An aerial gamma spectrum data denoising method
By training a sparse dictionary using the K-SVD algorithm, the problem of poor adaptability in airborne gamma spectrum data denoising was solved, achieving better noise filtering and signal recovery, and improving data accuracy.
Patent Information
- Application Number
- CN202211122147.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-09-15
- Publication Date
- 2025-12-23
- Estimated Expiration
- 2042-09-15
AI Technical Summary
Existing methods for denoising airborne gamma spectrum data are ineffective, suffering from poor adaptability, information loss, or high complexity.
The sparse dictionary is trained using the K-SVD algorithm, the sparse representation vector is solved using the OMP algorithm, and the sparse dictionary atoms are optimized using the SVD algorithm. The sparse dictionary is updated column by column to reconstruct the denoised airborne gamma spectrum signal.
It effectively filters out noise, reduces the impact of statistical fluctuations, preserves original data information, has better adaptability and smoothness, and its noise reduction effect is superior to other methods.
Smart Images
Figure CN115438739B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of nuclear detection data processing in nuclear technology exploration, in particular to an aerial gamma spectrum data denoising method. BACKGROUND
[0002] Aerial gamma spectrum measurement realizes the detection of the content and distribution of radionuclides in the ground, soil and atmosphere and other areas through a gamma spectrometer installed on an airplane. It is based on various disciplines and theoretical foundations, such as nuclear physics, geology, electronics, etc. Due to its high efficiency, low cost and wide range of applications, it is widely used in geological prospecting, nuclear accident emergency monitoring and engineering geological survey. During the process of aerial gamma spectrum measurement, statistical fluctuations and instrument noise are usually affected, so that the collected data contain certain noise interference components, which affects the calculation accuracy of radionuclides. Therefore, in data processing, denoising is an important prerequisite for ensuring the accuracy of aerial gamma spectrum measurement results.
[0003] The commonly used aerial gamma spectrum data denoising methods include MNF (Maximum noise fraction), NASVD (Noise Adjusted Singular Value Decomposition), least squares moving smoothing method and wavelet transform. The MNF uses statistical theory to realize data denoising. The NASVD method extracts the main components of the spectrum by PC analysis method, and reconstructs the original data using the above main components, thereby realizing the filtering of noise, but at the same time, part of the useful information is lost. The least squares moving smoothing method needs to manually select the number of fitting points according to the signal characteristics, so it lacks adaptability. The wavelet transform filters the high-frequency components in the spectrum data to achieve the effect of denoising, but the corresponding decomposition and reconstruction scale needs to be manually selected according to the characteristics of the data, and the adaptability is poor. The spectrum denoising method based on wavelet threshold Wiener filter reduces the influence of statistical fluctuations on the spectrum data by combining the double wavelet basis with the Wiener filter, but this method requires that the signal and noise have a priori, which increases the complexity of the denoising process. SUMMARY
[0004] The purpose of the present application is to provide an aerial gamma spectrum data denoising method to solve the problem of poor effect of the existing denoising method.
[0005] The present application is implemented as follows: an aerial gamma spectrum data denoising method, comprising the following steps:
[0006] a. read in original aerial gamma spectrum data, initialize parameters, set original data length as L, determine training frame number PX with 50 as a step length, and segmentally process the original data to reduce noise;
[0007] b. initialize sparse dictionary D, and initialize its sparsity as K;
[0008] c. solve sparse representation vector x by using OMP algorithm;
[0009] d. decompose matrix sparse dictionary D and Let d i and x i be zero, and solve error matrix E, according to the principle of min||E-d i x i ||, optimize d i and x i by using SVD algorithm;
[0010] e. update sparse dictionary atoms column by column, and judge whether the sparse dictionary is updated completely, if yes, proceed to the next step, otherwise return to step d;
[0011] f. judge whether the maximum iteration number is reached, if yes, proceed to the next step, otherwise return to step b;
[0012] g. obtain updated sparse dictionary D and sparse representation vector x;
[0013] h. reconstruct the original signal by using the updated sparse dictionary and sparse representation vector x obtained in step g, to obtain the aerial gamma spectrum signal after noise reduction.
[0014] Further, the present application can be realized according to the following technical scheme:
[0015] In the step a, the average value is obtained with 50 as a step length, and the obtained average value is used as an input variable of training sparse dictionary, at this time, the training frame number of the input variable is PX= floor (L / 50).
[0016] In the step b, the input variable obtained in the step a is used as an initial value of initializing sparse dictionary D.
[0017] In the step a, in the step b, the dimension of the initialized over-complete redundant sparse dictionary is PX*LL, wherein the value of LL is determined according to the principle of LL=2 / 3*PX.
[0018] The present application can filter out the interference noise in the aerial gamma spectrum data well by using K-SVD to train the sparse dictionary D, reduce the influence of statistical fluctuations on the spectrum data, and at the same time, the signal after noise reduction has better smoothness, retains the effective information of the original data and restores the signal peak and valley characteristics, and at the same time avoids the process of manual parameter adjustment, and has strong adaptability.
[0019] In order to ensure that the noise is effectively filtered out while retaining the useful information in the original data, and improve the adaptability in the noise reduction process, the present application proposes to apply the K-SVD algorithm to the aerial gamma spectrum data noise reduction, so as to achieve the purpose of noise reduction and eliminate the influence of statistical fluctuations on the data. That is, the K-SVD training sparse dictionary is applied to the spectrum data noise reduction, the data collected by the stability test is processed, the sparse dictionary atoms are iteratively updated and selected to extract the characteristic information of the data, and the signal after noise reduction is reconstructed, so as to realize the noise reduction of the spectrum data. BRIEF DESCRIPTION OF DRAWINGS
[0020] Figure 1 is a flowchart of the present application.
[0021] Figure 2 is the noise reduction effect comparison of the present application on the upper measurement window data.
[0022] Figure 3 is the noise reduction effect comparison of the present application on the lower measurement window data.
[0023] Figure 4 is the noise reduction effect comparison of the present application and the S-G method.
[0024] Figure 5 is the noise reduction effect comparison of the present application and the NASVD method.
[0025] Figure 6 is the comparison of the mean square error values of the upper measurement window data after noise reduction by the present application and different noise reduction methods.
[0026] Figure 7 is the comparison of the mean square error values of the lower measurement window data after noise reduction by the present application and different noise reduction methods.
[0027] Figure 8 is the comparison of the SNR values after noise reduction by the present application and different noise reduction methods. DETAILED DESCRIPTION
[0028] As shown in Figure 1 , the aerial gamma spectrum data noise reduction method of the present application comprises the following steps:
[0029] a, read the original aerial gamma spectrum data, initialize the parameters, set the original data length as L, determine the training frame number PX with 50 as the step length, and segment the original data for noise reduction processing;
[0030] The average value is obtained in steps of 50, and the obtained average value is taken as the input variable for training the sparse dictionary, and the training frame number of the input variable is PX = floor(L / 50).
[0031] b. Initialize the sparse dictionary D, and initialize the sparsity thereof to K; the input variable obtained in the step a is taken as the initial value of the initialized sparse dictionary D. The dimension of the initialized over-complete redundant sparse dictionary is PX*LL, wherein the value of LL is determined according to the following principle: LL = 2 / 3*PX.
[0032] c. Solve the sparse representation vector x by using the OMP algorithm, first solve the atom that matches the residual most, and then obtain the vector result by using the least square method according to the selected atom.
[0033] d. Decompose the matrix sparse dictionary D and Let d i and x i be zero, and solve the error matrix E according to the principle of min||E-d i x i ||, decompose the error matrix E by using the SVD algorithm, so as to realize the optimization of d i and x i .
[0034] e. Update the sparse dictionary atom column by column, and judge whether the sparse dictionary is updated completely, if yes, proceed to the next step, otherwise return to step d.
[0035] f. Judge whether the maximum iteration number is reached, if yes, proceed to the next step, otherwise return to step b.
[0036] g. Obtain the updated sparse dictionary D and the sparse representation vector x.
[0037] h. Reconstruct the original signal by using the updated sparse dictionary and the sparse representation vector x obtained in the g step, and obtain the denoised aerial gamma spectrum signal.
[0038] It is assumed that the value of most elements in the N-dimensional original signal y is 0, and the signal is called strictly sparse. However, most of the original signals y in the aerial gamma spectrum data do not have sparsity, and therefore, the original signal needs to be sparsely represented. The sparse dictionary sparsely represents the original signal by using the atoms in the dictionary, so that the original signal has sparsity or compressibility in a certain transform domain. The process can be represented by formula (1):
[0039] y = Dx (1)
[0040] Where y is the original signal in N×1 dimensions, D is the N×K dimensional sparse dictionary, and x is the K×1 dimensional sparse representation vector. That is, after the original signal y is sparsed using the sparse dictionary, a vector x with only a few non-zero elements is obtained. In other words, the sparse representation vector x at this point has a certain degree of sparsity. This process can be specifically represented by equation (2):
[0041]
[0042] Where Y is an N×M dimensional sample matrix, and each column represents a training sample, for a total of M samples; D = {d1, d2, ..., d...} k} is a sparse dictionary, where each column represents an atom, and there are K atoms in total; X is a sparse matrix, where each column represents the sparse representation vector of the sample under the corresponding sparse dictionary; ε represents the reconstruction error. Since solving the l0 norm is an NP-hard problem, it can be transformed into solving a convex optimization problem, that is, into solving the l1 norm problem, as shown in equation (3):
[0043]
[0044] The process can be specifically represented as follows:
[0045]
[0046] Since the initial value of the K-SVD sparse dictionary is not optimal, it is necessary to update the sparse dictionary atoms to optimize its performance. The K-SVD sparse dictionary is updated column by column, and the sparse dictionary atom is updated once through K iterations. The criterion for whether the sparse dictionary atom is optimal is the residual value after each update. First, the sparse dictionary D is fixed, and the sparse representation vector x is obtained using algorithms such as OMP. Then, the sparse dictionary atoms are updated column by column by solving the optimization algorithm of equation (2). The error solution process is as follows: equation (5):
[0047]
[0048] Where E k Given the error matrix, performing SVD decomposition on it yields the following equation:
[0049] E k =UAV T (6)
[0050] Where U and V are unitary matrices and their column vectors are all orthogonal bases, Λ is a diagonal matrix, and d is obtained by taking the first column vector of matrix U. k To represent this, take the product of the first column vector of V and the first element of Λ, and pair it with x. iThe updating of the sparse dictionary is completed by the expression.
[0051] As shown in Figure 2 and Figure 3 The present application has better smoothness for the signals after noise reduction of the upper measurement window data and the lower measurement window data, retains the effective information of the original data, and restores the signal wave peak and valley characteristics.
[0052] As shown in Figure 4 and Figure 5 The present application can better eliminate the influence of statistical fluctuation compared with the S-G method, and has better smoothness compared with the NASVD method.
[0053] As shown in Figure 6 and Figure 7 In the noise reduction method of the present application, the mean square deviation of the data after noise reduction of the upper measurement window data and the data after noise reduction of the lower measurement window data is the minimum, that is, the data after noise reduction has higher stability.
[0054] As shown in Figure 8 The SNR value after noise reduction of the present application is compared with different noise reduction methods, and the noise of the data obtained by the present application is effectively filtered out.
Claims
1. A method for denoising airborne gamma-ray spectral data, characterized in that, Includes the following steps: a. Read in the raw airborne gamma spectrum data, initialize the parameters, set the raw data length to L, determine the number of training frames PX with a step size of 50, and perform noise reduction processing on the raw data in segments. b. Initialize the sparse dictionary D and initialize its sparsity to K; c. Solve for the sparse representation vector x using the OMP algorithm; d. Decomposition of matrix sparse dictionary D and Let d i and x i The value is zero, and the error matrix E is solved based on min||Ed. i x i ||Principle, using the SVD algorithm to analyze d i and x i optimization; e. Update the sparse dictionary atoms column by column, and determine whether the sparse dictionary has been updated. If it has, proceed to the next step; otherwise, return to step d. f. Determine if the maximum number of iterations has been reached. If it has, proceed to the next step; otherwise, return to step b. g. Obtain the updated sparse dictionary D and sparse representation vector x; h. Reconstruct the original signal using the updated sparse dictionary and sparse representation vector x obtained in step g, and obtain the denoised airborne gamma spectrum signal. First, fix the sparse dictionary D, and use the OMP algorithm to obtain the sparse representation vector x. Then, further update the sparse dictionary atoms column by column by solving the optimization algorithm of equation (2). The error solution process is as follows: equation (5): Where E k Given the error matrix, performing SVD decomposition on it yields the following equation: AND k =UΛV T (6) Where U and V are unitary matrices and their column vectors are all orthogonal bases, Λ is a diagonal matrix, and d is obtained by taking the first column vector of matrix U. k To represent this, take the product of the first column vector of V and the first element of Λ, and pair it with x. i This is done by representing the sparse dictionary and thus completing an update.
2. The airborne gamma spectrum data denoising method according to claim 1, characterized in that, in In step a, the average value is calculated with a step size of 50, and the calculated average value is used as the input variable for training the sparse dictionary. At this time, the number of training frames for the input variable is PX = floor(L / 50).
3. The airborne gamma spectrum data denoising method according to claim 2, characterized in that, In step b, the input variables obtained in step a are used as the initial values for initializing the sparse dictionary D.
4. The airborne gamma spectral data denoising method according to claim 1, characterized in that, in In step a, in step b, the dimension of the complete redundant sparse dictionary is initialized to PX*LL, where the value of LL is determined by the principle that LL = 2 / 3*PX.