A spectral line denoising method based on fractional-order iterative discrete wavelet transform

Abstract

The present invention belongs to the technical field of spectral data analysis and processing, and discloses a spectral line denoising method based on fractional-order iterative discrete wavelet transform, wherein G-L fractional-order processing is performed on the original detection spectral line signal of the sample to be tested, and an optimal fractional order is obtained by searching by an iterative method; Fourier transform is performed on the optimal fractional order of the signal; iterative discrete wavelet decomposition and reconstruction are performed to obtain optimal wavelet transform coefficients; and the optimal wavelet transform coefficients are corrected and wavelet reconstruction is performed to obtain a reconstructed estimated signal; and a p-order fractional Fourier transform is performed on the transformed signal to obtain a denoised spectral line signal. The present invention denoises the spectral line by combining fractional-order Fourier transform and iterative discrete wavelet, which can clearly retain the details in the signal without sharpening or over-smoothing, improves the signal-to-noise ratio, is scientific and reasonable, has a simple process, is easy to operate, and has intuitive and easy-to-understand results. Compared with the existing denoising methods, the denoising effect is better.

Description

Technical Field

[0001] The present invention belongs to the technical field of spectral data analysis and processing, and in particular relates to a spectral line denoising method based on fractional-order iterative discrete wavelet transform. Background Art

[0002] Currently, spectral line denoising is an essential part of spectral preprocessing. Its purpose is to remove noise generated during signal transmission due to factors such as the instrument system, the detection environment, and the properties of the sample itself, thereby preserving the original characteristics and detailed information of the spectral line as much as possible, thereby improving the measurement accuracy and signal-to-noise ratio of the X-ray spectrum and facilitating subsequent signal analysis.

[0003] In recent years, numerous signal denoising methods have been developed, including derivative denoising, Fourier transform denoising, and wavelet transform denoising. First- and second-order derivatives are the most commonly used methods for spectral denoising. However, traditional integer-order derivatives cannot detect gradual slopes or varying curvatures that may contain useful information about the target variable. High-frequency noise also reduces the spectral signal-to-noise ratio as the derivative order increases. Fractional-order derivative (FOD) algorithms fall between traditional integer-order derivatives and the zeroth and second-order derivatives. Compared to integer-order derivatives, fractional-order differentials are becoming increasingly attractive in the field of signal processing.

[0004] The iterative discrete wavelet transform (IDWT) performs multiresolution analysis of signals in the time-frequency domain. The fractional Fourier transform (FFT) is a generalization of the traditional fast Fourier transform (FFT), enabling better separation of chirp signals and noise. The fractional iterative discrete wavelet transform (IDWT) combines the advantages of both methods, extending multiresolution analysis to the time-generalized frequency domain, creating a new time-frequency domain analysis method. Compared to the iterative discrete wavelet transform (IDWT), the fractional wavelet transform's greatest advantage is the addition of a variable order p, allowing for more flexible adjustment of the wavelet coefficients.

[0005] Traditional spectral line denoising methods use a constant deviation between the wavelet coefficients and the true wavelet coefficients, which reduces the accuracy of wavelet coefficient reconstruction and leads to poor denoising results. Fractional derivatives vary over very small time intervals, ensuring that the signal-to-noise ratio changes slowly, allowing for the detection of more features of certain spectral signals and the extraction of more details. This is also easy to implement. Therefore, using a suitable FOD for denoising, rather than traditional integer derivatives, is crucial.

[0006] Through the above analysis, the problems and defects of the existing technology are: the existing spectral signal denoising method has poor denoising effect and low wavelet coefficient reconstruction accuracy. Summary of the Invention

[0007] In view of the problems existing in the prior art, the present invention provides a spectral line denoising method based on fractional-order iterative discrete wavelet transform.

[0008] The present invention is implemented as follows: a spectral line denoising method based on fractional-order iterative discrete wavelet transform, the spectral line denoising method based on fractional-order iterative discrete wavelet transform comprising:

[0009] First, the original detection line signal of the sample to be tested is processed by GL fractional order to convert the signal into a v-order fractional differential form;

[0010] Secondly, the optimal fractional order is searched by iterative method; the optimal fractional order of the signal is Fourier transformed;

[0011] Then, iterative discrete wavelet decomposition and reconstruction are performed to obtain the optimal wavelet transform coefficients; the optimal wavelet transform coefficients are corrected by the improved threshold function.

[0012] Finally, the modified wavelet transform coefficients are subjected to wavelet reconstruction to obtain a reconstructed estimated signal; the transformed signal is subjected to a -p-order fractional Fourier transform to obtain a denoised output signal.

[0013] Furthermore, the spectral line denoising method based on fractional-order iterative discrete wavelet transform includes the following steps:

[0014] Step 1: Obtain the original spectral line signal of the sample to be tested, perform v-order GL fractional order processing on the obtained original spectral line signal; use an iterative method to determine the optimal fractional order of the spectral line signal; map the original spectral line signal to the optimal fractional order wavelet time-frequency domain, and then perform fractional Fourier transform to obtain the transformed signal;

[0015] Step 2: performing multi-layer discrete wavelet decomposition on the transformed signal using a wavelet basis to obtain a multi-layer discrete wavelet decomposition layer; performing discrete wavelet reconstruction based on the discrete wavelet decomposition layer to obtain a first-order low-frequency approximation coefficient corresponding to each discrete wavelet decomposition layer;

[0016] Step 3: Select an optimal decomposition layer and a first-order low-frequency approximation coefficient corresponding to the optimal decomposition layer from the multiple discrete wavelet decomposition layers; perform iterative discrete wavelet decomposition on the first-order low-frequency approximation coefficient corresponding to the optimal decomposition layer to obtain an optimal wavelet transform coefficient;

[0017] Step 4: correct the optimal wavelet transform coefficients by using an improved threshold function, and perform wavelet reconstruction on the corrected wavelet transform coefficients to obtain a reconstructed estimated signal; perform a -p-order GL fractional wavelet transform on the reconstructed estimated signal to obtain a denoised output spectral signal.

[0018] Furthermore, performing v-order GL fractional-order processing on the acquired original spectral line signal includes:

[0019] First, the original spectrum line signal f(t) is processed using the GL differential form. The function f(t) has a v-order continuous derivative on the interval [b, a]. The v-order GL fractional differential of f(t) is defined as:

[0020]

[0021] Γ(v+1)=v! ;

[0022] Where f(t) represents the original spectral line signal, f(t) = s(t) + n(t), s(t) represents the effective spectral signal, and n(t) represents the noise signal; [(ba) / h] represents the integer part of (ba) / h; v represents the differential order, h represents the differential step size, b and a represent the upper and lower limits of the differential, respectively, m represents the order, Γ represents the gamma function, and ! represents the factorial operation;

[0023] Secondly, the spectrum line signal is divided into n parts at equal intervals h = 1, n = [(b a ) / h ] = [b a ], b and a represent the upper and lower limits of the difference, respectively, and the differential expression of the v-order fractional differential of the original spectrum line signal is obtained:

[0024]

[0025] Where v represents the differential order, m represents the order, v∈(0,2], and when v=0, no original spectrum line signal processing is performed.

[0026] Furthermore, the method of determining the optimal fractional order of the spectral line signal by using an iterative method includes:

[0027] An iterative method is used, with a v value ranging from 0 to 2 and an iteration step of 0.01, to iterate the optimal fractional order p; the optimal fractional order p is the fractional order that maximizes the signal-noise ratio (SNR).

[0028] Furthermore, in step 3, the first-order low-frequency approximation coefficients corresponding to the optimal decomposition layer are subjected to iterative discrete wavelet decomposition to obtain the optimal wavelet transform coefficients, which include:

[0029] (1) performing iterative discrete wavelet decomposition on the first-order low-frequency approximation coefficient of the obtained optimal decomposition layer to obtain the second-order low-frequency approximation coefficient; performing the next iteration based on the obtained second-order low-frequency approximation coefficient;

[0030] (2) The number of iterations is increased by one, and the obtained iterative result is subjected to discrete wavelet decomposition to obtain the current quadratic low-frequency approximation coefficient;

[0031] (3) Iterate in sequence until the difference between the result of the 1st iteration and the result of the 1-1th iteration for N consecutive times is less than the preset accuracy, then stop iterating and obtain the result of the most recent iteration; otherwise, return to step (2);

[0032] (4) Determine the optimal wavelet transform coefficient after reconstruction at the rth layer after l+N consecutive iterations:

[0033]

[0034] Among them, w r,k represents the kth wavelet coefficient of the rth layer, represents the kth low-frequency wavelet coefficient of the rth layer, b r,k Represents the kth high-frequency wavelet coefficient of the rth layer.

[0035] Furthermore, the improved threshold function is as follows:

[0036]

[0037] Among them, sgn represents the step function, represents the modified wavelet coefficient, w j,k represents the kth wavelet coefficient of the jth layer after decomposition, λ represents the set threshold; at this time, j=r.

[0038] Another object of the present invention is to provide a spectral line denoising method based on fractional-order iterative discrete wavelet transform, wherein the spectral line denoising method based on fractional-order iterative discrete wavelet transform comprises:

[0039] A signal acquisition module is used to obtain the original detection spectrum line signal of the sample to be tested;

[0040] The signal conversion module is used to perform GL fractional-order processing on the original detection line signal of the sample to be tested, and convert the signal into a v-order fractional differential form;

[0041] The optimal coefficient determination module is used to use an iterative method to search for the optimal fractional order; perform Fourier transform on the optimal fractional order of the signal; perform iterative discrete wavelet decomposition and reconstruction to obtain the optimal wavelet transform coefficient; and modify the optimal wavelet transform coefficient through an improved threshold function;

[0042] The signal reconstruction module is used to perform wavelet reconstruction on the modified wavelet transform coefficients to obtain a reconstructed estimated signal; and perform a -p-order fractional Fourier transform on the transformed signal to obtain a denoised output signal.

[0043] Another object of the present invention is to provide a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the spectral line denoising method based on fractional-order iterative discrete wavelet transform.

[0044] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the spectral line denoising method based on fractional-order iterative discrete wavelet transform.

[0045] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0046] The present invention performs a 0-2 order FRFT transform on a spectral line signal containing noise, and obtains the optimal fractional order p in this transform. The present invention utilizes the fact that after performing an iterative discrete wavelet transform on the signal in the p-order domain, the signal itself and the noise have different characteristics. As the decomposition scale increases, the signal itself does not change, while the noise gradually decreases to zero. By setting a threshold, the wavelet coefficients below the threshold are regarded as noise, and the wavelet coefficients above the threshold are regarded as the signal itself. The wavelet coefficients on both sides of the threshold are processed separately to achieve spectral line denoising.

[0047] The present invention denoises the spectral lines by combining fractional Fourier transform and iterative discrete wavelet, which can clearly retain the details in the signal without sharpening or over-smoothing, improve the signal-to-noise ratio, and is scientific and reasonable, with a simple process and easy operation. The results are intuitive and easy to understand, and the denoising effect is better than that of existing denoising methods.

[0048] The expected benefits and commercial value of the technical solution of the present invention after transformation are as follows: The spectral line denoising method based on fractional-order iterative discrete wavelet transform proposed in the present invention improves the accuracy of wavelet coefficient reconstruction, enabling the detection of more features of spectral signals, the extraction of more details, and the improvement of denoising effect. It can be used for signal preprocessing in equipment such as X-ray fluorescence spectrometers, reducing costs by approximately 15%;

[0049] Does the technical solution of the present invention solve the technical problems that people have always been eager to solve but have never been successful: People have never stopped researching signal preprocessing for a long time, but the inability to retain more signal features and the low signal-to-noise ratio have always been industry problems. The present invention uses a spectral line denoising method based on fractional-order iterative discrete wavelet transform to greatly improve the accuracy and stability of signal denoising, and improves the wavelet threshold function to avoid the fixed deviation problem of the soft threshold function.

[0050] The iterative discrete wavelet transform of the present invention performs multi-resolution analysis on the time-frequency domain of the signal, and the fractional-order Fourier transform is a generalization of the traditional fast Fourier transform, which enables a better separation of the chirp signal and noise. The fractional-order iterative discrete wavelet transform combines the characteristics of the two, generalizing the multi-resolution analysis to the time domain-generalized frequency domain, becoming a new time-frequency domain analysis method. Compared with the iterative discrete wavelet transform, the biggest advantage of the fractional-order wavelet transform is that it adds a variable order p, which can more flexibly adjust the wavelet coefficients. The method of combining the fractional-order Fourier transform and the iterative discrete wavelet to denoise the spectrum can clearly retain the details in the signal without sharpening or over-smoothing, thereby improving the signal-to-noise ratio. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 1 is a schematic diagram of a spectral line denoising method based on fractional-order iterative discrete wavelet transform provided by an embodiment of the present invention;

[0052] Figure 2 This is a flow chart of a spectral line denoising method based on fractional-order iterative discrete wavelet transform provided by an embodiment of the present invention;

[0053] Figure 3 This is a result diagram after denoising the original spectral line signal obtained from the soil sample in Example 1 provided in an embodiment of the present invention;

[0054] Figure 4 Schematic diagram of 7 discrete wavelet decomposition layers provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0056] In order to enable those skilled in the art to fully understand how to implement the present invention, this section provides an explanatory embodiment that expands on the technical solutions of the claims.

[0057] like Figure 1-Figure 2 As shown, the spectral line denoising method based on fractional-order iterative discrete wavelet transform provided by the embodiment of the present invention includes the following steps:

[0058] S101, obtaining the original spectral line signal of the sample to be tested, performing v-order GL fractional order processing on the obtained original spectral line signal; using an iterative method to determine the optimal fractional order of the spectral line signal; mapping the original spectral line signal to the optimal fractional order wavelet time-frequency domain, and then performing a fractional Fourier transform to obtain a transformed signal;

[0059] S102, performing multi-layer discrete wavelet decomposition on the transformed signal using a wavelet basis to obtain multi-layer discrete wavelet decomposition layers; performing discrete wavelet reconstruction based on the discrete wavelet decomposition layers to obtain a first-order low-frequency approximation coefficient corresponding to each discrete wavelet decomposition layer;

[0060] S103, selecting an optimal decomposition layer and a first-order low-frequency approximation coefficient corresponding to the optimal decomposition layer from the multiple discrete wavelet decomposition layers; performing iterative discrete wavelet decomposition on the first-order low-frequency approximation coefficient corresponding to the optimal decomposition layer to obtain an optimal wavelet transform coefficient;

[0061] S104, correcting the optimal wavelet transform coefficients by using an improved threshold function, and performing wavelet reconstruction on the corrected wavelet transform coefficients to obtain a reconstructed estimated signal; performing a -p-order GL fractional wavelet transform on the reconstructed estimated signal to obtain a denoised output spectral signal.

[0062] The spectral line denoising method based on fractional-order iterative discrete wavelet transform provided in an embodiment of the present invention comprises the following steps:

[0063] Step 1: Obtain the original spectrum line signal f(t) of the sample to be tested. The signal f(t) consists of the effective spectrum signal s(t) and the noise signal n(t), that is:

[0064] f(t)=s(t)+n(t) (1)

[0065] Where f(t) represents the original spectrum line signal, s(t) represents the effective spectrum signal, and n(t) represents the noise signal.

[0066] Step 2: Perform GL fractional-order processing on the original spectral line signal f(t), that is, use the GL differential form. The function f(t) has v-order continuous derivatives on the interval [b, a]. Then the v-order GL fractional differential expression of f(t) is:

[0067]

[0068] Γ(v+1)=v! (3)

[0069] Where v is the differential order, h is the differential step size, b and a are the upper and lower limits of the differential, m is the order, Γ is the gamma function, and ! is the factorial operation.

[0070] Step 3: During the duration of the signal f(t), divide it into n parts at equal intervals h=1, where n=[(ba) / h]=[ba], [(ba) / h] represents the integer part of (ba) / h, and b and a represent the upper and lower limits of the difference, respectively. Then, according to (2), the differential expression of the v-order fractional differential of f(t) can be derived as follows:

[0071]

[0072] Where v represents the differential order, m represents the order, v∈(0,2], and when v=0, no original spectrum line signal processing is performed.

[0073] Step 4: Use the iterative method with v values ​​ranging from 0 to 2 and an iteration step of 0.01 to find the optimal fractional order p that maximizes the signal-to-noise ratio (SNR).

[0074] Step 5: Map the original spectrum line signal f(t) to the p-order wavelet time-frequency domain, and obtain the transformed signal f after fractional Fourier transform (FRFT). p (t).

[0075] Step 6: Use the wavelet basis to perform L-layer discrete wavelet decomposition to obtain L-layer discrete wavelet decomposition layers, and then reconstruct the corresponding first-order low-frequency approximation coefficient a according to each layer of discrete wavelet decomposition layers. j,k , j=1,…,L. When decomposing the number of layers, the rth layer is the optimal decomposition layer, and its corresponding first low-frequency approximation coefficient is a r,k When the signal is decomposed by wavelet, the wavelet transform coefficients can be expressed as:

[0076] w j,k =a j,k +b j,k (5)

[0077] Among them, w j,k represents the kth wavelet coefficient of the jth layer after the decomposition of the original spectral signal f(t), a j,k Represents the kth low-frequency wavelet coefficient of the jth layer of the effective spectral signal s(t), b j,k Represents the kth high-frequency wavelet coefficient of the jth layer of the noise signal n(t).

[0078] Step 7: A low-frequency approximation coefficient a of the optimal decomposition layer r obtained in step 6 r,k Perform iterative discrete wavelet decomposition, define e as the number of iterations, when e = 1, the low-frequency approximation coefficient a r,k Perform discrete wavelet decomposition to obtain the quadratic low-frequency approximation coefficient And use it as the basis for this iteration and proceed to the next iteration;

[0079] Step 8: Let l = l + 1, and the result of the previous iteration Perform discrete wavelet decomposition to further obtain the current quadratic low-frequency approximation coefficient

[0080] Step 9: If the difference between the result of the 1st iteration and the result of the 1-1th iteration is greater than the preset precision ε, return to step 8; if the difference between the result of the 1st iteration and the result of the 1-1th iteration for N consecutive times is less than the preset precision ε, the iteration result is considered reliable, the iteration is stopped, and the most recent iteration result is obtained. Otherwise, return to step 8; after l+N consecutive iterations, the optimal wavelet transform coefficient after reconstruction is obtained at the rth layer as follows:

[0081]

[0082] Where w r,k is the kth wavelet coefficient of the rth layer, is the kth low-frequency wavelet coefficient of the rth layer, b r,k is the kth high-frequency wavelet coefficient of the rth layer, and N is determined by the actual accuracy requirement.

[0083] Step 10: Correct the obtained wavelet coefficients by using the improved threshold function to obtain the corrected wavelet coefficients The improved threshold function is as follows:

[0084]

[0085] Where, is the wavelet coefficient after denoising, w j,k is the kth wavelet coefficient of the jth layer after decomposition, λ is the set threshold. In this case, j=r.

[0086] Step 11: Perform wavelet reconstruction on the corrected wavelet coefficients to obtain the reconstructed estimated signal

[0087] Step 12: Perform a -p-order GL fractional wavelet transform on the filtered signal to restore the time domain waveform, and then the signal after noise suppression can be obtained. Realize spectral line denoising.

[0088] In order to prove the creativity and technical value of the technical solution of the present invention, this section provides application examples of the claimed technical solution on specific products or related technologies.

[0089] The spectral line denoising method based on fractional-order iterative discrete wavelet transform provided by an embodiment of the present invention is applied to the processing of soil sample spectral signals. The specific steps are as follows:

[0090] Step 1: Use the TS-XH4000-SOIL handheld X-ray fluorescence analyzer to detect the GBW07380 (GSD-29) soil sample and obtain the original spectral line signal f(t) of the sample to be tested. The signal f(t) consists of the effective spectral signal s(t) and the noise signal n(t), that is:

[0091] f(t)=s(t)+n(t) (1)

[0092] Step 2: Use the GL differential form to process the obtained original spectral line signal f(t). The function f(t) has a v-order continuous derivative on the interval [b, a]. Then the v-order GL fractional differential of f(t) is defined as:

[0093]

[0094] Γ(v+1)=v! ;

[0095] Where f(t) represents the original spectral line signal, f(t) = s(t) + n(t), s(t) represents the effective spectral signal, and n(t) represents the noise signal; [(ba) / h] represents the integer part of (ba) / h; v represents the differential order, h represents the differential step size, b and a represent the upper and lower limits of the differential, respectively, m represents the order, Γ represents the gamma function, and ! represents the factorial operation;

[0096] Step 3: During the duration of the signal f(t), divide it into 2048 parts at equal intervals h = 1. Then, according to (2), the differential expression of the v-order fractional differential of f(t) can be obtained as follows:

[0097]

[0098] Where v represents the differential order, m represents the order, v∈(0,2], and when v=0, no original spectrum line signal processing is performed.

[0099] Step 4: Use the iterative method with the v value ranging from 0 to 2 and the iteration step size of 0.01 to find the optimal fractional order p that maximizes the signal-to-noise ratio (SNR).

[0100] Step 5: Map the original spectrum line signal f(t) to the p-order wavelet time-frequency domain, and obtain the transformed signal f after fractional Fourier transform. p (t).

[0101] Step 6: Use the wavelet basis to perform 7-layer discrete wavelet decomposition to obtain 7 layers of discrete wavelet decomposition layers, and then reconstruct the corresponding first-order low-frequency approximation coefficient a according to each layer of discrete wavelet decomposition layers. j,k , j=1,…,7. When decomposing the number of layers, the 7th layer is the optimal decomposition layer, and its corresponding first-order low-frequency approximation coefficient is a 7,k When the signal is decomposed by wavelet, the wavelet transform coefficients can be expressed as:

[0102] w 7,k =a 7,k +b 7,k (5)

[0103] Among them, w 7,k represents the kth wavelet coefficient of the 7th layer after the decomposition of the original spectrum signal f(t), a 7,k Represents the kth low-frequency wavelet coefficient of the 7th layer of the effective spectral signal s(t), b 7,k Represents the kth high-frequency wavelet coefficient of the 7th layer of the noise signal n(t).

[0104] Step 7: The first low-frequency approximation coefficient a of the 7th layer of the optimal decomposition obtained in step 6 7,k Perform iterative discrete wavelet decomposition, define e as the number of iterations, when e = 1, the low-frequency approximation coefficient a r,k Perform discrete wavelet decomposition to obtain the quadratic low-frequency approximation coefficient And use it as the basis for this iteration and proceed to the next iteration;

[0105] Step 8: Let l = l + 1, and the result of the previous iteration Perform discrete wavelet decomposition to further obtain the current quadratic low-frequency approximation coefficient

[0106] Step 9: If the difference between the result of the 1st iteration and the result of the 1-1th iteration is greater than the preset precision ε, return to step 8; if the difference between the result of the 1st iteration and the result of the 1-1th iteration for N consecutive times is less than the preset precision ε, the iteration result is considered reliable, the iteration is stopped, and the most recent iteration result is obtained. Otherwise, return to step 8; after l+N consecutive iterations, the optimal wavelet transform coefficient after reconstruction is obtained at the rth layer as follows:

[0107]

[0108] Where w 7,k is the kth wavelet coefficient of the 7th layer, is the kth low-frequency wavelet coefficient of the 7th layer, b 7,k is the kth high-frequency wavelet coefficient of the 7th layer, and N is determined by the actual accuracy requirement.

[0109] Step 10: Correct the obtained wavelet coefficients by using the improved threshold function to obtain the corrected wavelet coefficients The improved threshold function is as follows:

[0110]

[0111] Where sgn represents the step function, is the wavelet coefficient after denoising, w j,k is the kth wavelet coefficient of the jth layer after decomposition, λ is the set threshold. In this case, j=7.

[0112] Step 11: Perform wavelet reconstruction on the corrected wavelet coefficients to obtain the reconstructed estimated signal

[0113] Step 12: Perform a -p-order GL fractional wavelet transform on the filtered signal to restore the time domain waveform, and then the signal after noise suppression can be obtained. To achieve spectral line denoising, Figure 3 As shown, it can be seen that the noise information of the original detection spectrum line signal f(t) is effectively removed, and the details in the signal are clearly retained without sharpening or over-smoothing, thereby improving the signal-to-noise ratio.

[0114] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware portion can be implemented using dedicated logic; the software portion can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. Those skilled in the art will understand that the above-mentioned devices and methods can be implemented using computer-executable instructions and / or contained in processor control code, for example, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The device of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., or can be implemented by software executed by various types of processors, or can be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0115] The embodiments of the present invention have achieved some positive results during the development or use process, and indeed have great advantages over the existing technology. The following content describes them in conjunction with data, charts, etc. from the experimental process.

[0116] To verify the effectiveness of the method, we implemented it on a MATLAB software platform and compared it with a traditional wavelet denoising method. A more objective analysis of the signal-to-noise ratio (SNR) was performed. The greater the SNR, the better the denoising effect. A comparison of the SNR results for the GBW07380 (GSD-29) sample after denoising is shown in the table below.

[0117] Denoising methods Denoising (p=0.5) Hard threshold wavelet denoising Soft threshold wavelet denoising SNR 95.9403 81.8468 70.6132

[0118] It can be seen from the above table that compared with several other methods, the spectral line denoising method based on fractional-order iterative discrete wavelet transform proposed in this paper has a significant improvement in signal-to-noise ratio.

[0119] In summary, there is a constant deviation between the wavelet coefficients and the true wavelet coefficients of the traditional spectral line denoising method. The present invention denoises the spectral lines by combining fractional Fourier transform and iterative discrete wavelet, which can clearly retain the details in the signal and improve the signal-to-noise ratio. Compared with the existing denoising methods, the denoising effect is better.

[0120] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A spectral line denoising method based on fractional-order iterative discrete wavelet transform, characterized in that: The spectral line denoising method based on fractional-order iterative discrete wavelet transform includes: First, the original detection line signal of the sample to be tested is processed by GL fractional order to convert the signal into a v-order fractional differential form; Secondly, the optimal fractional order is searched by iterative method; the optimal fractional order of the signal is Fourier transformed; Then, iterative discrete wavelet decomposition and reconstruction are performed to obtain the optimal wavelet transform coefficients; the optimal wavelet transform coefficients are corrected by the improved threshold function. Finally, the modified wavelet transform coefficients are subjected to wavelet reconstruction to obtain the reconstructed estimated signal; the transformed signal is subjected to -p-order fractional Fourier transform to obtain the denoised spectral line signal; The spectral line denoising method based on fractional-order iterative discrete wavelet transform comprises the following steps: Step 1: Obtain the original spectral line signal of the sample to be tested, perform v-order GL fractional order processing on the obtained original spectral line signal; use an iterative method to determine the optimal fractional order of the spectral line signal; map the original spectral line signal to the optimal fractional order wavelet time-frequency domain, and then perform fractional Fourier transform to obtain the transformed signal; Step 2: performing multi-layer discrete wavelet decomposition on the transformed signal using a wavelet basis to obtain a multi-layer discrete wavelet decomposition layer; performing discrete wavelet reconstruction based on the discrete wavelet decomposition layer to obtain a first-order low-frequency approximation coefficient corresponding to each discrete wavelet decomposition layer; Step 3: Select an optimal decomposition layer and a first-order low-frequency approximation coefficient corresponding to the optimal decomposition layer from the multiple discrete wavelet decomposition layers; perform iterative discrete wavelet decomposition on the first-order low-frequency approximation coefficient corresponding to the optimal decomposition layer to obtain an optimal wavelet transform coefficient; Step 4: Correcting the optimal wavelet transform coefficients by using an improved threshold function, and performing wavelet reconstruction on the corrected wavelet transform coefficients to obtain a reconstructed estimated signal; performing a -p-order GL fractional wavelet transform on the reconstructed estimated signal to obtain a denoised output spectral signal; In step 3, the first-order low-frequency approximation coefficients corresponding to the optimal decomposition layer are subjected to iterative discrete wavelet decomposition to obtain the optimal wavelet transform coefficients, which include: (1) performing iterative discrete wavelet decomposition on the first-order low-frequency approximation coefficient of the obtained optimal decomposition layer to obtain the second-order low-frequency approximation coefficient; performing the next iteration based on the obtained second-order low-frequency approximation coefficient; (2) The number of iterations is increased by one, and the obtained iterative result is subjected to discrete wavelet decomposition to obtain the current quadratic low-frequency approximation coefficient; (3) Iterate in sequence until the difference between the result of the 1st iteration and the result of the 1-1th iteration for N consecutive times is less than the preset accuracy, then stop iterating and obtain the result of the most recent iteration; otherwise, return to step (2); (4) Determine the optimal wavelet transform coefficient after reconstruction at the rth layer after l+N consecutive iterations: Among them, w r,k represents the kth wavelet coefficient of the rth layer, represents the kth low-frequency wavelet coefficient of the rth layer, b r,k Represents the kth high-frequency wavelet coefficient of the rth layer.

2. The spectral line denoising method based on fractional-order iterative discrete wavelet transform according to claim 1, characterized in that: The performing v-order GL fractional-order processing on the acquired original spectral line signal comprises: First, the original spectral line signal f(t) is processed using the differential form of GL. The function f(t) has a v-order continuous derivative on the interval [b, a]. The v-order GL fractional differential of f(t) is defined as: Γ(v+1)=v! ; Where f(t) represents the original spectral line signal, f(t) = s(t) + n(t), s(t) represents the effective spectral signal, and n(t) represents the noise signal; [(ba) / h] represents the integer part of (ba) / h; v represents the differential order, h represents the differential step size, b and a represent the upper and lower limits of the differential, respectively, m represents the order, Γ represents the gamma function, and ! represents the factorial operation; Secondly, the spectrum line signal is divided into n parts at equal intervals h = 1, n = [(b a ) / h ] = [b a ], b and a represent the upper and lower limits of the difference, respectively, and the differential expression of the v-order fractional differential of the original spectrum line signal is obtained: Wherein, v represents the differential order, m represents the order, v∈(0, 2], and when v=0, the original spectrum line signal processing is not performed.

3. The spectral line denoising method based on fractional-order iterative discrete wavelet transform according to claim 1, characterized in that: The method of determining the optimal fractional order of the spectral line signal by an iterative method comprises: An iterative method is used, with a v value ranging from 0 to 2 and an iteration step of 0.01, to iterate the optimal fractional order p; the optimal fractional order p is the fractional order that maximizes the signal-noise ratio (SNR).

4. The spectral line denoising method based on fractional-order iterative discrete wavelet transform according to claim 1, characterized in that: The improved threshold function is as follows: Among them, sgn represents the step function, represents the modified wavelet coefficient, w j,k represents the kth wavelet coefficient of the jth layer after decomposition, λ represents the set threshold; at this time, j=r.

5. A spectral line denoising method based on fractional-order iterative discrete wavelet transform according to any one of claims 1 to 4, characterized in that: The functions of the spectral line denoising method based on fractional-order iterative discrete wavelet transform include: A signal acquisition module is used to obtain the original detection spectrum line signal of the sample to be tested; The signal conversion module is used to perform GL fractional-order processing on the original detection line signal of the sample to be tested, and convert the signal into a v-order fractional differential form; The optimal coefficient determination module is used to use an iterative method to search for the optimal fractional order; perform Fourier transform on the optimal fractional order of the signal; perform iterative discrete wavelet decomposition and reconstruction to obtain the optimal wavelet transform coefficient; and modify the optimal wavelet transform coefficient through an improved threshold function; The signal reconstruction module is used to perform wavelet reconstruction on the modified wavelet transform coefficients to obtain a reconstructed estimated signal; and perform a -p-order fractional Fourier transform on the transformed signal to obtain a denoised output signal.

6. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the spectral line denoising method based on fractional-order iterative discrete wavelet transform as described in any one of claims 1 to 4.

7. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the steps of the spectral line denoising method based on fractional-order iterative discrete wavelet transform as described in any one of claims 1 to 4.

8. An information data processing terminal, characterized in that: The information data processing terminal is used to implement the spectral line denoising method based on fractional-order iterative discrete wavelet transform as described in claim 5.

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