CN115795272A - Spectral line denoising method based on fractional order iterative discrete wavelet transform - Google Patents
Spectral line denoising method based on fractional order iterative discrete wavelet transform Download PDFInfo
- Publication number
- CN115795272A CN115795272A CN202211272187.1A CN202211272187A CN115795272A CN 115795272 A CN115795272 A CN 115795272A CN 202211272187 A CN202211272187 A CN 202211272187A CN 115795272 A CN115795272 A CN 115795272A
- Authority
- CN
- China
- Prior art keywords
- signal
- spectral line
- order
- optimal
- fractional order
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Landscapes
- Complex Calculations (AREA)
Abstract
The 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, which comprises the steps of performing G-L fractional order processing on an original detection spectral line signal of a sample to be detected, and searching by adopting an iterative method to obtain an optimal fractional order; performing Fourier transform on the optimal fractional order of the signal; carrying out iterative discrete wavelet decomposition and reconstruction to obtain an optimal wavelet transform coefficient; correcting the optimal wavelet transform coefficient and performing wavelet reconstruction to obtain a reconstructed estimation signal; the invention carries out-p-order fractional Fourier transform on the transformed signal to obtain the denoised spectral line signal, and carries out denoising on the spectral line by adopting a method combining fractional Fourier transform and iterative discrete wavelet, thereby clearly retaining the details in the signal, having no phenomena of sharpening and excessive smoothing, improving the signal-to-noise ratio, being scientific and reasonable, having simple flow, convenient operation, intuitive result, popular and easy understanding, and having better denoising effect compared with the existing denoising method.
Description
Technical Field
The invention belongs to the technical field of spectral data analysis and processing, and particularly relates to a spectral line denoising method based on fractional order iterative discrete wavelet transform.
Background
At present, spectral line denoising is an essential part in the spectrum preprocessing process. The method aims to remove noise generated by influence of various factors such as instrument systems, detection environments, properties of samples and the like in the transmission process of signals and obtain original characteristics and detail information of spectral lines as much as possible, so that the test accuracy and the signal-to-noise ratio of an X-ray spectrum are improved, and the subsequent analysis work of the signals is facilitated.
In recent years, signal denoising methods are many, and common methods include derivative denoising, fourier transform denoising, wavelet transform denoising, and the like, wherein first and second derivatives are the most common methods in spectral denoising. However, conventional integer order derivatives cannot detect gradual slopes or different curvatures that may contain useful information about the target variable, and high frequency noise also reduces the spectral signal-to-noise ratio as the order of the derivative increases. The Fractional Order Derivative (FOD) algorithm is intermediate between the conventional integer and zeroth and second order derivatives. Fractional order differentiation is becoming increasingly attractive in the signal processing field as compared to integer order derivatives.
The iterative discrete wavelet transform is used for analyzing the multi-resolution of the time-frequency domain of the signal, and the fractional Fourier transform is used for popularizing the traditional fast Fourier transform, so that the Chirp signal and the noise can be better separated. The fractional order iterative discrete wavelet transform combines the characteristics of the two, and the multi-resolution analysis is popularized to a time domain-generalized frequency domain, so that the method becomes a novel time-frequency domain analysis method. Compared with the iterative discrete wavelet transform, the greatest advantage of the fractional order wavelet transform is that a variable order p is added, and the wavelet coefficients can be adjusted more flexibly.
The wavelet coefficient of the traditional spectral line denoising method has constant deviation with the real wavelet coefficient, so that the reconstruction precision of the wavelet coefficient is reduced, and the denoising effect is poor. The fractional derivative will change over a small time interval to ensure that the signal-to-noise ratio changes slowly and to allow more features of certain spectral signals to be detected, more details to be extracted, and ease of implementation. Therefore, it is crucial to use a suitable FOD in denoising rather than the conventional integer order derivative.
Through the above analysis, the problems and defects of the prior art are as follows: the existing spectral signal denoising method has poor denoising effect and low wavelet coefficient reconstruction precision.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a spectral line denoising method based on fractional order iteration discrete wavelet transform.
The invention is realized in such a way that a spectral line denoising method based on fractional order iterative discrete wavelet transform comprises the following steps:
firstly, performing G-L fractional order processing on an original detection spectral line signal of a sample to be detected, and converting the signal into a v-order fractional order differential form;
secondly, searching by adopting an iterative method to obtain an optimal fractional order; performing Fourier transform on the optimal fractional order of the signal;
then, carrying out iterative discrete wavelet decomposition and reconstruction to obtain an optimal wavelet transform coefficient; the optimal wavelet transform coefficients are modified by a modified threshold function,
finally, performing wavelet reconstruction on the corrected wavelet transform coefficient to obtain a reconstructed estimation signal; and carrying out-p-order fractional Fourier transform on the transformed signal to obtain a denoised output signal.
Further, the spectral line denoising method based on fractional order iterative discrete wavelet transform comprises the following steps:
acquiring an original spectral line signal of a sample to be detected, and performing v-order G-L fractional order processing on the acquired original spectral line signal; determining the optimal fractional order of the spectral line signal by adopting an iteration method; mapping the original spectral line signal to an optimal fractional wavelet time-frequency domain, and performing fractional Fourier transform to obtain a transformed signal;
performing multi-layer discrete wavelet decomposition on the transformed signal by using a wavelet basis to obtain a multi-layer discrete wavelet decomposition layer; performing discrete wavelet reconstruction according to the discrete wavelet decomposition layers to obtain a primary low-frequency approximation coefficient corresponding to each discrete wavelet decomposition layer;
selecting an optimal decomposition layer and a primary low-frequency approximation coefficient corresponding to the optimal decomposition layer from the multiple discrete wavelet decomposition layers; performing iterative discrete wavelet decomposition on the primary low-frequency approximation coefficient corresponding to the optimal decomposition layer to obtain an optimal wavelet transform coefficient;
step four, the optimal wavelet transform coefficient is corrected through an improved threshold function, and wavelet reconstruction is carried out on the corrected wavelet transform coefficient to obtain a reconstructed estimation signal; and performing-p-order G-L fractional order wavelet transformation on the reconstructed estimation signal to obtain a denoised output spectrum signal.
Further, the v-order G-L fractional order processing on the obtained original spectral line signal includes:
firstly, the acquired original spectral line signal f (t) is processed in a differential form of G-L. If the function f (t) has a continuous derivative of order v over the interval [ b, a ], the fractional G-L order derivative of order v of f (t) is defined as:
Γ(v+1)＝v！；
wherein 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; [ (b-a)/h ] denotes the integer part of (b-a)/h; v denotes a differential order, h denotes a differential step, b and a denote upper and lower limits of the difference, respectively, m denotes an order, Γ denotes a gamma function, and! Indicating to perform a factorial operation;
secondly, dividing the spectral line signal into n parts according to equal interval h =1, wherein n = [ (b-a)/h ] = [ b-a ], and b and a respectively represent the upper and lower limits of the difference, and obtaining a difference expression of v-order fractional order differential of the original spectral line signal:
where v denotes the order of differentiation, m denotes the order, v ∈ (0,2), and when v =0, the original spectral line signal processing is not performed.
Further, the determining the optimal fractional order of the spectral line signal by using the iterative method includes:
adopting an iteration method, wherein the v value range is from 0 to 2, the iteration step length is 0.01, and the optimal fractional order p is iterated; the optimal fractional order p is a fractional order that maximizes a Signal-to-Noise Ratio (SNR).
Further, the step three of performing iterative discrete wavelet decomposition on the primary low-frequency approximation coefficient corresponding to the optimal decomposition layer to obtain an optimal wavelet transform coefficient includes:
(1) Performing iterative discrete wavelet decomposition on the obtained primary low-frequency approximation coefficient of the optimal decomposition layer to obtain a secondary low-frequency approximation coefficient; performing next iteration based on the obtained secondary low-frequency approximation coefficient;
(2) Adding one to the iteration times, and performing discrete wavelet decomposition on the obtained iteration result to obtain a current secondary low-frequency approximation coefficient;
(3) Sequentially iterating until the difference value between the l iteration result of the continuous N times and the l-1 iteration result is smaller than the preset precision, and stopping iteration to obtain the latest iteration result; otherwise, returning to the step (2);
(4) Determining the best wavelet transform coefficient after reconstruction is obtained at the r-th layer after continuous l + N iterations:
wherein w r,k The kth wavelet coefficient representing the r-th layer,
k-th low-frequency wavelet coefficient representing the r-th layer, b r,k Representing the kth high frequency wavelet coefficient of the r-th layer.
Further, the improved threshold function is as follows:
wherein sgn represents a step function,
representing the modified wavelet coefficients, w j,k Expressing the kth wavelet coefficient of the j layer after decomposition, and expressing lambda as a set threshold; at this time, j = r.
Another object of the present invention is to provide a spectral line denoising method based on fractional order iterative discrete wavelet transform, including:
the signal acquisition module is used for acquiring an original detection spectral line signal of a sample to be detected;
the signal conversion module is used for performing G-L fractional order processing on an original detection spectral line signal of a sample to be detected and converting the signal into a v-order fractional order differential form;
the optimal coefficient determining module is used for searching by adopting an iteration method to obtain an optimal fractional order; performing Fourier transform on the optimal fractional order of the signal; carrying out iterative discrete wavelet decomposition and reconstruction to obtain an optimal wavelet transform coefficient; correcting the optimal wavelet transform coefficient through an improved threshold function;
the signal reconstruction module is used for performing wavelet reconstruction on the corrected wavelet transform coefficient to obtain a reconstructed estimation signal; and carrying out-p-order fractional Fourier transform on the transformed signal to obtain a denoised output signal.
It is a further object of the invention to provide a computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps of the method for spectral line denoising based on fractional order iterative discrete wavelet transform.
It is a further object of the present invention 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.
By combining the technical scheme and the technical problem to be solved, the technical scheme to be protected by the invention has the advantages and positive effects that:
the invention obtains the optimal fractional order p in the 0-2 order FRFT conversion of the spectral line signal containing noise. The invention utilizes the characteristic that after the iterative discrete wavelet transform is carried out on the signal in the p-order domain, the signal and the noise have different characteristics, the signal does not change along with the increase of the decomposition scale, and the noise gradually decreases to zero.
The method for denoising the spectral line by combining the fractional Fourier transform and the iterative discrete wavelet can clearly keep the details in the signal, has no phenomena of sharpening and excessive smoothing, improves the signal-to-noise ratio, is scientific and reasonable, has simple flow, convenient operation, intuitive result, popular and easy understanding, and has better denoising effect compared with the existing denoising method.
The expected income and commercial value after the technical scheme of the invention is converted are as follows: the spectral line denoising method based on fractional order iterative discrete wavelet transform provided by the invention improves the reconstruction precision of wavelet coefficients, so that more characteristics of spectral signals can be detected, more details can be extracted, the denoising effect is improved, the spectral line denoising method can be used for preprocessing signals in equipment such as an X-ray fluorescence spectrum analyzer and the like, and the cost is reduced by about 15%;
the technical scheme of the invention solves the technical problem that people are eagerly to solve but can not be successfully solved all the time: the research on signal preprocessing is never stopped for a long time, but more signal characteristics cannot be reserved and the signal-to-noise ratio is low and always is an industrial problem.
The iterative discrete wavelet transform is used for analyzing the multi-resolution of the time-frequency domain of the signal, and the fractional Fourier transform is used for popularizing the traditional fast Fourier transform, so that a Chirp signal and noise can be better separated. The fractional order iterative discrete wavelet transform combines the characteristics of the two, and the multi-resolution analysis is popularized to a time domain-generalized frequency domain, so that the method becomes a novel time-frequency domain analysis method. Compared with the iterative discrete wavelet transform, the greatest advantage of the fractional order wavelet transform is that a variable order p is added, and the wavelet coefficients can be adjusted more flexibly. The spectral line is denoised by adopting a method combining fractional Fourier transform and iterative discrete wavelet, so that the details in the signal can be clearly reserved, the phenomena of sharpening and over-smoothing are avoided, and the signal-to-noise ratio is improved.
Drawings
FIG. 1 is a schematic diagram of a spectral line denoising method based on fractional order iterative discrete wavelet transform according to an embodiment of the present invention;
FIG. 2 is a flowchart of a spectral line denoising method based on fractional order iterative discrete wavelet transform according to an embodiment of the present invention;
FIG. 3 is a graph showing a result of denoising an original spectral line signal obtained from a soil sample in example 1 according to the present invention;
fig. 4 is a schematic diagram of a 7-layer discrete wavelet decomposition layer provided by an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
This section is an explanatory embodiment expanding on the claims so as to fully understand how the present invention is embodied by those skilled in the art.
As shown in fig. 1-2, 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:
s101, acquiring an original spectral line signal of a sample to be detected, and performing v-order G-L fractional order processing on the acquired original spectral line signal; determining the optimal fractional order of the spectral line signal by adopting an iteration method; mapping the original spectral line signal to an optimal fractional wavelet time-frequency domain, and performing fractional Fourier transform to obtain a transformed signal;
s102, performing multi-layer discrete wavelet decomposition on the transformed signal by utilizing a wavelet basis to obtain a multi-layer discrete wavelet decomposition layer; performing discrete wavelet reconstruction according to the discrete wavelet decomposition layers to obtain a primary low-frequency approximation coefficient corresponding to each discrete wavelet decomposition layer;
s103, selecting an optimal decomposition layer and a primary low-frequency approximation coefficient corresponding to the optimal decomposition layer from the multiple discrete wavelet decomposition layers; performing iterative discrete wavelet decomposition on the primary low-frequency approximation coefficient corresponding to the optimal decomposition layer to obtain an optimal wavelet transform coefficient;
s104, correcting the optimal wavelet transform coefficient through an improved threshold function, and performing wavelet reconstruction on the corrected wavelet transform coefficient to obtain a reconstructed estimation signal; and performing-p-order G-L fractional order wavelet transformation on the reconstructed estimation signal to obtain a denoised output spectrum signal.
The spectral line denoising method based on fractional order iteration discrete wavelet transform provided by the embodiment of the invention comprises the following steps:
step 1: obtaining an original spectral line signal f (t) of a sample to be detected, wherein the signal f (t) consists of an effective spectral line signal s (t) and a noise signal n (t), namely:
f(t)＝s(t)+n(t) (1)
where f (t) represents the original spectral line signal, s (t) represents the effective spectral signal, and n (t) represents the noise signal.
Step 2: and G-L fractional order processing is carried out on the original spectral line signal f (t), namely a differential form of G-L is adopted, the function f (t) has a continuous derivative of v order in an interval [ b, a ], and a V order G-L fractional order differential expression of f (t) is as follows:
Γ(v+1)＝v！ (3)
wherein v is the differential order, h is the differential step length, b and a are the upper and lower limits of the difference, m is the order, gamma function, and! Is a factorial operation.
And step 3: if n parts are divided at equal intervals h =1 within the duration of the signal f (t), n = [ (b-a)/h ] = [ b-a ], [ (b-a)/h ] represents an integer part of (b-a)/h, and b and a represent the upper and lower limits of the difference, respectively, the difference expression of the v-order fractional differential of f (t) is derived from (2) as follows:
where v denotes the order of differentiation, m denotes the order, v ∈ (0,2), and when v =0, the original spectral line signal processing is not performed.
And 4, step 4: and (3) adopting an iteration method, wherein the v value range is from 0 to 2, the iteration step length is 0.01, and searching an optimal fractional order p which enables the Signal-to-Noise Ratio (SNR) to reach the maximum.
And 5: mapping an original spectral line signal f (t) to a p-order wavelet time-frequency domain, and obtaining a transformed signal f after fractional Fourier transform (FRFT) p (t)。
Step 6: using wavelet base to make L-layer discrete wavelet decomposition to obtain L-layer discrete wavelet decomposition layer, then according to the discrete wavelet decomposition layer of every layer reconstructing correspondent primary low-frequency approximation coefficient a j,k J =1, …, L. Obtaining the r-th layer as the optimal decomposition layer when the number of the decomposition layers is obtained, and the corresponding first-order low-frequency approximation coefficient is a r,k . When wavelet decomposing a signal, the wavelet transform coefficients can be expressed as:
w j,k ＝a j,k +b j,k (5)
wherein, w j,k The kth wavelet coefficient, a, of the j-th layer after decomposition of the original spectral line signal f (t) j,k The kth low-frequency wavelet coefficient of the jth layer, b, representing the effective spectral signal s (t) j,k The kth high frequency wavelet coefficient of the jth layer representing the noise signal n (t).
And 7: the first low frequency approximation coefficient a of the optimal decomposition layer r obtained in the step 6 r,k Performing iterative discrete wavelet decomposition, defining e as iteration number, and when e =1, matching oneSub-low frequency approximation coefficient a r,k Performing discrete wavelet decomposition to obtain secondary low-frequency approximation coefficient
Taking the iteration as the background of the iteration, and performing the next iteration;
and 8: let l = l +1, for the last iteration result
Performing discrete wavelet decomposition to further obtain current secondary low-frequency approximation coefficient
And step 9: if the difference value between the l-th iteration result and the l-1 st iteration result is greater than the preset precision epsilon, returning to the step 8; if the difference value between the l-th iteration result and the l-1-th iteration result of the N continuous times is smaller than the preset precision epsilon, the iteration result is considered to be reliable, the iteration is stopped, and the latest iteration result is obtained
Otherwise, go back to step 8; obtaining the reconstructed optimal wavelet transform coefficient at the r-th layer after continuous l + N iterations as follows:
in the formula, w r,k Is the kth wavelet coefficient of the r-th layer,
is the kth low-frequency wavelet coefficient of the r-th layer, b r,k The k-th high frequency wavelet coefficient of the r-th layer, N, is determined by actual precision requirements.
Step 10: the obtained wavelet coefficient is corrected through an improved threshold function to obtain a corrected wavelet coefficient
The improved threshold function is as follows:
in the formula (I), the compound is shown in the specification,
for denoised wavelet coefficients, w j,k And lambda is a set threshold value for the kth wavelet coefficient of the j layer after decomposition. At this time, j = r.
Step 11: performing wavelet reconstruction on the corrected wavelet coefficient to obtain a reconstructed estimation signal
Step 12: the filtered signal is subjected to-p-order G-L fractional order wavelet transform to restore the time domain waveform, so that the signal with noise suppressed can be obtained
And realizing spectral line denoising.
In order to prove the creativity and the technical value of the technical scheme of the invention, the part is the application example of the technical scheme of the claims on specific products or related technologies.
The spectral line denoising method based on fractional order iterative discrete wavelet transform provided by the embodiment of the invention is applied to the processing of soil sample spectral signals, and comprises the following specific steps:
step 1: detecting a GBW07380 (GSD-29) SOIL sample by adopting a TS-XH4000-SOIL type handheld X fluorescence analyzer, and obtaining an original spectral line signal f (t) of the sample to be detected, wherein the signal f (t) consists of an effective spectral line signal s (t) and a noise signal n (t), namely:
f(t)＝s(t)+n(t) (1)
step 2: the acquired original spectral line signal f (t) is processed in a differential form of G-L. If the function f (t) has a continuous derivative of order v over the interval [ b, a ], the fractional G-L order derivative of order v of f (t) is defined as:
Γ(v+1)＝v！；
wherein 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; [ (b-a)/h ] denotes the integer part of (b-a)/h; v denotes a differential order, h denotes a differential step, b and a denote upper and lower limits of the difference, respectively, m denotes an order, Γ denotes a gamma function, and! Indicating to perform factorial operation;
and 3, step 3: for the duration of the signal f (t), the signal is divided into 2048 parts at equal intervals of h =1, and then the differential expression of the v fractional order differential of f (t) is derived from (2) as follows:
where v denotes the order of differentiation, m denotes the order, v ∈ (0,2), and when v =0, the original spectral line signal processing is not performed.
And 4, step 4: and (3) adopting an iteration method, wherein the v value range is from 0 to 2, the iteration step length is 0.01, and searching the optimal fractional order p which enables the signal-to-noise ratio SNR to reach the maximum.
And 5: mapping an original spectral line signal f (t) to a p-order wavelet time-frequency domain, and obtaining a transformed signal f after fractional Fourier transform p (t)。
Step 6: using wavelet base to make 7-layer discrete wavelet decomposition to obtain 7-layer discrete wavelet decomposition layers, then according to the discrete wavelet decomposition layer of every layer reconstructing correspondent primary low-frequency approximation coefficient a j,k J =1, …,7. Obtaining the 7 th layer as the optimal decomposition layer during the decomposition layer number, and the corresponding first low frequency approximation coefficient as a 7,k . When wavelet decomposing a signal, the wavelet transform coefficients can be expressed as:
w 7,k ＝a 7,k +b 7,k (5)
wherein, w 7,k The kth wavelet coefficient, a, of the 7 th layer after decomposition of the original spectral line signal f (t) 7,k The kth low-frequency wavelet coefficient of layer 7, b, representing the effective spectral signal s (t) 7,k The kth high frequency wavelet coefficient of layer 7 representing the noise signal n (t).
And 7: for the first low frequency approximation coefficient a of the optimal decomposition 7 th layer obtained in the step 6 7,k Performing iterative discrete wavelet decomposition, defining e as iteration times, and when e =1, performing primary low-frequency approximation coefficient a r,k Performing discrete wavelet decomposition to obtain secondary low-frequency approximation coefficient
Taking the iteration as the background of the iteration, and performing the next iteration;
and 8: let l = l +1, for the last iteration result
Performing discrete wavelet decomposition to further obtain current secondary low-frequency approximation coefficient
And step 9: if the difference value between the l-th iteration result and the l-1-th iteration result is greater than the preset precision epsilon, returning to the step 8; if the difference value between the l-th iteration result and the l-1-th iteration result of the N continuous times is smaller than the preset precision epsilon, the iteration result is considered to be reliable, the iteration is stopped, and the latest iteration result is obtained
Otherwise, returning to the step 8; the reconstructed optimal wavelet transform coefficient at the r-th layer after l + N iterations is as follows:
in the formula, w 7,k For the kth wavelet coefficient of layer 7,
is the kth low frequency wavelet coefficient of layer 7, b 7,k The k-th high frequency wavelet coefficient of the 7 th layer, N, is determined by actual precision requirements.
Step 10: the obtained wavelet coefficient is corrected through an improved threshold function to obtain a corrected wavelet coefficient
The improved threshold function is given by:
in the formula, sgn represents a step function,
for denoised wavelet coefficients, w j,k And lambda is a set threshold value for the kth wavelet coefficient of the j layer after decomposition. At this time, j =7.
Step 11: performing wavelet reconstruction on the corrected wavelet coefficient to obtain a reconstructed estimation signal
Step 12: the filtered signal is subjected to-p-order G-L fractional order wavelet transform to restore the time domain waveform, so that the signal with noise suppressed can be obtained
The spectral line denoising is realized, as shown in fig. 3, it can be seen that the noise information of the original detection spectral line signal f (t) is effectively removed, the details in the signal are clearly retained, the phenomena of sharpening and over-smoothing are avoided, and the signal-to-noise ratio is improved.
It should be noted that embodiments of the present invention can be realized in hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or specially designed hardware. It will be appreciated by those skilled in the art that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, for example such code provided on a carrier medium such as a diskette, CD-or DVD-ROM, a programmable memory such as read-only memory (firmware) or a data carrier such as an optical or electronic signal carrier. The apparatus of the present invention may 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 by software executed by various types of processors, or by a combination of hardware circuits and software, e.g., firmware.
The embodiment of the invention has some positive effects in the process of research and development or use, and indeed has great advantages compared with the prior art, and the following contents are described by combining data, charts and the like in the test process.
In order to verify the effect of the method, the method is realized on a matlab software platform and compared with the traditional wavelet denoising method. By a more objective analysis of the signal-to-noise ratio. The larger the SNR is, the better the denoising effect is. The SNR effect of the GBW07380 (GSD-29) sample after denoising is compared as shown in the following table.
| Denoising method | Denoising by the method of the text (p = 0.5) | Hard threshold wavelet de-noising | Soft threshold wavelet de-noising |
| SNR | 95.9403 | 81.8468 | 70.6132 |
As can be seen from the above table, the spectral line denoising method based on fractional order iterative discrete wavelet transform proposed herein has a large improvement in signal-to-noise ratio compared to other methods.
In summary, the wavelet coefficient of the traditional spectral line denoising method has constant deviation with the real wavelet coefficient, the invention denoises the spectral line by adopting the method of combining fractional Fourier transform and iterative discrete wavelet, can clearly keep the details in the signal, improves the signal-to-noise ratio, and has better denoising effect compared with the traditional denoising method.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. A spectral line denoising method based on fractional order iterative discrete wavelet transform is characterized by comprising the following steps:
firstly, performing G-L fractional order processing on an original detection spectral line signal of a sample to be detected, and converting the signal into a v-order fractional order differential form;
secondly, searching by adopting an iterative method to obtain an optimal fractional order; performing Fourier transform on the optimal fractional order of the signal;
then, carrying out iterative discrete wavelet decomposition and reconstruction to obtain an optimal wavelet transform coefficient; the optimal wavelet transform coefficients are modified by a modified threshold function,
finally, performing wavelet reconstruction on the corrected wavelet transform coefficient to obtain a reconstructed estimation signal; and carrying out-p-order fractional Fourier transform on the transformed signal to obtain a denoised spectral line signal.
2. The spectral line denoising method based on fractional order iterative discrete wavelet transform as claimed in claim 1, wherein the spectral line denoising method based on fractional order iterative discrete wavelet transform comprises the steps of:
acquiring an original spectral line signal of a sample to be detected, and performing v-order G-L fractional order processing on the acquired original spectral line signal; determining the optimal fractional order of the spectral line signal by adopting an iteration method; mapping the original spectral line signal to an optimal fractional wavelet time-frequency domain, and performing fractional Fourier transform to obtain a transformed signal;
performing multi-layer discrete wavelet decomposition on the transformed signal by using a wavelet basis to obtain a multi-layer discrete wavelet decomposition layer; performing discrete wavelet reconstruction according to the discrete wavelet decomposition layers to obtain a primary low-frequency approximation coefficient corresponding to each discrete wavelet decomposition layer;
selecting an optimal decomposition layer and a primary low-frequency approximation coefficient corresponding to the optimal decomposition layer from the multiple discrete wavelet decomposition layers; performing iterative discrete wavelet decomposition on the primary low-frequency approximation coefficient corresponding to the optimal decomposition layer to obtain an optimal wavelet transform coefficient;
step four, the optimal wavelet transform coefficient is corrected through an improved threshold function, and wavelet reconstruction is carried out on the corrected wavelet transform coefficient to obtain a reconstructed estimation signal; and performing-p-order G-L fractional order wavelet transformation on the reconstructed estimation signal to obtain a denoised output spectrum signal.
3. The spectral line denoising method based on fractional order iterative discrete wavelet transform as claimed in claim 2, wherein said v-order G-L fractional order processing on the acquired original spectral line signal comprises:
firstly, the acquired original spectral line signal f (t) is processed in a differential form of G-L. If the function f (t) has a continuous derivative of order v over the interval [ b, a ], the fractional G-L order derivative of order v of f (t) is defined as:
Γ(v+1)＝v！；
wherein 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; [ (b-a)/h ] denotes the integer part of (b-a)/h; v denotes a differential order, h denotes a differential step, b and a denote upper and lower limits of the differential, respectively, m denotes an order, Γ denotes a gamma function,! Indicating to perform a factorial operation;
secondly, dividing the spectral line signal into n parts according to equal interval h =1, wherein n = [ (b-a)/h ] = [ b-a ], and b and a respectively represent the upper and lower limits of the difference, and obtaining a difference expression of v-order fractional order differential of the original spectral line signal:
where v denotes the order of differentiation, m denotes the order, v ∈ (0,2), and when v =0, the original spectral line signal processing is not performed.
4. The method for spectral line denoising based on fractional order iterative discrete wavelet transform as claimed in claim 2, wherein said iteratively determining the optimal fractional order of the spectral line signal comprises:
adopting an iteration method, wherein the v value range is from 0 to 2, the iteration step length is 0.01, and the optimal fractional order p is iterated; the optimal fractional order p is a fractional order that maximizes a Signal-to-Noise Ratio (SNR).
5. The spectral line denoising method based on fractional order iterative discrete wavelet transform as claimed in claim 2, wherein the step three of performing iterative discrete wavelet decomposition on the primary low frequency approximation coefficient corresponding to the optimal decomposition layer to obtain the optimal wavelet transform coefficient comprises:
(1) Performing iterative discrete wavelet decomposition on the obtained primary low-frequency approximation coefficient of the optimal decomposition layer to obtain a secondary low-frequency approximation coefficient; performing next iteration based on the obtained secondary low-frequency approximation coefficient;
(2) Adding one to the iteration times, and performing discrete wavelet decomposition on the obtained iteration result to obtain a current secondary low-frequency approximation coefficient;
(3) Sequentially iterating until the difference value between the l-th iteration result and the l-1 st iteration result of continuous N times is smaller than the preset precision, and stopping iteration to obtain the latest iteration result; otherwise, returning to the step (2);
(4) Determining the best wavelet transform coefficient after reconstruction is obtained at the r-th layer after continuous l + N iterations:
wherein, w r,k The kth wavelet coefficient representing the r-th layer,
k-th low frequency wavelet coefficient representing the r-th layer, b r,k Representing the kth high frequency wavelet coefficient of the r-th layer.
6. The spectral line denoising method of claim 2, wherein the improved threshold function is as follows:
wherein sgn represents a step function,
representing the modified wavelet coefficients, w j,k Expressing the kth wavelet coefficient of the j layer after decomposition, and expressing lambda as a set threshold; at this time, j =r。
7. A method for spectral line denoising based on fractional order iterative discrete wavelet transform as claimed in any one of claims 1-6, wherein the function of the spectral line denoising based on fractional order iterative discrete wavelet transform comprises:
the signal acquisition module is used for acquiring an original detection spectral line signal of a sample to be detected;
the signal conversion module is used for performing G-L fractional order processing on an original detection spectral line signal of a sample to be detected and converting the signal into a v-order fractional order differential form;
the optimal coefficient determining module is used for searching by adopting an iteration method to obtain an optimal fractional order; performing Fourier transform on the optimal fractional order of the signal; carrying out iterative discrete wavelet decomposition and reconstruction to obtain an optimal wavelet transform coefficient; correcting the optimal wavelet transform coefficient through an improved threshold function;
the signal reconstruction module is used for performing wavelet reconstruction on the corrected wavelet transform coefficient to obtain a reconstructed estimation signal; and carrying out-p-order fractional Fourier transform on the transformed signal to obtain a denoised output signal.
8. A computer device, characterized in that it comprises a memory and a processor, said memory storing a computer program which, when executed by said processor, causes said processor to carry out the steps of the method for spectral line denoising based on fractional order iterative discrete wavelet transform according to any one of claims 1-6.
9. A computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to carry out the steps of the spectral line denoising method based on fractional order iterative discrete wavelet transform according to any one of claims 1-6.
10. An information data processing terminal, characterized in that the information data processing terminal is configured to implement the spectral line denoising method based on fractional order iterative discrete wavelet transform as claimed in claim 7.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211272187.1A CN115795272A (en) | 2022-10-18 | 2022-10-18 | Spectral line denoising method based on fractional order iterative discrete wavelet transform |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211272187.1A CN115795272A (en) | 2022-10-18 | 2022-10-18 | Spectral line denoising method based on fractional order iterative discrete wavelet transform |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN115795272A true CN115795272A (en) | 2023-03-14 |
Family
ID=85433132
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211272187.1A Pending CN115795272A (en) | 2022-10-18 | 2022-10-18 | Spectral line denoising method based on fractional order iterative discrete wavelet transform |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115795272A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116644281A (en) * | 2023-07-27 | 2023-08-25 | 东营市艾硕机械设备有限公司 | Yacht hull deviation detection method |
-
2022
- 2022-10-18 CN CN202211272187.1A patent/CN115795272A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116644281A (en) * | 2023-07-27 | 2023-08-25 | 东营市艾硕机械设备有限公司 | Yacht hull deviation detection method |
| CN116644281B (en) * | 2023-07-27 | 2023-10-24 | 东营市艾硕机械设备有限公司 | Yacht hull deviation detection method |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Prasad et al. | FLAGCAL: a flagging and calibration package for radio interferometric data | |
| CN109871733B (en) | Self-adaptive sea clutter signal denoising method | |
| CN110503060B (en) | Spectral signal denoising method and system | |
| CN110207689B (en) | Pulsar signal denoising and identifying method based on wavelet entropy | |
| CN115700544A (en) | Chromatographic signal denoising method combining empirical mode decomposition and wavelet soft threshold | |
| CN115795272A (en) | Spectral line denoising method based on fractional order iterative discrete wavelet transform | |
| CN111982489B (en) | Weak fault feature extraction method for selectively integrating improved local feature decomposition | |
| CN116088320B (en) | Sparse double-space non-convex penalty self-adaptive Chirp modal cross aliasing decomposition method | |
| CN114886378A (en) | Improved complementary set modal decomposition-based joint denoising method and system | |
| Vargas et al. | Electrocardiogram signal denoising by clustering and soft thresholding | |
| CN111091107A (en) | Face region edge detection method and device and storage medium | |
| CN114077852A (en) | Intelligent denoising method for strong noise spectrum signal | |
| CN102542284B (en) | Method for identifying spectrum | |
| CN111582205B (en) | Noise reduction method based on multi-resolution singular value decomposition model | |
| CN115797318A (en) | Spectral data preprocessing method and device, computer equipment and storage medium | |
| CN114814897A (en) | Combined filtering method for weakening GNSS multipath error | |
| CN113011321B (en) | Spectral signal denoising method, system, terminal and readable storage medium based on joint dictionary | |
| AU2021104217A4 (en) | A system and method for optimum wavelet basis function selection for ecg arrhythmia denoising using artificial intelligence | |
| CN102105814B (en) | System and method for seismic trace analysis | |
| CN108680958B (en) | Seismic data noise reduction method based on peak value transformation | |
| CN111142134A (en) | Coordinate time series processing method and device | |
| Kuang et al. | Joint empirical mode decomposition and optimal frequency band estimation for adaptive low-frequency noise suppression | |
| CN113742985B (en) | Processing method and device for ecosystem carbon flux measurement signals and electronic equipment | |
| CN113031074B (en) | Logging curve denoising method, device, equipment and storage medium | |
| CN117421561B (en) | Turbulence denoising method and system based on parameter optimization VMD (virtual machine direction detector) combined wavelet |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |