CN112986301A - ISLA seed local average spectrum-forming algorithm based on SLA algorithm - Google Patents
ISLA seed local average spectrum-forming algorithm based on SLA algorithm Download PDFInfo
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Abstract
Compared with the traditional MCA method, the novel spectrum processing method greatly improves the energy resolution, compensates the counting rate loss of the SLA algorithm, effectively reduces the half-height width of a spectral line, sharpens a spectral peak, and does not cause the counting rate loss.
Description
Technical Field
The invention relates to the technical field of mineral exploration, in particular to an ISLA seed local average spectrum-forming algorithm based on an SLA algorithm.
Background
With the development of mineral exploration technology, X fluorescence spectrum analysis is used as an element content analysis technology, and can perform quantitative or semi-quantitative analysis on the element content in a sample. Semiconductor detectors are widely adopted with higher energy resolution, and most of detectors commonly used in X-ray fluorescence spectroscopy at present are electric refrigeration type semiconductor detectors, such as Si-Pin detectors, SDDs, FAST SDDs and the like. Driven by electronic technology and nuclear signal processing technology, the energy resolution of a measurement system is close to the inherent resolution of a detector, and in some specific application occasions, the detector with the best energy resolution is still insufficient to complete the screening of each element in a sample, and the content of each element cannot be effectively calculated (G.Bertuccio et al, 2016; Er-Lei Chen et al, 2017; R.J.Cooper et al, 2018).
In order to further improve the measurement accuracy and more effectively screen elements in the X fluorescence spectrum, a plurality of scholars and researchers have studied on improving the counting rate and the spectral line energy resolution, and corresponding research results are obtained. Digital pulse shaping is an effective pulse processing method, regardless of counting rate or energy resolution, and can effectively improve the accuracy of measurement results. Common digital forming methods include triangulation (a.regadio, et al., 2014; n.menaa, et al.,2011), digital trapezoidal (g.zeng, et al.,2017), pinnacle (v.t.jordanov,2012), CR-RCmDigital filter shaping (Huai-Qiang Zhang, et al.,2019) and unit pulse shaping (v.t. jordanov, 2015; Hong x. et al., 2018). Different forming methods have different application environments and can also achieve different application effects, such as piled-up pulse correction (m.e. hammada et al, 2019), counting rate saturation correction (Mahdi haghatatyafhara et al, 2019), and the like.
Digital pulse forming belongs to a preprocessing mode in a spectrum forming process, in the research of improving energy resolution, mostly, deconvolution is used for carrying out postprocessing on obtained spectral lines, the postprocessing method needs to model the obtained spectral lines as functions of two variables, namely an input spectral line and a response function of a detector, and the response function of the detector is determined by probability distribution of the amplitudes of input pulses and output pulses. Several post-processing methods are common, including spectral smoothing (Yong-Li Liu et al, 2019; Xing-Ke Ma et al, 2019), maximum likelihood estimation (Harriet Linda et al, 2018), and maximum entropy (Alessandro barduci et al, 2013), all of which involve very complicated deconvolution mathematical modeling processes, are computationally intensive and not versatile, and require re-modeling analysis every time a detector is replaced (l.j.meng et al, 2000).
In order to solve the above problems, the prior art includes a pulse removal method (Tang l., et al.,2018a) and a pulse repair method (Tang l., et al.,2018b) to improve the reliability of the pulse amplitude, thereby reducing the statistical fluctuation of the measurement result. On the basis, the invention provides an improved seed averaging algorithm (ISLA) by taking an MCA spectral analysis method and a seed averaging algorithm (SLA) (Valentin T. Jordanov,2005) as comparison objects, theoretical derivation and application effect evaluation are carried out on the ISLA, and results show that compared with the traditional MCA method, the novel spectral processing method has larger improvement on energy resolution, makes up for counting rate loss of the SLA algorithm and has good application effect.
Disclosure of Invention
The invention aims to provide an ISLA seed local average spectrum-forming algorithm based on an SLA algorithm.
In order to achieve the purpose, the invention is implemented according to the following technical scheme:
the invention relates to two variable parameters, including a parameter 2R +1 representing the size of an averaging window and a parameter N representing the number of seeds averaged within the averaging window; taking an average window parameter R equal to 1, taking the number of seeds participating in the average each time as 3, in the algorithm execution process, firstly, regarding each read pulse amplitude as one seed, then determining the range of an active window according to the size of the current seed, when the number of the seeds in the area reaches the maximum value N of the number of the seeds set by the SLA algorithm, carrying out averaging operation on the seeds in the area, updating the counting on the corresponding addresses through the pulse amplitude average value, wherein the counting value increased on each address is the number N of the averaged seeds, finally, resetting the averaged seeds and the number of the seeds in the active window, and simultaneously, starting to read the next pulse amplitude to carry out a new round of seeding.
The amplitude sample number calculation method required by ISLA seed local average spectrum-forming algorithm simulation is as follows: initially selecting 200-80000 sample number simulation ranges, determining the sample number C at intervals of 50, and generating 2048 random numbers of 1-C through a uniform distribution function, namely randomly sampling 2048 times in a sample pool with the capacity of C; if the number of samples C is less than 2048, the number of occurrences of some samples is inevitably greater, while the number of occurrences of some samples is less, and specifically, the number of occurrences of each sample can be counted by a tabulate function, so as to obtain the difference between the actual occurrence probability and the average probability of each sample, and then the average error is obtained by dividing the sum of squares of errors occurring in each random variable by the total number of samples.
Preferably, 65536 is selected as the number of amplitude samples required for simulation by the ISLA seed local average spectroscopy algorithm.
In the simulation of the ISLA seed local average spectrum-forming algorithm, the average window size is 2R +1, the number of the averaged seeds is N, and X is used0Representing the original pulse amplitude sequence defining an averaging window in the range X0-R,X0+R]The probability density function is f (X), the cumulative distribution function is F (X), if XAIs the pulse amplitude, X, obtained after averaging the seeds in the local windowAAnd X0Having the same probability distribution function, but limited in scope to [ X ]A-R,XA+R]Within the interval; when the number of seeds in the averaging window reaches a set threshold value N-5, the pulse amplitude X after averagingAAs shown in formula (1):
assuming that the probability density function f (x) of the original pulse amplitude sequence is symmetric about the mean value μ, and μ represents the peak position of the probability density function, then f (μ -b) ═ f (μ + b) can be obtained for any value b; xABy X participating in the averagingi(i is 0 to 4) and XiHas the same probability density function, and can obtain X obtained by ISLA seed local average spectral forming algorithm processingAAlso formed by XiThe probability density function of (2) determines that the symmetry of the original distribution is not changed after the ISLA seed local average spectral algorithm is transformed no matter what the parameter setting is.
If the original distribution is an independent gaussian peak, the distribution obtained after transformation by the ISLA seed local averaging spectral algorithm will have the same average value, i.e. the peak position is kept unchanged, and the symmetry is kept.
In the simulation of the ISLA seed local average spectrum-forming algorithm, if the probability density function f (X) of the original pulse amplitude sequence is symmetrical and continuously approaches to mu on two sides of the average value mu, X obtained after the ISLA seed local average spectrum-forming algorithm is transformedAThe variance of (a) is necessarily smaller than the variance of the original pulse amplitude sequence, and the derivation process is as follows:
the above theory can be simplified as shown in formula (2) by setting the average value μ to 0 without loss of generality;
the left side of expression (2) can be further expanded as shown in expression (3).
To prove the inequality (2), only the inequality needs to be proved
The left side of the device can be further expanded as shown in formula (4).
Since f (x) is symmetrical and increases all the way towards the mean, here the mean is set to 0, giving for example x0Mu is 0
Likewise, e.g. x0Not equal to mu
On the basis, the formula (4) can further derive a formula (5);
the above reasoning shows that the ISLA seed local average spectral algorithm reduces the variance, thereby reducing the full width at half maximum of the spectral line and sharpening the spectral peak.
The invention has the beneficial effects that:
compared with the prior art, the ISLA algorithm provided by the invention after optimizing the SLA not only effectively reduces the half-height width of a spectral line and sharpens a spectral peak, but also does not cause counting rate loss, provides a real-time, efficient and universal processing method for reducing noise of a detector, has provable theoretical guarantee, and has great application significance for improving the energy resolution of the detector.
Drawings
FIG. 1 is a schematic diagram of a multichannel spectral analysis;
fig. 2 is the SLA algorithm implementation principle (R ═ 1, N ═ 3);
fig. 3 is an implementation principle of the ISLA algorithm (R ═ 1, N ═ 3);
FIG. 4 is a graph of simulation results of sample number values;
FIG. 5 is a graph of the MCA spectroscopy results obtained with different numbers of amplitude samples;
FIG. 6 is a graph of the results of different algorithms for forming spectra;
FIG. 7 is a graph of ISLA spectroscopy results for different parameters;
FIG. 8 is a spectrum obtained before and after the SLA algorithm;
fig. 9 is a spectrum obtained before and after the ISLA algorithm is used.
Detailed Description
The invention will be further described with reference to the drawings and specific embodiments, which are illustrative of the invention and are not to be construed as limiting the invention.
The method for forming the spectrum comprises the following steps:
the traditional spectrum analysis method in the X-ray fluorescence spectrum analysis is Multi-Channel spectrum analysis (MCA), and when the traditional spectrum analysis method cannot meet the requirement of energy resolution, the foreign research team (Valentin t. jordanov,2005) proposes sla (seeds Local averaging) algorithm to optimize the energy resolution of the spectral line, but the method has the defect of count rate loss. The invention provides an ISLA (improved selected Local averaging) algorithm on the basis of an SLA algorithm, so that the counting rate is ensured not to be lost while the energy resolution is improved.
MCA adopts a single pulse spectrum forming mode, each pulse amplitude is received and stored in FIFO, and the most key part in the spectrum forming process is the corresponding relation between the pulse amplitude and the channel address. For the example of MCA of 2048 tracks, the pulse amplitudes 0-2000 mv correspond to addresses 0-2048, so we approximate that each mv corresponds to one address, and the spectrum forming principle is shown in FIG. 1.
The SLA algorithm is a seed local averaging algorithm realized by probability density conversion on the basis of MCA, and comprises an averaging window parameter R and the number N of seeds in an active window. When the average window parameter is R, the window size is 2 × R +1, and the spectrum formation principle is shown in fig. 2.
Firstly, the read pulse amplitude is regarded as a seed, then the range of the active window is determined according to the size of the current seed, as shown in a red area of fig. 2, when the number of the seeds in the area reaches the maximum value N of the number of the seeds set by the SLA algorithm, the seeds in the area are averaged, the count value on the corresponding track address is updated through the pulse amplitude average value, and finally the averaged seeds and the number of the seeds in the active window are cleared. In the SLA profiling process shown in fig. 2, the average window size is 3, and the number of seeds is 3. From this, we can easily see that the MCA method can be actually regarded as a special SLA algorithm, in which the value of the parameter R is 0 and the value of the parameter N is 1.
ISLA: after optimizing the SLA algorithm, the present invention proposes an improved seed averaging algorithm (ISLA), the spectral principle of which is shown in fig. 3. The ISLA algorithm is the same as the SLA algorithm in that pulse amplitude is adopted as seeds to be sown in a local window, averaging is carried out when the number of the seeds reaches a threshold value set by the algorithm, and the counting on a corresponding track address is updated through the average value of the pulse amplitude; the place where the ISLA algorithm is superior to the SLA algorithm is that the former calculates the number of pulses averaged in a local window when counting on an updated track address, updates the count value according to the value of the number N of pulses, and the latter simply adds one to the count on the track address, thereby causing the count rate to be impaired.
Similar to the SLA algorithm, the ISLA algorithm involves two variable parameters, one is the size of the averaging window, which is expressed by the parameter 2 × R +1 in the present invention, and the other is the number of seeds averaged within the averaging window, which is expressed by the parameter N in the present invention. In the principle description of the ISLA algorithm of FIG. 3, the averaging window parameter R is equal to 1 and the number of seeds participating in averaging each time is 3. In the algorithm execution process, firstly, each read pulse amplitude is regarded as a seed, then the range of the active window is determined according to the size of the current seed, as shown in a dark color area of fig. 3, when the number of the seeds in the area reaches the maximum value N of the number of the seeds set by the SLA algorithm, the seeds in the area are averaged, the count on the corresponding addresses is updated through the pulse amplitude average value, the count value increased on each address is the averaged number N of the seeds, finally, the averaged seeds and the number of the seeds in the active window are cleared, and meanwhile, the next pulse amplitude is read to perform a new round of seeding.
Theoretical derivation and simulation:
as described above, the essence of MCA is the SLA algorithm in which the parameter R takes a value of 0 and the parameter N takes a value of 1, and each pulse amplitude corresponds to a count value in the final measured spectrogram, so that MCA represents the probability density over the pulse amplitude, and ISLA averages the probability density within a specified range, thereby obtaining a new probability density. For a single spectral peak, the mean μ represents the peak position, while the variance determines the full width at half maximum (FWHM) of the spectral line. The peak position and half-height width of the ISLA algorithm will be discussed below in terms of theoretical derivation and simulation of the two indicators, mean and variance, respectively, before first calculating the number of amplitude samples required for simulation of the algorithm.
Number of amplitude samples:
in the algorithm simulation process, a randomly generated normal distribution sequence is usually used as a pulse amplitude sample, the probability of taking out one pulse amplitude information from a sample pool within the same sampling time can be calculated according to the number of samples, and it can be estimated that the greater the number of samples is, the more similar the probability of taking out any one pulse amplitude information within the same time is. When the probability of taking out any pulse amplitude information tends to be stable, the number of samples at the moment can be regarded as an optimal value, and the calculation process is as follows: the simulation range of the number of samples is initially selected to be 200-80000, after the number of samples C is determined at intervals of 50, 2048 random numbers for generating 1-C are generated through a uniform distribution function, namely 2048 times of random sampling are performed in a sample pool with the capacity of C. If the number of samples C is less than 2048, there are more samples and fewer samples, and the number of occurrences of each sample can be counted by a tabulate function, so as to obtain the difference between the actual occurrence probability and the average probability of each sample, and then the average error is obtained by dividing the sum of squares of errors occurring in each random variable by the total number of samples, and the calculation result is shown in fig. 4.
As can be seen from fig. 4, when the number of samples is 20000 or less, the average error tends to decrease more significantly as the number increases, while when the number of samples is 60000 or less, the average error is not significantly affected by the increase in the sample volume. Therefore, the random sampling of large samples is met to the maximum extent, the correlation caused by calculation is reduced, the average error of each random number can be reduced as much as possible by increasing the number of samples, but if the number of static sample pools is large, the resource waste is caused, and the efficiency is limited. Therefore, 65536 was chosen as the number of amplitude samples used in the simulations herein. In practical use, due to limited hardware resources, dynamic samples updated in real time are usually adopted, and the sample capacity is usually 4096. Fig. 5 shows the MCA spectroscopy results obtained when different amplitude samples are taken, and it can be easily seen that, when the number of samples is larger, the probability that each sample is sampled is more similar, and the probability density graph obtained finally conforms to the normal distribution, and the MCA spectroscopy results are smoother.
Peak position:
in the ISLA algorithm simulation, the average window size is 2R +1, the number of the seeds to be averaged is N, and the invention uses X0Representing the original pulse amplitude sequence defining an averaging window in the range X0-R,X0+R]The probability density function is f (X), the cumulative distribution function is F (X), if XAIs the pulse amplitude, X, obtained after averaging the seeds in a local windowAAnd X0Having the same probability distribution function, but limited in scope to [ X ]A-R,XA+R]Within the interval. When the number of seeds in the averaging window reaches a set threshold value N (where N is 5), the pulse amplitude X after averagingAAs shown in equation 1.
Assuming that the probability density function f (x) of the original pulse amplitude sequence is symmetric about the mean value μ, where μ represents the peak position of the probability density function, f (μ -b) ═ f (μ + b) can be derived for any value of b. XABy X participating in the averagingi(i is 0 to 4) and XiHas the same probability density function, so that X obtained by ISLA algorithm processing can be obtainedAAlso formed by XiThe probability density function of (2) determines that the symmetry of the original distribution is not changed after ISLA transformation regardless of the parameter settings. It is noted that, if the original distribution is an independent gaussian peak,the distributions obtained after the ISLA transformation will have the same average value, i.e. the peak positions are kept unchanged while the symmetry is kept, and the spectra obtained by simulation with different algorithms are shown in fig. 6.
Half height width:
as mentioned above, if the probability density function f (X) of the original pulse amplitude sequence is symmetric and approaches to μ continuously on both sides of the mean μ, then X is obtained after ISLA transformationAThe variance of (c) is necessarily smaller than the variance of the original pulse amplitude sequence. The derivation process is as follows:
the above theory can be simplified as shown in formula (2) by setting the average value μ to 0 without loss of generality.
The left side of expression (2) can be further expanded as shown in expression (3).
To prove the inequality (2), we only need to prove the inequality
The left side of the device can be further expanded as shown in formula (4).
Since f (x) is symmetric and always increases towards the mean (here we assume the mean is 0), we can conclude that if x is0Mu is 0
Similarly, if x0Not equal to μ then | E [ X1|X0＝x0]|＜|x0Based on this, equation (4) can be further derived as equation (5).
The above reasoning shows that the algorithm does not change the probability density distribution nor break the symmetry of the original distribution, regardless of how the parameter values of the ISLA are set. For a single Gaussian peak, the full width at half maximum of the spectral line is positively correlated with the variance of the distribution, so that the ISLA algorithm can reduce the variance, further reduce the full width at half maximum of the spectral line and sharpen the spectral peak.
When the ISLA algorithm is simulated, 65536 pulse amplitude samples are taken, the ISLA algorithms with three different parameters are respectively adopted for spectrum formation, and the spectrum formation result is compared with the traditional MCA spectrum formation result, and the comparison result is shown in fig. 7.
As can be seen from the four spectral lines in fig. 7, the improvement effect on the FWHM of the spectral line is different when the ISLA algorithm takes different parameters, the FWHM obtained by each parameter is shown in table 1, and the FWHM of the ISLA algorithm is always smaller than that obtained by the MCA algorithm no matter what parameter the ISLA algorithm takes, so that the ISLA algorithm not only effectively reduces the FWHM of the spectral line, but also ensures that the count rate is not lost. Meanwhile, the measurement result obtained by taking different seed average numbers N when the average window size is fixed shows that the improvement effect on the spectral line FWHM is better when N is larger.
TABLE 1 Effect of different parameters on the results of the spectroscopy
Evaluation of application effects:
when the application effect evaluation is carried out on different spectrum forming methods, a measuring system adopts FASTSDD with the resolution as high as 122-129 eV as a detector, an excitation source adopts a Keyiwei KYW2000A type X-ray tube, and a measuring object adopts a self-made powdered iron ore sample. In the back-end electronic circuit, different spectrum forming algorithms are respectively called to perform multi-channel spectrum forming, the measured multi-channel spectrum is analyzed and compared, and the evaluation of the application effect of the different spectrum forming algorithms is as follows.
The counting rate of each element characteristic peak is swung around a certain value according to the decay randomness of the radioactive sample. When the statistical samples are large enough, the probability of each sample appearing is in accordance with the normal distribution, which is also a statistical characteristic of nuclear decay. In the experimental link, the iron ore sample is taken as a measurement object, and the measurement results obtained by using the traditional MCA and SLA algorithms are respectively shown as black and red spectral lines in fig. 8. As can be seen from the figure, the full width at half maximum of the spectral line obtained by the SLA algorithm is obviously smaller than that obtained by the MCA, and meanwhile, the counting rate loss caused by the local averaging process of the seeds in the SLA algorithm is also obviously shown.
In the previous subsection, we have found that the SLA algorithm can effectively reduce the full width at half maximum of the spectral line, but the counting rate loss is caused by the seed averaging process, and as described above, the ISLA algorithm is an optimization on the SLA algorithm, and the primary purpose of the optimization is to improve the energy resolution and ensure that the counting rate is not lost. In the experimental section, the result of using an iron ore sample as a measurement object, using an ISLA algorithm and performing a fast multi-pulse spectroscopy processing is shown in fig. 9.
In comparison, in fig. 9, the spectral lines processed by the ISLA algorithm are both reduced by half the height and width compared to MCA and SLA, and the count rate is guaranteed not to be lost.
Taking the K alpha and K beta peaks of iron element as analysis objects, respectively adopting MCA, SLA and ISLA algorithms to perform spectrum formation, wherein the counting rate analysis is shown in Table 2, wherein Ck-αDenotes the sum of the count rates of the k-alpha peaks, Ck-βRepresenting the sum of the count rates of the k-beta peaks. It is easy to see that, no matter the K α peak or the K β peak of the iron element, the sum of the counting rates obtained by the SLA algorithm is obviously smaller than that obtained by the MCA algorithm, while the sum of the counting rates obtained by the ISLA algorithm is approximately equal to that obtained by the MCA algorithm, that is, although the half-height width of the spectral line is reduced by the SLA algorithm, the counting rate is obviously lost, and the ISLA algorithm effectively compensates for the part of the counting rates. In the SLA algorithm and the ISLA algorithm, the parameter N is equal to 3, R is equal to 1, and the method is equivalent to the method of passing throughThe increase of one count is obtained by averaging the amplitudes of the three pulses, so that the sum of the count rates obtained by adopting the SLA algorithm is approximately equal to one third of the MCA algorithm in value, and the count on the channel address is updated by the ISLA algorithm through the seed average number N so as to make up for the count rate loss caused by the SLA algorithm.
TABLE 2 comparison of count rates for different spectroscopy algorithms
And (4) conclusion:
the invention describes three spectrum forming methods, describes the spectrum forming principle of each method, also carries out theoretical derivation and software simulation on an ISLA algorithm, and carries out detailed analysis on the spectrogram measured by each spectrum forming method in an application effect evaluation link. Simulation and experiment results show that the spectrogram obtained by the SLA algorithm has smaller full width at half maximum than the spectrogram obtained by MCA, but the counting rate is reduced by the average process of the seeds in the SLA algorithm. The ISLA algorithm provided after optimizing the SLA not only effectively reduces the half-height width of a spectral line and sharpens a spectral peak, but also does not cause counting rate loss. Admittedly, the ISLA algorithm provides a real-time, efficient and universal processing method for reducing the noise of the detector, and has a provable theoretical guarantee, which has great application significance for improving the energy resolution of the detector.
The technical solution of the present invention is not limited to the limitations of the above specific embodiments, and all technical modifications made according to the technical solution of the present invention fall within the protection scope of the present invention.
Claims (6)
1. An ISLA seed local average spectrum-forming algorithm based on an SLA algorithm is characterized in that: two variable parameters are involved, including a parameter 2R +1 representing the size of the averaging window and a parameter N representing the number of seeds averaged within the averaging window; taking an average window parameter R equal to 1, taking the number of seeds participating in averaging every time as 3, in the algorithm execution process, firstly, regarding each read pulse amplitude as one seed, then determining the range of an active window according to the size of the current seed, when the number of the seeds in the area reaches the maximum value N of the number of the seeds set by the SLA algorithm, averaging the seeds in the area, updating the count on the corresponding addresses through the pulse amplitude average value, wherein the count value increased every time on the addresses is the averaged number N of the seeds, finally, resetting the averaged seeds and the number of the seeds in the active window, and simultaneously starting to read the next pulse amplitude to perform a new round of seeding.
2. An SLA algorithm based ISLA seed local average spectral generation algorithm according to claim 1, wherein: the amplitude sample number calculation method required by ISLA seed local average spectrum-forming algorithm simulation is as follows: initially selecting a sample number simulation range of 200-80000, determining the sample number C at intervals of 50, and then generating 2048 random numbers of 1-C through a uniform distribution function, namely randomly sampling 2048 times in a sample pool with the capacity of C; if the number of samples C is less than 2048, the number of occurrences of some samples is inevitably greater, while the number of occurrences of some samples is less, and specifically, the number of occurrences of each sample can be counted by a tabulate function, so as to obtain the difference between the actual occurrence probability and the average probability of each sample, and then the average error is obtained by dividing the sum of squares of errors occurring in each random variable by the total number of samples.
3. An SLA algorithm based ISLA seed local average spectral generation algorithm according to claim 2, wherein: 65536 is selected for simulating the number of amplitude samples needed by the ISLA seed local average spectral algorithm.
4. An SLA algorithm based ISLA seed local average spectral generation algorithm according to claim 2, wherein: in the simulation of the ISLA seed local average spectrum-forming algorithm, the average window size is 2R +1, the number of the seeds to be averaged is N, and X is used0Representing the original pulse amplitude sequence defining an averaging window in the range X0-R,X0+R]The probability density function is f (X), the cumulative distribution function is F (X), if XAIs the pulse amplitude, X, obtained after averaging the seeds in a local windowAAnd X0Having the same probability distribution function, but limited in scope to [ X ]A-R,XA+R]Within the interval; when the number of seeds in the averaging window reaches a set threshold value N-5, the pulse amplitude X after averagingAAs shown in formula (1):
assuming that the probability density function f (x) of the original pulse amplitude sequence is symmetric about the mean value μ, and μ represents the peak position of the probability density function, then f (μ -b) ═ f (μ + b) can be obtained for any value b; xABy X participating in the averagingi(i is 0 to 4) and XiHas the same probability density function, and can obtain X obtained by ISLA seed local average spectral forming algorithm processingAAlso formed by XiThe probability density function of (2) determines that the symmetry of the original distribution cannot be changed after ISLA seed local average spectral algorithm transformation regardless of parameter setting.
5. An SLA algorithm based ISLA seed local average spectral generation algorithm according to claim 4, wherein: if the original distribution is an independent gaussian peak, the distribution obtained after transformation by the ISLA seed local averaging spectral algorithm will have the same average value, i.e. the peak position is kept unchanged, and the symmetry is kept.
6. An SLA algorithm based ISLA seed local average spectral generation algorithm according to claim 2, wherein: in the simulation of the ISLA seed local average spectrum-forming algorithm, if the probability density function f (X) of the original pulse amplitude sequence is symmetrical and continuously approaches to mu on two sides of the average value mu, X obtained after the ISLA seed local average spectrum-forming algorithm is transformedAThe variance of (A) is necessarily smaller than the original pulse amplitudeThe variance of the degree sequence is derived as follows:
the above theory can be simplified as shown in formula (2) by setting the average value μ to 0 without loss of generality;
the left side of expression (2) can be further expanded as shown in expression (3):
to prove the inequality (2), only the inequality needs to be proved
The left side of the device can be further expanded as shown in formula (4):
since f (x) is symmetrical and increases all the way towards the mean, here the mean is set to 0, giving for example x0E [ X ] 0 ═ μ ═ 01|X0＝x0]＝x0Same as x0Not equal to μ then | E [ X1|X0＝x0]|＜|x0On the basis, the formula (4) can further derive the formula (5);
the above reasoning shows that the ISLA seed local average spectral algorithm reduces the variance, thereby reducing the full width at half maximum of the spectral line and sharpening the spectral peak.
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