Noise Suppression Method for Nuclear Magnetic Resonance Data Based on Iterative Kalman Filter

Abstract

The present invention belongs to the field of nuclear magnetic resonance data processing. Specifically, it is a method for suppressing noise in nuclear magnetic resonance data based on iterative Kalman filtering, including: segmenting the acquired nuclear magnetic resonance echo data y(t), where the time t = 2nτ, τ is the half-echo interval time, n is the number of echoes, n = 1, 2, 3, … N, and the segmentation scheme is to intercept K parts at equal logarithmic intervals between t = 2τ and 2Nτ. Each segment of NMR echo data is denoted as y k , k = 1, 2, …, K; for the NMR echo data from the first segment to the Kth segment, perform extended Kalman filtering to obtain y k the model value M k corresponding to the segment echo data and the corresponding time t k ; the output y k the model value M k corresponding to the segment echo data and the corresponding time t k , k = 1, 2, …, K are substituted into the NMR echo forward function to obtain #imgabs0# with noise suppressed. This method does not require manual setting of Kalman filter coefficients, and the filtering is an adaptive process, so it has higher universality and accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of nuclear magnetic resonance data processing, and more specifically, it is a method for suppressing nuclear magnetic resonance data noise based on iterative Kalman filtering. Background Art

[0002] The nuclear magnetic resonance (NMR) method is based on the background field intensity and can be divided into high-field nuclear magnetic resonance (greater than 0.5T) and low-field nuclear magnetic resonance. Low-field nuclear magnetic resonance has the advantages of low cost and in-situ testing, so it is widely used in detecting the physical properties of substances, mainly including food science, polymer materials, and petroleum exploration. Low-field nuclear magnetic resonance excites hydrogen protons in the medium to resonate by applying radio frequency pulses (CPMG sequence), and the NMR echo curve can be collected using a receiving coil.

[0003] Patent ZL202010574811.8 invented a method and device for denoising nuclear magnetic resonance signals. By separating the signal-to-noise of multiple component signals separated from the nuclear magnetic resonance signal, the noise signal in the nuclear magnetic resonance signal is obtained, and then the denoising of the nuclear magnetic resonance signal is realized. This method does not require pre-setting the signal-to-noise separation threshold, ensuring the accuracy of signal-to-noise separation.

[0004] Patent 202110794109.7 invented a nuclear magnetic resonance noise suppression method applicable to geophysical nuclear magnetic resonance instruments. This method is based on multilinear singular value tensor decomposition. By algorithms such as single-channel signal Hankel transform, Tucker decomposition, and multi-channel signal fusion, the signal-to-noise ratio of FID is improved.

[0005] Patent 202011353261.3 invented a method for processing low signal-to-noise nuclear magnetic resonance echo signals. By performing singular value decomposition (SVD) filtering on the selected echo signals, a new signal matrix is constructed, and then the high signal-to-noise echo signals are restored. This method can improve the accuracy of inversion.

[0006] In summary, the current methods for suppressing nuclear magnetic resonance data noise mainly focus on methods such as SVD decomposition and blind source separation, which have the problems that the characteristic matrix requires artificial setting of parameters and the interpretability is not strong, and at the same time, the universality is relatively low. Therefore, the present invention proposes a method for suppressing nuclear magnetic resonance data noise based on iterative Kalman filtering. Summary of the Invention

[0007] The present invention aims to provide a method for nuclear magnetic resonance (NMR) noise suppression, a method for suppressing noise in NMR data based on iterative Kalman filtering. By performing segmented correction and prediction on the original data collected by NMR, the corresponding amplitude and relaxation time are obtained, and then the NMR echo signal is reconstructed to achieve noise suppression.

[0008] The present invention is implemented as follows:

[0009] A method for suppressing noise in NMR data based on iterative Kalman filtering, the method comprising:

[0010] Step 1: Segment the collected NMR echo data y(t), where the time t = 2nτ, τ is the half echo interval time, n is the number of echoes, n = 1, 2, 3, … N. The segmentation scheme is to intercept K portions at equal logarithmic intervals between t = 2τ and 2Nτ. Each segment of NMR echo data is denoted as y k , k = 1, 2, …, K;

[0011] Step 2: Perform extended Kalman filtering on the NMR echo data from the first segment to the K-th segment to obtain the model value M k corresponding to the segment echo data k and the corresponding time t k ;

[0012] Step 3: Substitute the model value M k corresponding to the segment echo data and the corresponding time t k , k = 1, 2, …, K obtained in Step 2 into the NMR echo forward function to obtain the k noise-suppressed

[0013] Further, Step 2 specifically includes:

[0014] Step A: Initialize, let k = 1, initialize M0, P0, M0 = [A0, T 20 , where the range of A0 is any real number between 1 and the maximum value M of the echo curve max , and the range of T 20 is any real number between 0.001 and 1. The prior error estimate P0 of the model is the covariance matrix of M0;

[0015] Step B: Construct the model space and measurement space of the NMR echo data, as shown in Equations (1) and (2) respectively:

[0016] M k+1 = F(M k ) + θ k (1)

[0017] y k = G(Mk-1 ) + ω k (2)

[0018] where M k is the model value corresponding to the y k -segment echo data, M k = [A k , T 2k , A k and T 2k are the amplitude and transverse relaxation time of the y k -segment echo data respectively, F is the state evolution function, θ k is the error of the model, and the mean is zero and the variance is R k , G(·) is the NMR echo forward function, ω k is the error of the measured echo data, and the mean is zero and the variance is S k , according to Equation (2), it can be known that G is a non-linear function, let q = 1;

[0019] Step C, the prediction equations of the NMR model and the model error based on the extended Kalman filter method are respectively:

[0020] M q|q-1 = FM q-1|q-1 (3)

[0021] P q|q-1 = FP q-1|q-1 F T + R q (4)

[0022] The correction equations of the NMR model and the model error based on the extended Kalman filter method are:

[0023] M q|q = M q|q-1 + C k (y k - G(M q|q-1 )) (5)

[0024] P q|q = (I - C q H q )P q|q-1 (6)

[0025] where C k is the Kalman filter coefficient, H q is the Jacobian matrix,

[0026] Step D, let q = q + 1, go to Step C until the average relative error Meet the requirements, where J is the number of sampling points of the k-th segment of echo data. After the error EOR meets the requirements, let k = k + 1, and go to step B until k = K, that is, the extended Kalman filtering process is performed on all K segments of NMR echo data.

[0027] The present invention has the following advantages and beneficial effects: Compared with the traditional low-field nuclear magnetic resonance noise suppression method, the nuclear magnetic resonance data noise suppression method based on iterative Kalman filtering does not require manual setting of Kalman filter coefficients, and the filtering is an adaptive process. Therefore, it has higher universality and accuracy. Description of the Drawings

[0028] Figure 1 Flowchart of the nuclear magnetic resonance data noise suppression method based on iterative Kalman filtering provided by the method of the present invention;

[0029] Figure 2 NMR echo data and segmentation results provided by the method of the present invention;

[0030] Figure 3 NMR echo data noise suppression results provided by the method of the present invention;

[0031] Figure 4 Statistical distribution diagram of the noise suppressed by the method of the present invention. Detailed Embodiments

[0032] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the 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.

[0033] See Figure 1 As shown, the flowchart of the nuclear magnetic resonance data noise suppression method based on iterative Kalman filtering provided by the present invention includes

[0034] Step 1: Segment the collected NMR echo data y(t), where the time t = 2nτ, τ is the half-echo interval time, n is the number of echoes, and n = 1, 2, 3,... N. The segmentation scheme is to intercept K parts at equal logarithmic intervals between t = 2τ and 2Nτ, and each segment of NMR echo data is denoted as y k , k = 1, 2,..., K. As Figure 2 shown, the gray curve is the NMR echo data. In this embodiment, N = 10 is taken, that is, y(t) is equally logarithmically divided into 10 segments, Figure 2 and the black dotted line in it is the segmentation result.

[0035] Step 2: Perform extended Kalman filtering on the NMR echo data from the 1st segment to the 10th segment. The specific process of the extended Kalman filtering includes:

[0036] A), Extended Kalman filter initialization. Let k = 1. Initialize M0 and P0. M0 = [A0, T 20 , where the range of A0 is any real number from 1 to the maximum value M of the echo curve, and the range of T max is any real number from 0.001 to 1. The prior error estimate P0 of the model is the covariance matrix of M0. In this embodiment, M0 = [20, 0.2]. 20

[0037] B), Construct the model space and measurement space of the NMR echo data, as shown in equations (1) and (2) respectively:

[0038] M k+1 = F(M k ) + θ k (1)

[0039] y k = G(M k-1 ) + ω k (2)

[0040] where M k is the model value corresponding to the y k -th segment of echo data, M k = [A k , T 2k , and A k and T 2k are the amplitude and transverse relaxation time of the y k -th segment of echo data respectively. F is the state evolution function, θ k is the error of the model, with a mean of zero and a variance of R k . G(·) is the NMR echo forward function, ω k is the error of the measured echo data, with a mean of zero and a variance of S k . According to equation (2), G is a non-linear function. Therefore, we use the extended Kalman filter method. Let q = 1.

[0041] C), The prediction equations for the NMR model and model error based on the extended Kalman filter method are respectively:

[0042] M q|q-1 = FM q-1|q-1 (3)

[0043] P q|q-1 = FP q-1|q-1 F T + R q (4)

[0044] ​The NMR model and the correction equation of the model error based on the extended Kalman filter method are:

[0045] M q|q =M q|q-1 +C k (y k -G(M q|q-1 )) (5)

[0046] P q|q =(IC q H q ) q|q-1 (6)

[0047] Among them C k is the Kalman filter coefficient, H q is the Jacobian matrix,

[0048] D), let q = q + 1, go to step C, until the average relative error Meet the requirements, where J is the number of sampling points of the k-th echo data. Output and update M k =M q|q In this embodiment, when k=1, q=16, the error requirement is met, that is, EOR is less than 1%, and the output M1=[20,0.15]. When the error EOR meets the requirement, set k=k+1. Go to step B, that is, perform Kalman filter processing on the second segment of echo data. Until k=10, that is, all 10 segments of NMR echo data have been processed by extended Kalman filter.

[0049] Step 3: Output M from step 2 k and the corresponding time t k Substituting (k=1,2,…,K) into the NMR echo forward function, we get That is, the noise suppression of nuclear magnetic resonance data based on iterative Kalman filtering is completed. Figure 3 The black curve is The gray curve is the collected NMR echo curve y(t). By comparison, it can be seen that after the extended Kalman filter, the noise of the NMR echo is suppressed, and the echo attenuation trend does not change. That is, the suppressed noise data, its statistical histogram is shown in Figure 4 As shown, Figure 4 The black curve in the middle is a Gaussian distribution with a mean of and a variance of 0.1. It can be seen that the suppressed noise is Gaussian distributed, indicating that no NMR echo signal is suppressed, proving the effectiveness of the extended Kalman filter method.

Claims

1. A method for noise suppression of nuclear magnetic resonance data based on iterative Kalman filtering, characterized in that, The method includes Step 1: Segment the acquired nuclear magnetic resonance echo data y(t). The time t = 2nτ, where τ is the half echo interval time and n is the number of echoes, n = 1, 2, 3, … N. The segmentation scheme is to intercept K segments at equal logarithmic intervals between t = 2τ and 2Nτ. Each segment of NMR echo data is denoted as y k , k = 1, 2, …, K; Step 2: Perform extended Kalman filtering on the NMR echo data from the first segment to the Kth segment to obtain y k The model value M corresponding to the segment echo data k and the corresponding time t k ; Step 3: Take the y output in Step 2 k The model value M corresponding to the k segment echo data and the corresponding time t k , substitute k = 1, 2, …, K into the NMR echo forward function to obtain the Specifically, step 2 includes: Step A, initialization: Let k = 1, initialize M0, P0, M0 = [A0, T 20 , where the range of A0 is any real number between 1 and the maximum value M of the echo curve max , and the range of T 20 is any real number between 0.001 and 1. The prior error estimate P0 of the model is the covariance matrix of M0; Step B: Construct a model space and a measurement space for NMR echo data, as shown in equations (1) and (2) respectively: M k+1 = F(M k ) + θ k (1) y k = G(M k-1 ) + ω k (2) where M k is the model value corresponding to the y k -th segment of echo data, and M k = [A k , T 2k , where A k and T 2k are respectively the amplitude and transverse relaxation time of the y k -th segment of echo data, F is the state evolution function, θ k is the error of the model, and its mean is zero and variance is R k , G(·) is the NMR echo forward function, ω k is the error of the measured echo data, and its mean is zero and variance is S k . According to Equation (2), G is a non-linear function. Let q = 1; Step C: The prediction equations for the NMR model and the model error based on the extended Kalman filter method are respectively: M q|q-1 = FM q-1|q-1 (3) P q|q-1 = FP q-1|q-1 F T + R q (4) The correction equations for the NMR model and the model error based on the extended Kalman filter method are: M q|q = M q|q-1 + C k (y k - G(M q|q-1 )) (5) P q|q = (I - C q H q )P q|q-1 (6) Among them, C k is the Kalman filter coefficient, H q is the Jacobian matrix, Step D, let q = q + 1, and go to Step C until the average relative error meets the requirement, where J is the number of sampling points of the k-th segment of echo data. After the error EOR meets the requirement, let k = k + 1, and go to Step B until k = K, that is, the extended Kalman filter processing is performed on all K segments of NMR echo data.

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