CN115826068A - MRS signal envelope extraction method based on self-adaptive Gaussian filtering - Google Patents
MRS signal envelope extraction method based on self-adaptive Gaussian filtering Download PDFInfo
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Abstract
The invention relates to the field of MRS (Magnetic Resonance Sounding) signal noise filtering, in particular to an MRS signal envelope extraction method based on adaptive Gaussian filtering, which comprises the following steps of: 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. Aiming at the problem that effective signal extraction is influenced by power frequency harmonic interference and random noise in a nuclear magnetic resonance detection signal, the precision of parameter extraction is obviously improved.
Description
Technical Field
The invention relates to the field of MRS (Magnetic Resonance Sounding) signal noise filtering, in particular to an MRS signal envelope extraction method based on adaptive Gaussian filtering.
Background
Magnetic Resonance Sounding (MRS) is a method of determining quantitatively the storage state of groundwater in geophysical manners that has attracted attention in recent years internationally. The hydrogen protons in the underground water are excited by an artificially generated magnetic field, so that the excited hydrogen protons jump from a steady state to an active state, and the hydrogen nuclei form macroscopic magnetic moments. When the excitation field stops, the hydrogen atomic nucleus spin generates a relaxation phenomenon, and MRS signals generated by the precession of macroscopic magnetic moments are collected through coils laid on the ground, so that the occurrence state of underground water is judged. The general expression for a full-wave nuclear magnetic resonance signal is:
the formula contains four important parameters for characterizing MRS signals: e 0 ，T 2 * ，f L ，
Respectively, an initial amplitude related to the subsurface water content, a relaxation time related to the aquifer porosity, a larmor frequency related to the geographical location, and an initial phase related to the aquifer conductivity.
Although the current MRS technology is mature, the MRS signal is generally in a nanovolt level, and the acquisition process is affected by complex environmental noise, including power frequency harmonic noise generated by a power detection device, random noise and spike noise in the natural world, which causes the quality of the MRS signal to deteriorate or even to be completely submerged by the noise.
Therefore, a great deal of research work is carried out by experts and scholars at home and abroad aiming at the problem of how to filter the noise in the MRS signal to realize effective extraction of the signal. And (3) filtering power frequency harmonic waves and random noise: lin Tingting et al, in a thesis of a magnetic resonance random noise reduction method based on improved short-time fourier transform (journal of physics, 16 th 2021), propose an improved short-time fourier transform method, which uses an analytic signal to replace a real-valued signal in conventional short-time fourier transform to obtain high-precision time-frequency distribution of an MRS signal, and then extracts a time-frequency domain peak amplitude and peak position reconstruction signal to eliminate random noise. Tian Baofeng et al, in the article, "noise suppression method for magnetic resonance signal based on reference coil and variable step size adaptation" (the article of geophysical sciences, vol. 55, no. 2012, no. 7: 2462-2472.), propose an adaptive noise cancellation algorithm based on a variable step size LMS (Least Mean Square, LMS) algorithm to filter the power frequency harmonics and part of random noise in MRS signal, but when the noise correlation between the reference coil and the detection coil is poor, the noise cancellation effect is affected. The paper "Journal application of a static optimization process explicit mode decomposition to MRS noise cancellation" by Ghanati et al (Journal of Applied geomics, no. 111, no. 5: 110-120. 2014) proposes extraction of effective MRS signal attenuation trend based on EMD method, but is only suitable for processing data with higher signal-to-noise ratio. A method for extracting a Complex envelope using spectral analysis and a sliding window is proposed in a paper "Complex angular recovery for surface magnetic resonance data using spectral analysis" by Lichao Liu et al, ohu university, denmark (Geophanic Journal International, vol.217, no. 217, 2019: 894-905.).
The patent CN114280679a discloses a method and a system for extracting parameters of a ground nuclear magnetic resonance signal, which construct a state space equation through a state vector and solve to obtain signal parameters; CN107957566A discloses a magnetic resonance sounding signal extraction method based on frequency selection singular spectrum analysis, which extracts MRS signals through the difference of singular spectrum characteristics of signals and noise; CN109885906A discloses a magnetic resonance sounding signal sparse noise elimination method based on particle swarm optimization, which constructs an oscillation atom library according to the characteristics of MRS signals and power frequency harmonic noise, and utilizes a particle swarm algorithm to select MRS signal atoms so as to remove power frequency harmonic and random white noise.
It can be seen that the MRS signal extraction method obtains a good denoising effect under a certain condition, but each algorithm has its own limitations. The gaussian filtering is used as a linear smoothing filtering method, processes signals in a weighted average mode, is suitable for eliminating gaussian noise, and is widely applied to a noise reduction process of image processing. Wang Mi et al, in a paper panchromatic multispectral image fusion method combining adaptive Gaussian filtering and an SFIM model (the journal of surveying and mapping, 1 st stage in 2018, 82-90 pages.), propose a panchromatic multispectral image fusion method combining adaptive Gaussian filtering and an SFIM model, and improve the definition of a simulated panchromatic image. Wang Yueyue et al propose an improved denoising algorithm for remote sensing images by combining two-dimensional EMD and adaptive Gaussian filter in the thesis of denoising remote sensing satellite images by combining two-dimensional EMD and adaptive Gaussian filter. The patent CN107958450B discloses a panchromatic multispectral image fusion method and system based on self-adaptive Gaussian filtering, belonging to the technical field of remote sensing image processing data fusion; the patent CN109740468B discloses a self-adaptive Gaussian low-pass filtering method for extracting black soil organic matter information, and belongs to the technical field of information extraction; patent CN114359076A discloses a self-adaptive weighted Gaussian curvature filtering method based on an image edge indication function, and belongs to the technical field of digital image processing. Therefore, the gaussian filtering is widely applied to the related fields such as image processing, but the adaptive gaussian filtering algorithm is not adopted for MRS signal processing yet.
Disclosure of Invention
Aiming at the problem that effective signal extraction is influenced by power frequency harmonic interference and random noise in a nuclear magnetic resonance detection signal, the invention provides a self-adaptive Gaussian filtering algorithm, which innovatively utilizes the self-adaptive solution of a Gaussian function as a filtering coefficient, processes a complex envelope signal by using the filtering algorithm, extracts a plurality of IMF components, obtains a margin, and obtains an MRS signal attenuation curve with noise removed by performing a modulus on the margin. Envelope information extracted by the algorithm can provide more accurate hydrogeological information through inversion, and compared with the traditional EMD algorithm, the accuracy of parameter extraction is obviously improved.
Through search and investigation, the method is not applied to the technical field of ground nuclear magnetic resonance, so the method is a brand-new application in the field of MRS signal processing.
The present invention is achieved in such a way that,
a MRS signal envelope extraction method based on adaptive Gaussian filtering comprises 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.
Further, the obtaining a complex envelope signal of a magnetic resonance full wave MRS signal includes:
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.
Further, the gaussian filter is constructed by setting a gaussian window function with length L =801, m =400, α =4.07, where L =2m +1, the 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 and ranges between [ -M, M ], and the length of the gaussian filter is represented by a parameter L.
The gaussian filter coefficients are expressed as formula (2):
further, the complex envelope signal s (n) is subjected to Gaussian filtering processing 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 Has a male partThe relationship of the formula (4),
where N represents the length of the signal s (N).
Further, the IMF component is screened from the instantaneous mean signal, which includes:
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 the 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 component r i Difference of (·).
Further, obtaining a margin according to the IMF component, and performing a modulo operation on the margin to obtain a signal envelope, including:
by r i (n) represents the ith IMF component, the signal to be decomposed is represented as a formula (7), org (n) represents the residual information after the signal decomposition, the extracted de-noised MRS attenuation curve is obtained by taking the modulus of the residual information,
compared with the prior art, the invention has the beneficial effects that:
aiming at the problem that the complexity of noise contained in an MRS signal and the conventional EMD algorithm are easy to generate modal aliasing, the invention selects the adaptive Gaussian filter as the MRS signal envelope extraction method, innovatively utilizes the adaptive solution of the Gaussian function as the filter coefficient, and realizes the effective extraction of the MRS signal. Compared with other methods, the method can effectively solve the problem that the traditional EMD algorithm is easy to generate modal aliasing, and a unique mode of adaptively determining the filter coefficient based on the number of the extreme points of the processed signal is adopted, so that the algorithm obtains excellent performance on extracting the envelope of the magnetic resonance sounding signal, the wide application of the method has great significance on improving the anti-interference capability and high-precision inversion of the high magnetic resonance sounding technology, and meanwhile, the method can be further expanded and applied to noise removal in other fields such as biomedicine.
Drawings
Fig. 1 is a block diagram of a flow chart for extracting an MRS signal envelope based on an adaptive gaussian filtering method according to an embodiment of the present invention;
FIG. 2 is a block diagram of a flow chart of an adaptive Gaussian filter algorithm provided by an embodiment of the invention;
fig. 3 shows an ideal MRS time-frequency image provided by an embodiment of the present invention, where (a) time and (b) frequency;
fig. 4 is a full-wave MRS signal time-frequency image provided by an embodiment of the present invention, where (a) time and (b) frequency;
fig. 5 is a decomposition result obtained after adaptive gaussian filtering is performed on a real part of a complex envelope signal according to an embodiment of the present invention;
fig. 6 is a decomposition result obtained after adaptive gaussian filtering is performed on an imaginary part of a complex envelope signal according to an embodiment of the present invention;
fig. 7 is an MRS signal envelope obtained from a resultant result from which a margin is extracted according to an embodiment of the present invention;
fig. 8 is a time-frequency image of the collected signal according to the embodiment of the present invention, where (a) time and (b) frequency;
FIG. 9 is an image of a full-wave signal converted to a complex envelope provided by an embodiment of the present invention;
fig. 10 shows an envelope of a signal and an ideal envelope of an acquired signal after adaptive gaussian filtering according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in fig. 1 and fig. 2, an adaptive gaussian filtering based MRS signal envelope extraction method includes the following steps:
step 1: magnetic resonance full wave MRS signal x acquired by 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 full-wave MRS signal to a complex envelope signal s (N) through Hilbert conversion and frequency spectrum shifting, wherein the signal length is N.
Step 2: a gaussian window function of length L =801, M =400, α =4.07, L =2m +1, σ = M/α is set, as in equation (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;
and step 3: an adaptive gaussian filter is designed and the filter coefficients are expressed as equation (2).
And 4, step 4: carrying out Gaussian filtering processing on the complex envelope signal s (n) to obtain a series of instantaneous mean value signals m i (N) as in equation (3), M1 is the filter length coefficient during algorithm execution, N e The number of extreme points of the signal to be processed is N, which represents the length of the signal s (N), as shown in formula (4).
And 5: determining IMF component according to formula (5), stopping decomposition if the screening stop condition satisfies that the value of eta in formula (6) is less than 20, otherwise, stopping decomposition i (n) as the signal s (n) to be processed, repeating step 4, knowing the IMF component conditions.
r i (n)＝s(n)-m i (n) (5)
Wherein s (-) is the signal to be processed and the corresponding IMF component r i Difference of (·).
And 6: by r i And (n) represents the ith IMF component, the signal to be decomposed can be represented as formula (7), org (n) represents the residual information after the signal is decomposed, and the modulus of the residual information is the extracted denoised MRS attenuation curve.
Example 1
This example is a simulation experiment of the method of the present invention conducted in the MATLAB 2021b programming environment.
The MRS signal envelope extraction method based on the self-adaptive Gaussian filtering comprises the following steps:
step 1: using a formula with a sampling rate of 25000Hz
Structuring the Larmor frequency f L =2325Hz ideal MRS signal with initial amplitude 100nV, relaxation time 0.2s, as shown in figure 3; setting the transmission frequency f T =2326Hz, amplitude is addedGaussian random noise of 50nV and 70-order power frequency harmonic waves with fundamental frequency of 49.9-50.1 Hz and amplitude of 50nV are obtained to obtain a noise-containing full-wave MRS signal model, as shown in FIG. 4; obtaining frequency deviation 1Hz, and obtaining a complex envelope signal s (n) through Hilbert transform and frequency spectrum shift;
and 2, step: a gaussian window function of length L =801, M =400, α =4.07, L =2m +1, σ = M/α is set, as in equation (1).
And 3, step 3: an adaptive gaussian filter is designed and the filter coefficients are expressed as equation (2).
And 4, step 4: respectively carrying out self-adaptive Gaussian filtering on the real part and the imaginary part of the MRS complex envelope signal s (n) to obtain a series of instantaneous mean signals m i (N) as in equation (3), M1 is the filter length coefficient during algorithm execution, N e And (4) calculating the number of extreme points of the signal to be processed according to the formula (4).
And 5: determining IMF component according to formula (5), stopping decomposition if the screening stop condition satisfies that the value of eta in formula (6) is less than 20, otherwise, stopping decomposition i (n) as the signal to be processed s (n), repeating step 4 until the IMF component condition.
r i (n)＝s(n)-m i (n)(5)
Step 6: by r i And (n) represents the ith IMF component, the signal to be decomposed may be represented as formula (7), org (n) represents the residual information after the signal is decomposed, at this time, the signal is decomposed into 7 IMF components and 1 residual, i.e., m =7, the real part decomposition result is shown in fig. 5, the imaginary part decomposition result is shown in fig. 6, and taking a modulus of the imaginary part decomposition result is the extracted denoised MRS attenuation curve, as shown in fig. 7.
Example 2
In this embodiment, the MRS signal collected in the field of the cultural square in the vinpocetine city is used as the processing target of the method of the present invention.
The MRS signal envelope extraction method based on the self-adaptive Gaussian filtering comprises the following steps:
step 1: for a group of observed MRS signals X (t) collected by a magnetic resonance depth sounding (MRS) water detector, the emission frequency is 2361Hz in the test process, the Larmor frequency of MRS signals generated by a signal source is 2360Hz, the initial amplitude is 100nV, the average relaxation time is 200ms, the sampling rate is 25000Hz, as shown in FIG. 8, time-frequency images of the collected signals are obtained, band-pass filtering is carried out on the time-frequency images to obtain the frequency deviation of 1Hz as shown in FIG. 9, complex envelope signals s (n) are obtained through Hilbert transform and frequency spectrum shifting, and the modulus of the complex envelope signals s (n) is obtained as shown in FIG. 9;
and 2, step: a gaussian window function of length L =801, M =400, α =4.07, L =2m +1, σ = M/α is set, as in equation (1).
And step 3: an adaptive gaussian filter is designed and the filter coefficients are expressed as equation (2).
And 4, step 4: respectively carrying out self-adaptive Gaussian filtering on the real part and the imaginary part of the MRS complex envelope signal s (n) to obtain a series of instantaneous mean signals m i (N) as in equation (3), M1 is the filter length coefficient during algorithm execution, N e And (4) calculating the number of extreme points of the signal to be processed according to the formula (4).
And 5: determining IMF components according to the formula (5), stopping decomposition if the screening stop condition meets the condition that the numerical value of eta in the formula (6) is less than 20, and otherwise, stopping the decomposition if the numerical value of r is not more than 20 i (n) as the signal s (n) to be processed, repeating step 4, knowing the IMF component conditions.
r i (n)＝s(n)-m i (n)(5)
Step 6: by r i And (n) represents the ith IMF component, the signal to be decomposed can be represented as formula (7), org (n) represents the residual information after the signal decomposition, and taking the modulus of the residual information is the extracted denoised MRS attenuation curve, as shown in fig. 10.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
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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