRS signal Reconstructed by formula (6), the coefficient matrix From formula (7), we can get:

[0025] (6),

[0026] (7),

[0027] T represents the matrix transpose symbol, is the sparse approximation coefficient.

[0028] Further: the judgment condition for terminating the iteration process in step S5 is:

[0029] According to formula (8), the residual ratio q is calculated:

[0030] (8),

[0031] in , E represents the expected value.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] The present invention is based on the magnetic resonance signal denoising method of constructing Gabor atom library sparse coding, and realizes the sparse representation of MRS signal by constructing Gabor dictionary. The algorithm solves the sparse representation coefficients, reconstructs the signal, iterates the decomposition, uses the residual ratio as a criterion, terminates the iterative process, and achieves high-quality reconstruction of the signal. By selecting atoms in the reconstructed signal, the signal-to-noise ratio is significantly improved and the signal characteristic parameters are accurately extracted. It has been verified that the method of the present invention is effective and superior in MRS signal denoising. The effectiveness of this method lies in significantly improving the signal-to-noise ratio of magnetic resonance detection data, and it has important practical application value for accurately extracting MRS signals in complex and strong noise environments. It simplifies the cumbersome process of multiple signal acquisitions and separate processing at each pulse moment in traditional denoising technology, reduces resource consumption in field experiments, and provides theoretical support and practical convenience for the development of magnetic resonance exploration technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 The ideal MRS signal and spectrum provided by the embodiment of the present invention, (A) is a time-amplitude diagram, (B) is a frequency-amplitude diagram;

[0035] Figure 2 The original signal, ideal signal and spectrum provided by the embodiment of the present invention, (A) is a time-amplitude diagram, (B) is a frequency-amplitude diagram;

[0036] Figure 3 The original signal, ideal signal, restored signal and spectrum provided by the embodiment of the present invention, (A) is a time-amplitude diagram, (B) is a frequency-amplitude diagram;

[0037] Figure 4 The measured MRS signal and spectrum provided by the embodiment of the present invention, (A) is a time-amplitude diagram, (B) is a frequency-amplitude diagram;

[0038] Figure 5 The measured original signal, restored signal and spectrum provided by the embodiment of the present invention, (A) is a time-amplitude diagram, (B) is a corresponding frequency-amplitude diagram;

[0039] Figure 6 A flow chart of a method for denoising a magnetic resonance signal based on constructing a Gabor atom library sparse coding according to an embodiment of the present invention. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solution and advantages of the present invention clearer and more intuitive, the present invention is 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 invention and are not used to limit the present invention.

[0041] As shown in FIG6 , a method for denoising a magnetic resonance signal based on constructing a Gabor atom library sparse coding comprises the following steps:

[0042] S1: Using a magnetic resonance sounder to collect a set of original noisy MRS signals , the Larmor frequency is , for the original noisy MRS signal Perform 10-fold interval downsampling to obtain a noisy MRS signal , the signal length is N; where t represents the time series, and n represents the noisy MRS signal after downsampling The nth sample point;

[0043] S2: Based on the characteristics of the MRS signal, the dictionary D is constructed using the Gabor function. Corresponding to a certain atomic combination in the dictionary D, the parameters contained therein include: is the scale factor, is the displacement factor, is the frequency factor, is the phase factor; discretize the scale factor, displacement factor, frequency factor and phase factor, change the value of each parameter, and obtain different atoms;

[0044] S3: Noisy MRS signal For sparse representation, use Algorithm to solve the sparse representation coefficient matrix , multiplied by the dictionary D to reconstruct the noisy MRS signal Key information in , Indicates the number of atoms, and the main information is obtained through formula (1) The residual signal :

[0045] (1),

[0046] S4: Main information The residual signal Use dictionary D for sparse coding to obtain the residual signal Key information The calculation process is the same as S3. After the i-th iteration, the residual signal of the i-th iteration is calculated by formula (2): :

[0047] (2)

[0048] Represents the main signal of the reconstructed i-1th residual signal, Represents the residual signal of the i-1th iteration;

[0049] S5: Residual ratio As a criterion, the iterative process is terminated. After i iterative decompositions, the signal is reconstructed. According to formula (3), it can be approximately considered that , in each decomposition process, corresponding to The parameters are , ;

[0050] (3),

[0051] S6: Reconstructing the signal The atoms in the are selected, and the frequency range is [ ] , , the remaining atoms are set to zero, and the MRS signal is restored using the atoms in the selected frequency range. It is expressed by formula (4), where This means selecting atoms that meet the frequency requirements:

[0052] (4).

[0053] The specific steps for constructing dictionary D in S2 are:

[0054] Combining atoms After discretization, the discrete atomic combination is obtained ,in , , , , , , , ,Change Substitute the parameter values ​​in the Gabor function to obtain different atoms, establish a dictionary D, and replace the first Atoms are denoted as , a total of h, then , Gabor function is formula (5):

[0055] (5).

[0056] A mathematical model that represents an atom.

[0057] Furthermore, S3 specifically includes:

[0058] Sparse approximation coefficient , noisy MRS signal Reconstructed by formula (6), the coefficient matrix From formula (7), we can get:

[0059] (6),

[0060] (7),

[0061] T represents the matrix transpose symbol.

[0062] Furthermore, the specific calculation steps for determining the conditions for terminating the iteration process in step S5 are:

[0063] According to formula (8), the residual ratio q is calculated:

[0064] (8),

[0065] in , E represents the expected value.

[0066] Embodiment 1,

[0067] This embodiment is a simulation experiment of the method of the present invention carried out in the MATLAB R2023a programming environment.

[0068] According to mathematical formula The Larmor frequency is 2325 Hz and the amplitude is is 100nV, relaxation time is 0.1s, the initial phase for The ideal MRS signal is Figure 1 As shown. Among them, Figure 1 (A) is the time-amplitude diagram. Figure 1 (B) in the figure is a frequency-amplitude diagram. Signal sampling frequency , time length Add -10dBW random noise to the MRS signal; add three power frequency harmonics: the frequencies are 2250Hz, 2300Hz, 2350Hz, and the phases are , , , with amplitudes of 160nV, 50nV, and 140nV respectively; two spike noises were added: the pulse durations were 10ms and 6ms respectively, the addition times were 50ms and 140ms respectively, and the noise intensity peaks were 1000nV and 500nV respectively. After mixing the noise with the signal, the original noisy MRS signal with a signal-to-noise ratio of 1.47dB was obtained ,like Figure 2 As shown, Figure 2 (A) is the time-amplitude diagram of the original signal and the ideal signal. Figure 2 (B) is the corresponding frequency-amplitude diagram. Perform 10-fold interval downsampling to obtain a noisy MRS signal , the number of signal points is N=3200.

[0069] In order to verify the effect of the method of the present invention, Figure 3 As shown, the original signal, ideal signal, and restored signal are compared and analyzed in the time domain and frequency domain. Figure 3 (A) is a time-amplitude diagram of three signals. Among them, the ideal signal and the restored signal are very similar. The ideal signal and the restored signal overlap. From the beginning of the figure, it can be seen that the ideal signal and the restored signal do not completely overlap. As time goes by, the ideal signal and the restored signal completely overlap. Figure 3 (B) in the figure is the corresponding frequency-amplitude diagram. After calculation, it can be obtained that the initial amplitude error is -0.08%, the relaxation time error is 1.81%, and its SNR = 18.20dB, which is 16.72dB higher than the SNR before processing. The key parameter errors obtained meet the application requirements.

[0070] Embodiment 2,

[0071] In this embodiment, the MRS signal collected on-site at the Changchun Cultural Square is used as the processing object of the method of the present invention. The original noisy MRS signal is generated by an Agilent 35670A signal source, and the Larmor frequency is set to , relaxation time , signal sampling frequency , transmission frequency is 2325Hz, 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 MRS signal is attenuated to the nanovolt level through spatial coupling, and a large amount of environmental noise is also introduced. Since the signal amplitude is attenuated during the coupling process, the signal obtained by the receiving coil coupling The amplitude is different from the initial signal source setting and the value is uncertain. Figure 4 As shown, Figure 4 (A) The time domain waveform of the measured MRS signal. Figure 4 (B) is the corresponding spectrum diagram, and its signal-to-noise ratio is calculated to be -16.75dB. Perform 10-fold interval downsampling to obtain a noisy MRS signal , the signal length is .

[0072] In order to verify the effect of the method of the present invention, Figure 5 As shown, the original signal and the restored signal are compared and analyzed in the time domain and frequency domain. Figure 5 (A) is the time-amplitude diagram of the two signals. Figure 5 (B) in the figure is the corresponding frequency-amplitude diagram. After calculation, it can be obtained that the relaxation time error is -4.20%, and its SNR is 13.86dB, which is 30.61dB higher than the SNR before processing. The key parameter errors obtained meet the application requirements.

[0073] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for denoising magnetic resonance signals based on constructing a Gabor atom library sparse coding, characterized in that: The method comprises the following steps: S1: Using a magnetic resonance sounder to collect a set of original noisy MRS signals , the Larmor frequency is , for the original noisy MRS signal Perform 10-fold interval downsampling to obtain a noisy MRS signal , the signal length is N; where t represents the time series, and n represents the noisy MRS signal after downsampling The nth sample point; S2: Use Gabor function to build dictionary D, Corresponding to a certain atomic combination in the dictionary D, the parameters contained therein include: is the scale factor, is the displacement factor, is the frequency factor, is the phase factor; discretize the scale factor, displacement factor, frequency factor and phase factor, change the value of each parameter, and obtain different atoms; S3: Noisy MRS signal For sparse representation, use Algorithm to solve the sparse representation coefficient matrix Multiply with dictionary D to reconstruct the noisy MRS signal Key information in , represents the number of atoms, Indicates The coefficient of atoms, , find the main information through formula (1) The residual signal : （1）， S4: Main information The residual signal Use dictionary D for sparse coding to obtain the residual signal Key information The calculation process is the same as step S3. The iteration number is calculated by formula (2) The residual signal : (2)， Represents the main signal of the reconstructed i-1th residual signal, Represents the residual signal of the i-1th iteration; S5: Residual ratio As a criterion, the iterative process is terminated. After i iterative decompositions, the signal is reconstructed. It is expressed by formula (3): , in each decomposition process, corresponding to for , ; Indicates the number of the last iteration, （3）， S6: Reconstructing the signal The atoms in the are selected, and the frequency range is [ ] , , z means that a total of z atoms are set in the dictionary D, and the remaining atoms are set to zero. The noisy MRS signal is restored using the atoms in the selected frequency range. The target signal in the image, the target signal after denoising It is expressed by formula (4), where This means selecting atoms that meet the frequency requirements: （4）。 2. The method for denoising magnetic resonance signals based on constructing Gabor atom library sparse coding according to claim 1, characterized in that: The specific steps of constructing the dictionary D in step S2 are: Combining atoms After discretization, we get the discrete atomic combination ,in , , , , , , , , change the parameter value in the atomic combination, substitute into the Gabor function to get different atoms, establish the dictionary D, and replace the first Atoms are denoted as , a total of h, then , Gabor function is formula (5): （5）， A mathematical model that represents an atom.

3. The method for denoising magnetic resonance signals based on constructing Gabor atom library sparse coding according to claim 1, characterized in that: Step S3 specifically includes: Noisy MRS signal Reconstructed by formula (6), the coefficient matrix From formula (7), we can get: （6）， （7）， T represents the matrix transpose symbol, is the sparse approximation coefficient.

4. The method for denoising magnetic resonance signals based on constructing Gabor atom library sparse coding according to claim 1, characterized in that: The judgment condition for terminating the iteration process in step S5 is: According to formula (8), the residual ratio q is calculated: （8）， in , E represents the expected value.

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