CN115826068A - MRS signal envelope extraction method based on self-adaptive Gaussian filtering - Google Patents

Abstract

The present invention relates to a magnetic resonance sounding (Magnetic Resonance Sounding, MRS) signal noise filtering field, in particular to an MRS signal envelope extraction method based on adaptive Gaussian filtering, comprising: obtaining the complex of the magnetic resonance full-wave MRS signal Envelope signal; Gaussian filter is used to obtain the instantaneous mean signal of the complex envelope signal; the IMF component is screened out from the instantaneous mean signal; the margin is obtained according to the IMF component, and the signal envelope is obtained by moduloing the margin. Aiming at the problem that there are power frequency harmonic interference and random noise in the nuclear magnetic resonance detection signal, which affect the effective signal extraction, the accuracy of parameter extraction is significantly improved.

Description

A Method of MRS Signal Envelope Extraction Based on Adaptive Gaussian Filter

technical field

The invention relates to the field of magnetic resonance sounding (Magnetic Resonance Sounding, MRS) signal noise filtering, in particular to an MRS signal envelope extraction method based on adaptive Gaussian filtering.

Background technique

式中包含表征MRS信号的四个重要参数：E₀，T₂ ^*，f_L，

分别表示与地下含水量有关的初始振幅、与含水层孔隙度相关的弛豫时间，与地理位置相关的拉莫尔频率，与含水层导电性有关的初始相位。NMR sounding (Magnetic Resonance Sounding, MRS) is a method of geophysical quantitative determination of groundwater storage status that has attracted international attention in recent years. The artificially generated magnetic field excites the hydrogen protons in the groundwater, so that the excited hydrogen protons transition from a steady state to an active state, and the hydrogen nuclei form a macroscopic magnetic moment. When the excitation field stops, the nuclear spin of the hydrogen atom undergoes a relaxation phenomenon, and the MRS signal generated by the macroscopic magnetic moment precession is collected through the coil laid on the ground, and then the occurrence state of the groundwater is judged. The general expression for a full-wave NMR signal is:

The formula contains four important parameters to characterize the MRS signal: E ₀ , T ₂ ^* , f _L ,

denote the initial amplitude related to the subsurface water content, the relaxation time related to the porosity of the aquifer, the Larmor frequency related to the geographical location, and the initial phase related to the conductivity of the aquifer, respectively.

Although the current MRS technology is relatively mature, MRS signals are generally at the nanovolt level, and the acquisition process will be affected by complex environmental noise, including power frequency harmonic noise generated by power detection devices, random noise and spike noise in nature, etc., resulting in The MRS signal quality deteriorates and is even completely drowned by noise.

Therefore, experts and scholars at home and abroad have carried out a lot of research work on how to filter out the noise in the MRS signal to realize the effective extraction of the signal. For the filtering of power frequency harmonics and random noise: Lin Tingting et al. proposed a method in the paper "MRI Random Noise Reduction Method Based on Improved Short-Time Fourier Transform" ("Acta Physica", No. 16, 2021) The improved short-time Fourier transform method uses the analytical signal instead of the real-valued signal in the conventional short-time Fourier transform to obtain the high-precision time-frequency distribution of the MRS signal, and then extracts the peak amplitude and peak phase of the time-frequency domain to reconstruct the signal to eliminate random noise. Tian Baofeng and others proposed a method based on variable step size in the paper "MRI Signal Noise Suppression Method Based on Reference Coil and Variable Step Size Adaptation" ("Journal of Geophysics", Vol. 55, No. 7, 2012: 2462-2472.) The adaptive noise cancellation algorithm of the LMS (Least MeanSquare, LMS) algorithm filters out the power frequency harmonics and some random noise in the MRS signal, but when the noise correlation between the reference coil and the detection coil is poor, the noise cancellation effect is affected. In the paper "Jointapplication of a statistical optimization process empirical modedecomposition to MRS noise cancellation" ("Journal of Applied Geophysics", 2014, Vol. 111, No. 5: 110-120.), Ghanati et al. proposed an effective MRS signal based on the EMD method. Attenuation trend extraction, but only suitable for processing data with high signal-to-noise ratio. Lichao Liu et al. from Aarhus University in Denmark proposed a method using Spectral Analysis and Sliding Window Methods to Extract Complex Envelopes.

Patent CN114280679A discloses "a method and system for extracting ground nuclear magnetic resonance signal parameters", which constructs state space equations through state vectors and solves them to obtain signal parameters; CN107957566A discloses "magnetic resonance sounding signal extraction based on frequency-selective singular spectrum analysis Method", which extracts MRS signals through the difference in the singular spectrum characteristics of signals and noises; CN109885906A discloses "a sparse denoising method for magnetic resonance sounding signals based on particle swarm optimization", based on MRS signals and power frequency harmonics The characteristics of the noise, construct the oscillatory atom library, use the particle swarm algorithm to select the MRS signal atoms, and realize the removal of power frequency harmonics and random white noise.

It can be seen that the above MRS signal extraction methods all achieve better denoising effects under certain conditions, but each algorithm also has its own limitations. Gaussian filtering is a linear smoothing filtering method that processes signals by means of weighted average. It is suitable for eliminating Gaussian noise and is widely used in the noise reduction process of image processing. Wang Mi and others proposed an adaptive Gaussian filter in the paper "A Panchromatic Multispectral Image Fusion Method Combining Adaptive Gaussian Filtering and SFIM Model" ("Journal of Surveying and Mapping", No. 1, 2018: 82-90.) The panchromatic multispectral image fusion method combined with the SFIM model improves the clarity of the simulated panchromatic image. Wang Yueyue and others proposed an improved remote sensing image denoising algorithm combining two-dimensional EMD and adaptive Gaussian filtering in the paper "Remote Sensing Satellite Image Denoising Combining Two-dimensional EMD and Adaptive Gaussian Filtering". Patent CN107958450B discloses "panchromatic multispectral image fusion method and system based on adaptive Gaussian filter", which belongs to the field of remote sensing image processing data fusion technology; patent CN109740468B discloses "an adaptive Gaussian low-pass filter for black soil organic matter information extraction Filtering method", which belongs to the technical field of information extraction; patent CN114359076A discloses "an adaptive weighted Gaussian curvature filtering method based on an image edge indicator function", which belongs to the technical field of digital image processing. It can be seen that the Gaussian filter is widely used in image processing and other related fields, but the adaptive Gaussian filter algorithm has not been used in MRS signal processing.

Contents of the invention

Aiming at the problem that there are power frequency harmonic interference and random noise in the NMR detection signal, which affect the effective signal extraction, the present invention proposes an adaptive Gaussian filtering algorithm, which innovatively uses the adaptive solution of the Gaussian function as the filtering coefficient, The complex envelope signal is processed by this filter algorithm, several IMF components are extracted, and the margin is obtained, and the MRS signal attenuation curve with noise removed can be obtained by taking the modulus of the margin. The envelope information extracted by the algorithm can provide more accurate hydrogeological information through inversion. Compared with the traditional EMD algorithm, the accuracy of parameter extraction is significantly improved.

After searching and investigating, the method has not been applied in the field of ground nuclear magnetic resonance technology, so this invention is a brand new application in the field of MRS signal processing.

The present invention is achieved like this,

A method for extracting envelopes of MRS signals based on adaptive Gaussian filtering, the method comprising:

obtaining a complex envelope signal of a magnetic resonance full-wave MRS signal;

The Gaussian filter is used to obtain the instantaneous mean signal of the complex envelope signal;

Filter out the IMF component from the instantaneous mean signal;

The margin is obtained according to the IMF component, and the signal envelope is obtained by moduloing the margin.

Further, said obtaining the complex envelope signal of the magnetic resonance full-wave MRS signal includes:

Perform spectrum analysis on the magnetic resonance full-wave MRS signal x ₁ (n) collected by the instrument to obtain the Larmor frequency f _L , obtain the frequency deviation according to the transmission frequency f _T of the instrument system, and realize the magnetic Conversion of resonant full-wave MRS signal to complex envelope signal s(n), with signal length N.

Further, the Gaussian filter is constructed by setting a Gaussian window function of length L=801, M=400, α=4.07, wherein L=2M+1, and the Gaussian window function is formula (1):

Among them, σ=M/α, α is a parameter that is inversely proportional to the standard deviation σ, k is an integer, and the range is [-M, M], and the parameter L represents the length of the Gaussian filter.

The Gaussian filter coefficients are expressed as formula (2):

Further, Gaussian filtering is performed on the complex envelope signal s(n) to obtain a series of instantaneous mean signal m _i (n), the instantaneous mean signal m _i (n) is formula (3), and M1 is the Filter length coefficient, N _e is the number of extreme points of the signal to be processed, where M1 and N _e have the relationship of formula (4),

Among them, N represents the length of the signal s(n).

Further, the IMF component is screened out from the instantaneous mean signal, including:

According to the formula (5), the instantaneous mean signal m _i (n) is determined for the IMF component, and the sieving stop condition satisfies that the value of η in the formula (6) is less than 20, then the decomposition is stopped; otherwise, r _i (n) is used as the Process the signal s(n), repeat the process of performing Gaussian filtering on the complex envelope signal s(n), until the IMF component condition is satisfied,

r _i (n)=s(n)-m _i (n)(5)

Wherein, s(·) is the difference between the signal to be processed and the corresponding IMF component r _i (·).

Further, the margin is obtained according to the IMF component, and the signal envelope is obtained by moduloing the margin, including:

Use r _i (n) to represent the i-th IMF component, then the signal to be decomposed is expressed as formula (7), org(n) represents the residual information after decomposing the signal, and its modulo is the extracted denoising MRS decay curve,

Compared with the prior art, the present invention has the beneficial effects of:

Aiming at the complexity of the noise contained in the MRS signal and the problem of modal aliasing easily produced by the traditional EMD algorithm, the present invention chooses adaptive Gaussian filtering as the method for extracting the envelope of the MRS signal, and innovatively uses the adaptive solution of the Gaussian function as the filter coefficient , to achieve effective extraction of MRS signals. Compared with other methods, this method can not only effectively solve the problem of modal aliasing easily produced by the traditional EMD algorithm, but also adopts a unique method of adaptively determining the filter coefficients based on the number of extreme points of the processed signal, which makes the algorithm in Excellent performance has been obtained in extracting the envelope of magnetic resonance sounding signals. Its wide application is of great significance for improving the anti-interference ability and high-precision inversion of magnetic resonance sounding technology. At the same time, this method can also be extended to biological Noise removal in other fields such as medicine.

Description of drawings

Fig. 1 is the flowchart of extracting MRS signal envelope based on adaptive Gaussian filter method provided by the embodiment of the present invention;

Fig. 2 is the block flow diagram of adaptive Gaussian filtering algorithm provided by the embodiment of the present invention;

Fig. 3 is the ideal MRS time-frequency image provided by the embodiment of the present invention, (a) time, (b) being frequency;

Fig. 4 is the time-frequency image of the full-wave MRS signal provided by the embodiment of the present invention, (a) time, (b) frequency;

Fig. 5 is the decomposition result obtained after the real part of the complex envelope signal provided by the embodiment of the present invention is subjected to adaptive Gaussian filtering;

Fig. 6 is the decomposition result obtained after adaptive Gaussian filtering is performed on the imaginary part of the complex envelope signal provided by the embodiment of the present invention;

Fig. 7 is the MRS signal envelope obtained from the synthesis result of extracting the margin provided by the embodiment of the present invention;

Fig. 8 is the time-frequency image of the acquisition signal provided by the embodiment of the present invention, (a) time, (b) frequency;

FIG. 9 is an image of a full-wave signal converted into a complex envelope provided by an embodiment of the present invention;

FIG. 10 is a signal envelope and an ideal envelope obtained after adaptive Gaussian filtering of the collected signal provided by the embodiment of the present invention.

Detailed ways

In order to make the object, technical solution and advantages of the present invention more clear, the present invention will be further described in detail below in conjunction with the examples. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

As shown in Figure 1 and Figure 2, an MRS signal envelope extraction method based on adaptive Gaussian filtering includes the following steps:

Step 1: Perform spectrum analysis on the magnetic resonance full-wave MRS signal x ₁ (n) collected by the instrument to obtain the Larmor frequency f _L , obtain the frequency deviation according to the transmission frequency f _T of the instrument system, and obtain the frequency deviation through Hilbert transform and spectrum The transfer realizes the conversion of the full-wave MRS signal to the complex envelope signal s(n), and the signal length is N.

Step 2: Set a Gaussian window function with length L=801, M=400, α=4.07, L=2M+1, σ=M/α, as in formula (1).

Among them, σ=M/α, α is a parameter that is inversely proportional to the standard deviation σ, k is an integer, the range is [-M, M], and the parameter L is used to represent the length of the Gaussian filter;

Step 3: Design an adaptive Gaussian filter, and the filter coefficients are expressed as formula (2).

Step 4: Perform Gaussian filtering on the complex envelope signal s(n) to obtain a series of instantaneous mean signal m _i (n), as shown in formula (3), M1 is the filter length coefficient during the algorithm execution process, Ne _is The number of extreme points of the signal to be processed, N represents the length of the signal s(n), as shown in formula (4).

Step 5: Determine the IMF component according to the formula (5), if the sieving stop condition satisfies the value of η in the formula (6) is less than 20, then stop the decomposition, otherwise take r _i (n) as the signal to be processed s (n) , repeat step 4 to know the IMF component condition.

r _i (n)=s(n)-m _i (n) (5)

Wherein, s(·) is the difference between the signal to be processed and the corresponding IMF component r _i (·).

Step 6: Use r _i (n) to represent the i-th IMF component, then the signal to be decomposed can be expressed as formula (7), org(n) represents the residual information after the signal is decomposed, and its modulo is the extracted MRS decay curve after denoising.

Example 1

This embodiment is a simulation experiment of the method of the present invention carried out under the MATLAB 2021b programming environment.

An MRS signal envelope extraction method based on adaptive Gaussian filtering, comprising the following steps:

构造拉莫尔频率f_L＝2325Hz，初始振幅为100nV，弛豫时间为0.2s的理想MRS信号，如图3所示；设置发射频率f_T＝2326Hz，加入幅值为50nV的高斯随机噪声，以及基波频率在49.9至50.1Hz，幅值为50nV的70次工频谐波，得到含噪的全波MRS信号模型，如图4所示；获得频率偏差1Hz，通过希尔伯特变换及频谱搬移获得复包络信号s(n)；Step 1: With a sampling rate of 25000Hz, use the formula

Construct an ideal MRS signal with a Larmor frequency f _L =2325Hz, an initial amplitude of 100nV, and a relaxation time of 0.2s, as shown in Figure 3; set the transmission frequency f _T =2326Hz, and add Gaussian random noise with an amplitude of 50nV, As well as the 70th power frequency harmonic with a fundamental frequency of 49.9 to 50.1Hz and an amplitude of 50nV, a noisy full-wave MRS signal model is obtained, as shown in Figure 4; the frequency deviation is 1Hz, and the Hilbert transform and Spectrum shifting to obtain complex envelope signal s(n);

Step 2: Set a Gaussian window function with length L=801, M=400, α=4.07, L=2M+1, σ=M/α, as in formula (1).

Step 3: Design an adaptive Gaussian filter, and the filter coefficients are expressed as formula (2).

Step 4: Perform adaptive Gaussian filtering on the real and imaginary parts of the MRS complex envelope signal s(n), respectively, to obtain a series of instantaneous mean signals m _i (n), as shown in formula (3), M1 is the The filter length coefficient of , Ne _is the number of extreme points of the signal to be processed, as shown in formula (4).

Step 5: Determine the IMF component according to the formula (5), if the sieving stop condition satisfies the value of η in the formula (6) is less than 20, then stop the decomposition, otherwise take r _i (n) as the signal to be processed s (n) , repeat step 4 until the IMF component condition.

r _i (n)=s(n)-m _i (n)(5)

Step 6: Use r _i (n) to represent the i-th IMF component, then the signal to be decomposed can be expressed as formula (7), org(n) represents the residual information after decomposing the signal, at this time, the signal is decomposed into 7 IMF components and 1 margin, i.e. m=7, the real part decomposition result is shown in Figure 5, and the imaginary part decomposition result is shown in Figure 6, and its modulus is the extracted MRS attenuation curve after denoising, As shown in Figure 7.

Example 2

In this embodiment, the MRS signal collected on the spot in Changchun Cultural Square is used as the processing object of the method of the present invention.

An MRS signal envelope extraction method based on adaptive Gaussian filtering, comprising the following steps:

Step 1: For a group of observed MRS signals X(t) collected by the magnetic resonance sounding (MRS) water detector, the transmission frequency during the test is 2361 Hz, and the Larmor frequency of the MRS signal generated by the signal source is 2360 Hz. The amplitude is 100nV, the average relaxation time is 200ms, and the sampling rate is 25000Hz. As shown in Figure 8, the time-frequency image of the collected signal is processed by band-pass filtering, and the frequency deviation shown in Figure 9 is obtained as 1Hz. The complex envelope signal s(n) is obtained by Halbert transform and spectrum shift, and its modulo is taken, as shown in Figure 9;

Step 2: Set a Gaussian window function with length L=801, M=400, α=4.07, L=2M+1, σ=M/α, as in formula (1).

Step 3: Design an adaptive Gaussian filter, and the filter coefficients are expressed as formula (2).

Step 4: Perform adaptive Gaussian filtering on the real and imaginary parts of the MRS complex envelope signal s(n), respectively, to obtain a series of instantaneous mean signals m _i (n), as shown in formula (3), M1 is the The filter length coefficient of , Ne _is the number of extreme points of the signal to be processed, as shown in formula (4).

Step 5: Determine the IMF component according to the formula (5), if the sieving stop condition satisfies the value of η in the formula (6) is less than 20, then stop the decomposition, otherwise take r _i (n) as the signal to be processed s (n) , repeat step 4 to know the IMF component condition.

r _i (n)=s(n)-m _i (n)(5)

Step 6: Use r _i (n) to represent the i-th IMF component, then the signal to be decomposed can be expressed as formula (7), org(n) represents the residual information after the signal is decomposed, and its modulo is the extracted The MRS attenuation curve after denoising is shown in Figure 10.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention should be included in the protection of the present invention. within range.

Claims (6)

1. A self-adaptive Gaussian filtering-based MRS signal envelope extraction method is characterized by comprising the following steps:

obtaining a complex envelope signal of a magnetic resonance full wave MRS signal;

acquiring an instantaneous mean value signal of the complex envelope signal by adopting a Gaussian filter;

screening IMF components from the instantaneous mean value signal;

and obtaining a margin according to the IMF component, and performing modulus operation on the margin to obtain a signal envelope.

2. The adaptive gaussian filtering based MRS signal envelope extraction method according to claim 1, wherein said obtaining a complex envelope signal of a magnetic resonance full wave MRS signal comprises:

magnetic resonance full wave MRS signal x collected for instrument ₁ (n) performing spectral analysis to obtain Larmor frequency f _L According to the transmission frequency f of the instrument system _T And obtaining frequency deviation, and realizing the conversion from the MRS signal to the complex envelope signal s (N) through Hilbert conversion and frequency spectrum shifting, wherein the signal length is N.

3. The adaptive gaussian filtering based MRS signal envelope extraction method according to claim 1, wherein said gaussian filter is constructed by setting a gaussian window function of length L =801, m =400, α =4.07, where L =2m +1, said gaussian window function being formula (1):

where σ = M/α, α is a parameter inversely proportional to the standard deviation σ, k is an integer, ranging between [ -M, M ], the length of the gaussian filter is represented by a parameter L;

the gaussian filter coefficients are expressed as formula (2):

4. the adaptive Gaussian filter-based MRS signal envelope extraction method according to claim 3,

gaussian filtering is carried out on the complex envelope signal s (n) to obtain a series of instantaneous mean value signals m _i (n), instantaneous mean signal m _i (N) is formula (3), M1 is the filter length coefficient during algorithm execution, N _e The number of extreme points of the signal to be processed, wherein M1 and N _e Having the relationship of the formula (4),

where N represents the length of the signal s (N).

5. The adaptive gaussian filtering based MRS signal envelope extraction method according to claim 1, wherein the filtering of the IMF component from the instantaneous mean signal comprises:

the instantaneous mean value signal m is calculated according to the formula (5) _i (n) determining IMF component, if the screening stop condition meets the condition that the numerical value of eta in the formula (6) is less than 20, stopping decomposition, otherwise, stopping r _i (n) as the signal s (n) to be processed, repeating the process of performing Gaussian filtering processing on the complex envelope signal s (n) until an IMF component condition is satisfied,

r _i (n)＝s(n)-m _i (n) (5)

wherein s (-) is the signal to be processed and the corresponding IMF componentr _i Difference of (·).

6. The adaptive gaussian filtering-based MRS signal envelope extraction method of claim 1, wherein obtaining residuals according to the IMF component, and performing a modulo operation on the residuals to obtain a signal envelope comprises:

by r _i (n) represents the ith IMF component, the signal to be decomposed is represented as formula (7), org (n) represents the residual information after the signal decomposition, the model of the residual information is the extracted de-noised MRS attenuation curve,

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