CN109633761B - Magnetic resonance signal power frequency noise reduction method based on wavelet transformation modulus maximum value method - Google Patents
Magnetic resonance signal power frequency noise reduction method based on wavelet transformation modulus maximum value method Download PDFInfo
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Abstract
The invention belongs to the field of noise reduction of nuclear magnetic resonance sounding signals, and discloses a method for reducing power frequency noise of a magnetic resonance signal based on a wavelet transform modulus maximum value method, which comprises the following steps: performing n-layer wavelet decomposition on the full-wave magnetic resonance observation signal acquired by the nuclear magnetic resonance underground water detector, wherein n is 5-7; extracting detail coefficient d of each layer1，…，dnAnd the last layer approximation coefficient an(ii) a Updating detail coefficients of each layer by using a wavelet transform modulus maximum denoising algorithm; and reconstructing the signal by using the reconstructed wavelet coefficients. The method has simple process and high operation speed, and can realize better noise reduction effect by processing single detection signal.
Description
Technical Field
The invention relates to a method for reducing noise of a nuclear Magnetic Resonance Sounding (MRS) signal, in particular to a processing method for reducing power frequency noise contained in a Magnetic Resonance signal by using a wavelet transform modulus maximum value method.
Background
The magnetic resonance underground water detection technology has the advantages that hydrogeological information such as the position, the water content, the medium porosity, the conductivity and the like of an underground 0-150m deep aquifer can be directly inverted, and the magnetic resonance underground water detection technology is widely applied to the field of underground water exploration in China in recent years and provides reliable technical support for relieving pressure of arid regions. However, the MRS signal is very weak, only has a nanovolt level, and is very easily interfered by environmental noise, especially when the MRS signal is detected in cities and surrounding areas with dense power lines, power frequency interference is the most common and serious interference in MRS measurement, which seriously reduces the accuracy of signal characteristic parameter extraction and affects the result of hydrogeological parameters in inversion interpretation. Therefore, the effective elimination of power frequency noise is of great importance in the magnetic resonance underground water detection process.
Patent CN104459809A discloses a full-wave nuclear magnetic resonance signal noise filtering method based on independent component analysis, which mainly aims at power frequency harmonic interference or certain single frequency interference in a full-wave nuclear magnetic resonance signal. Firstly, acquiring an MRS signal by using a nuclear magnetic resonance depth sounding water detector, obtaining the frequency of power frequency harmonic interference or certain single-frequency interference contained in the acquired signal through spectrum analysis, and constructing an input channel signal by adopting a digital orthogonal method to solve the underdetermined blind source separation problem; then, taking the constructed input channel signal and the acquired MRS signal as input signals to perform independent component analysis to obtain a separated MRS signal; and finally, solving the problem of uncertain amplitude of the separated MRS signal by adopting a spectrum correction method, and further extracting the de-noised MRS signal. Patent CN104614778A discloses a method for eliminating noise of nuclear magnetic resonance underground water detection signals based on ICA, which includes entering three groups of nuclear magnetic resonance response data, performing fourier transform on the three groups of data respectively, determining power frequency harmonics contained near the nuclear magnetic resonance center frequency of each group of data, then constructing sine functions and cosine functions having the same frequency as the power frequency harmonics, having the same length as the data corresponding to the nuclear magnetic resonance, and forming observation signals with the nuclear magnetic resonance response data, separating each group of observation signals by using an independent component analysis algorithm to obtain unmixed signals, performing data reconstruction to eliminate interference of the power frequency harmonics, taking the three groups of nuclear magnetic resonance data without the power frequency harmonics as the observation signals, and then processing by using the ICA algorithm to weaken the interference of residual random noise. In Geophys [2003,53,103-120], Legchenko and Valla published a paper "Removal of power-line harmonics from magnetic resonance sources" to reduce power frequency noise by a combination of block cancellation, sine cancellation and notch.
According to the full-wave nuclear magnetic resonance signal noise filtering method based on independent component analysis, input channel signals except for an observation signal channel are constructed by using a digital orthogonal method, and no additional instrument and equipment is needed to collect multi-channel input channel signals according to the requirements of the traditional ICA, so that the harsh condition of ICA application is broken, a large amount of manpower and material resources are saved, but the method needs to separate noisy signals and carry out frequency spectrum correction on the separated signals, wherein the method comprises the steps of carrying out centralization and whitening on the signals, judging the gauss of the signals and the noise, setting the FastICA algorithm convergence condition, and having complex calculation steps and difficult control of non-professional personnel; according to the nuclear magnetic resonance underground water detection signal noise elimination method based on ICA, a reference coil is not needed to be laid in the test process, the operation is simple and convenient, the detailed characteristics of signals cannot be damaged when power frequency noise is suppressed, but the method requires at least three groups of data, the calculation process is complex, and the calculation amount is large; the trap method is a method which is common at present for removing power frequency noise, but when the frequency of the noise is close to the frequency of a magnetic resonance signal, effective signals are easily lost.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a magnetic resonance signal power frequency noise reduction method based on a wavelet transform mode maximum value method, which can effectively reduce power frequency noise without losing signal components, has good practicability on low signal-to-noise ratio full-wave magnetic resonance signals interfered by power frequency, can obtain obvious noise reduction effect by processing single acquisition signals, and can improve detection efficiency.
The present invention is achieved in such a way that,
a magnetic resonance signal power frequency noise reduction method based on a wavelet transform modulus maximum value method comprises the following steps:
a. adding power frequency noise into an ideal magnetic resonance observation signal to construct a full-wave magnetic resonance signal containing the power frequency noise, and performing n-layer wavelet decomposition on the noise-containing signal, wherein n is 5-7;
b. extracting detail coefficient d of each layer1，…，dnAnd the last layer approximation coefficient an；
c. Updating detail coefficients of each layer by using a wavelet transform modulus maximum denoising algorithm;
d. and reconstructing the signal by using the reconstructed wavelet coefficients.
Further, step c comprises:
1) solving the wavelet coefficient modulus maximum value point and the corresponding modulus maximum value on each scale;
2) setting a threshold value on the maximum scale, and updating a mode maximum value point generated by a signal on the maximum scale;
3) updating the module maximum value point on the scale J-1 according to the module maximum value point of the scale J and the neighborhood range thereof;
4) reserving the position of the module maximum value point corresponding to the position of the dimension 2 on the dimension 1;
5) and reconstructing the wavelet coefficient by using the residual modulus maximum value points on each scale.
Further, determining the wavelet coefficient modulus maxima points and their corresponding modulus maxima at each scale comprises:
solving the mean square error sigma of the power frequency noise;
taking the mean square error sigma of the power frequency noise into the formula (1) to obtain the threshold lambda, the formula (1)
Where λ is a real number and N is the length of the highest level detail coefficient.
Further, setting a threshold value on the maximum scale, and updating a modulus maximum value point generated by the signal on the maximum scale comprises:
and carrying out hard threshold processing on the modulus maximum value of the detail coefficient of the highest layer, when the modulus maximum value of the detail coefficient of the highest layer is greater than the threshold lambda, keeping the corresponding modulus maximum value point, otherwise, removing the corresponding modulus maximum value point, and updating the modulus maximum value point of the detail coefficient on the maximum scale.
Further, updating the modulo maximum point on the scale J-1 according to the modulo maximum point of the scale J and its neighborhood range includes: construction of search neighborhood U (x) using modulo maximum point position at maximum scaleJn) Wherein x isJnRepresenting the nth modulo maximum point on the scale J, in the neighborhood U (x)Jn) Searching detail coefficient modulus maximum value point on the dimension J-1 in the inner mode, and reserving the region U (x) on the dimension J-1Jn) The inner modulo maximum point is cleared of the remaining modulo maximum points, thereby updating the detail coefficient modulo maximum point on the scale J-1.
Further, preserving the position of the modulo maximum point on scale 1 corresponding to the scale 2 position comprises: and setting the modulus maximum value points of other positions as 0.
Further, after the step 3) is finished, J is made J-1, whether J is larger than 2 is judged, and if J is larger than 2, the step 3) is circulated, and the circulation is stopped until the scale number is 2.
Compared with the prior art, the invention has the beneficial effects that: the method is mainly applied to magnetic resonance underground water detection, firstly, wavelet transformation is carried out on magnetic resonance signals, detail coefficients of all layers and an approximation coefficient of the last layer are extracted, a mode maximum denoising algorithm is used for updating the detail coefficients of all layers, and the reconstructed wavelet coefficients are used for reconstructing the signals, so that power frequency noise is reduced, the magnetic resonance signals are guaranteed to have no loss, and effective data are provided for later inversion and interpretation of hydrogeological parameters. In addition, the method has simple process and high operation speed, can realize better noise reduction effect by processing single detection signal, and has important significance and practical value in the field of magnetic resonance noise reduction.
Drawings
FIG. 1 is a flow chart of a method for reducing power frequency noise of a magnetic resonance signal based on wavelet transformation;
FIG. 2 is an ideal time domain diagram of a magnetic resonance observation signal;
FIG. 3 is a frequency domain diagram of an ideal magnetic resonance observation signal;
FIG. 4 is a time domain diagram of a magnetic resonance observation signal containing power frequency noise;
FIG. 5 is a frequency domain plot of a magnetic resonance observation signal containing power frequency noise;
FIG. 6 is a diagram of detail coefficients of wavelet transform of a magnetic resonance signal containing power frequency noise;
fig. 7 is a diagram of the wavelet transform approximation coefficients of the magnetic resonance signal containing power frequency noise.
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.
A magnetic resonance signal power frequency noise reduction method based on a wavelet transform modulus maximum value method comprises the following steps:
a. adding power frequency noise (the signal is an ideal magnetic resonance signal time domain graph as shown in fig. 2, and the signal is an ideal magnetic resonance signal frequency domain graph as shown in fig. 3) into an ideal magnetic resonance observation signal, constructing a full-wave magnetic resonance signal containing the power frequency noise (the signal is a magnetic resonance signal time domain graph containing the power frequency noise as shown in fig. 4, and the signal is a magnetic resonance signal frequency domain graph containing the power frequency noise as shown in fig. 5), and performing n-layer wavelet decomposition on the signal containing the noise, wherein n is generally 5-7;
b. extracting detail coefficient d of each layer1，…，dn(see FIG. 6) and the last layer approximation coefficient an(see FIG. 7);
c. updating detail coefficients of each layer by using a wavelet transform modulus maximum denoising algorithm;
d. reconstructing the signal using the reconstructed wavelet coefficients, where the wavelet coefficients include detail coefficients and approximation coefficients;
the wavelet transform modulus maximum denoising algorithm in the step c specifically comprises the following steps:
firstly, solving the mean square error sigma of power frequency noise;
secondly, the mean square error sigma of the power frequency noise is substituted into the calculation threshold lambda,
where λ is a real number and N is the length of the highest level detail coefficient;
thirdly, performing hard threshold processing on the modulus maximum of the highest level detail coefficient, namely when the modulus maximum of the highest level detail coefficient is greater than the threshold lambda, retaining the corresponding modulus maximum point, otherwise, removing the corresponding modulus maximum point, thereby updating the modulus maximum point of the detail coefficient on the maximum scale, wherein the maximum scale is equivalent to the maximum number of layers, for example: if 7 layers of decomposition are performed on the signal, the maximum dimension is 7;
fourth, the search neighborhood U (x) is constructed using the positions of the modulo maxima points at the maximum dimensionJn) Wherein x isJnRepresenting the nth modulo maximum point on the scale J, in the neighborhood U (x)Jn) Inner search scale J-1, the retention dimension J-1 is located in the neighborhood U (x)Jn) The inner modular maximum point, the remaining modular maximum points are removed, and the detail coefficient modular maximum point on the scale J-1 is updated, where the relationship between the scale and the maximum scale is specified as follows: n is 7, the maximum scale is 7, the scales comprise 7, 6, 5, 4, 3, 2 and 1, and the total number of the scales is 7;
fifthly, enabling J to be J-1, and circulating the content of the fourth step until the number of scales is 2, and stopping circulation;
sixthly, the maximum value point corresponding to the maximum value point position on J-2 on J-1 is reserved, and the module maximum value points of other positions are set to be 0.
Example 1
This example is a simulation experiment of the method of the present invention conducted in the programming environment of matlabR2014 a.
The simulation algorithm of the magnetic resonance signal power frequency noise reduction method based on wavelet transformation, referring to fig. 1, comprises the following steps:
a. adding power frequency noise into an ideal magnetic resonance observation signal, constructing a full-wave magnetic resonance signal containing the power frequency noise, and performing 7-layer wavelet decomposition on the noise-containing signal;
b. extracting detail coefficient d of each layer1，…，d7And the last layer approximation coefficient a7；
c. Updating detail coefficients of each layer by using a wavelet transform modulus maximum denoising algorithm;
d. and reconstructing the signal by using the reconstructed wavelet coefficients.
The wavelet transform modulus maximum denoising algorithm in the step c specifically comprises the following steps:
firstly, solving the mean square error sigma of power frequency noise;
secondly, the mean square error sigma of the power frequency noise is substituted into the calculation threshold lambda,
where λ is a real number and N is the length of the highest level detail coefficient;
third, hard thresholding the modulus maxima of the layer 7 detail coefficientsI.e. when d7When the modulus maximum value is larger than the threshold lambda, the corresponding modulus maximum value point is reserved, otherwise, the corresponding modulus maximum value point is eliminated, and thus, the modulus maximum value point of the detail coefficient of the 7 th layer is updated;
fourth, the search neighborhood U (x) is constructed using the modulo maximum point position of the layer 7 detail coefficients7n) In the neighborhood of U (x)7n) Searching detail coefficient module maximum value point on the inner search scale 6, and reserving the area positioned in the neighborhood U (x) on the inner search scale 67n) The inner module maximum value point, and the rest module maximum value points are removed, so that the detail coefficient module maximum value point on the scale 6 is updated;
fifth, search neighborhood U (x) is constructed using the position of the modulo maximum point of the level 6 detail coefficient6n) In the neighborhood of U (x)6n) Searching detail coefficient module maximum value point on the dimension 5 in the inner mode, and reserving the position of the neighborhood U (x) on the dimension 56n) Clearing the other module maximum value points, thereby updating the detail coefficient module maximum value point on the scale 5;
sixth, the search neighborhood U (x) is constructed using the position of the modulo maximum point of the level 5 detail coefficient5n) In the neighborhood of U (x)5n) Searching detail coefficient module maximum value point on the scale 4 in the inner way, and reserving the maximum value point which is positioned in the neighborhood U (x) on the scale 45n) Clearing the other module maximum value points, thereby updating the detail coefficient module maximum value point on the scale 4;
seventh, a search neighborhood U (x) is constructed using the positions of the modulo maximum points of the level 4 detail coefficients4n) In the neighborhood of U (x)4n) Searching detail coefficient module maximum value point on the scale 3 in the inner way, and reserving the maximum value point which is positioned in the neighborhood U (x) on the scale 34n) Clearing the other module maximum value points, thereby updating the detail coefficient module maximum value point on the scale 3;
eighth, the search neighborhood U (x) is constructed using the position of the modulo maximum point of the level 3 detail coefficient3n) In the neighborhood of U (x)3n) Searching detail coefficient module maximum value point on the scale 2 in the inner mode, and reserving the maximum value point which is positioned in the neighborhood U (x) on the scale 23n) Clearing the other module maximum value points, thereby updating the detail coefficient module maximum value point on the scale 2;
and ninthly, reserving a maximum value point corresponding to the maximum value point on the scale 1 and the scale 2, and setting the module maximum value points of other positions as 0.
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 (2)
1. A magnetic resonance signal power frequency noise reduction method based on a wavelet transform modulus maximum value method is characterized by comprising the following steps:
a. adding power frequency noise into an ideal magnetic resonance observation signal, constructing a full-wave magnetic resonance signal containing the power frequency noise, and performing n-layer wavelet decomposition on the noise-containing signal, wherein n is 7;
b. extracting detail coefficient d of each layer1，…，dnAnd the last layer approximation coefficient an；
c. Updating detail coefficients of each layer by using a wavelet transform modulus maximum denoising algorithm;
d. reconstructing a signal by using the reconstructed wavelet coefficients;
the step c comprises the following steps:
1) solving the wavelet coefficient modulus maximum value point and the corresponding modulus maximum value on each scale;
2) setting a threshold value on the maximum scale, and updating a mode maximum value point generated by a signal on the maximum scale;
3) updating the module maximum value point on the scale J-1 according to the module maximum value point of the scale J and the neighborhood range thereof;
4) reserving the position of the module maximum value point corresponding to the position of the dimension 2 on the dimension 1;
5) reconstructing wavelet coefficients by using the residual modulus maximum points on each scale;
setting a threshold value on the maximum scale, and updating a module maximum value point generated by the signal on the maximum scale comprises the following steps:
performing hard threshold processing on the modulus maximum value of the detail coefficient of the highest layer, when the modulus maximum value of the detail coefficient of the highest layer is larger than a threshold lambda, keeping the corresponding modulus maximum value point, otherwise, removing the corresponding modulus maximum value point, and updating the modulus maximum value point of the detail coefficient on the largest scale;
according to the modulus maximum point of the scale J and the neighborhood range thereof, updating the modulus maximum point on the scale J-1 comprises the following steps: construction of search neighborhood U (x) using modulo maximum point position at maximum scaleJn) Wherein x isJnRepresenting the nth modulo maximum point on the scale J, in the neighborhood U (x)Jn) Searching detail coefficient modulus maximum value point on the dimension J-1 in the inner mode, and reserving the region U (x) on the dimension J-1Jn) Clearing the other module maximum value points, thereby updating the detail coefficient module maximum value point on the scale J-1;
preserving the positions of the modulo maximum points on scale 1 corresponding to the scale 2 positions includes: setting the maximum value points of the modules at other positions as 0;
finding wavelet coefficient modulus maxima points and their corresponding modulus maxima at each scale comprises:
solving the mean square error sigma of the power frequency noise;
taking the mean square error sigma of the power frequency noise into the formula (1) to obtain the threshold lambda, the formula (1)
Where λ is a real number and N is the length of the highest level detail coefficient.
2. The method of claim 1, wherein after step 3) is completed, J is J-1, whether J is greater than 2 is determined, and if J is greater than 2, step 3) is repeated until the number of scales is 2, and the circulation is stopped.
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