CN107179310B - Raman spectrum characteristic peak recognition methods based on robust noise variance evaluation - Google Patents
Raman spectrum characteristic peak recognition methods based on robust noise variance evaluation Download PDFInfo
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Abstract
The invention discloses a kind of Raman spectrum characteristic peak recognition methods based on robust noise variance evaluation, step are as follows：(1) it is reference by the Gaussian noise that 0, variance is 1 of average, it is determined that with reference to hundredths and its percentile；Difference normalization is carried out to Raman spectrum data, data after normalization are sorted from small to large, calculate the hundredths of each data, then the percentile with reference to corresponding to hundredths is tried to achieve by linear interpolation, and by it with being divided by with reference to percentile, series of noise standard deviation is obtained, takes the median of standard deviation as the noise estimated standard deviation σ of the spectroscopic data；(2) peak value and valley of Raman spectrum data are asked for, by each peak value compared with the minimum valley at left and right sides of it, if greater than r times of noise criteria difference σ, then it is assumed that be the characteristic peak of Raman spectrum.This method need not go background process to Raman spectrum in advance, and without artificially setting any parameter, it is possible to achieve the automation of spectral peak identification.
Description
Technical Field
The invention relates to a spectral characteristic peak identification method, in particular to a Raman spectral characteristic peak identification method based on robust noise variance estimation.
Background
The Raman spectrum analysis has the advantages of rapidness, simplicity, repeatability, no damage to samples and the like, and is widely applied to the fields of agriculture, medicine, food, petrochemical industry and the like. The Raman spectrum analysis comprises the steps of spectrum preprocessing, feature extraction, feature classification and the like, wherein the feature extraction is a core link in the design of a Raman spectrum analysis system. Because the Raman spectral line displacement is irrelevant to the frequency of incident light and only relevant to the vibration and rotation energy level of molecules, each substance has corresponding Raman spectrum characteristic peak distribution, the position and the size of the Raman spectrum characteristic peak directly reflect the structure and the content information of the substance, and whether the spectral peak directly influences the accuracy of sample characteristic classification can be well judged.
The commonly used spectrum peak identification methods at present include an amplitude method, a continuous wavelet transform method, a derivative method and the like. The amplitude method is characterized in that a threshold value is set, a first point larger than the threshold value is taken as a starting point of a spectral peak, a subsequent maximum point is taken as a high point of the spectral peak, and a next first point smaller than the threshold value is taken as an end point of the spectral peak, so that the method is simple in principle, high in calculation speed and easy to be influenced by baseline drift, and the selection of the comparison threshold value has a large influence on the accuracy of spectral peak detection; the continuous wavelet transform method decomposes signals into superposition of a series of wavelet functions, converts time domain peak searching into ridge line peak searching of a wavelet coefficient matrix, has high peak searching accuracy, has strong inhibition capability on noise and background, but has large calculation amount, is not suitable for real-time operation, needs to determine a ridge line length threshold and a ridge line signal-to-noise ratio threshold, but is closely related to selection of wavelet scales, and the significance of the ridge line signal-to-noise ratio is not very clear, so that the method is not stable enough and is not easy to use; the basic idea of the derivative method is to regard the spectral line as a continuous curve, determine the derivative of each point on the spectral line, and then determine the position of the spectral peak according to the property of the derivative. The lower limit of the local signal-to-noise ratio at the spectral peak should be 6 times the noise standard deviation, depending on the definition of the local signal-to-noise ratio. However, the actual spectral data contains characteristic peaks and baseline noise, and there is baseline shift, and how to estimate the standard deviation of the noise is a problem worthy of study.
The traditional noise estimation method is mostly manual or semi-manual, and needs to find a piece of data which does not contain characteristic peaks, outliers and obvious baseline tilt from the spectrum in advance, and then estimate the noise standard deviation. If the spectral data acquired each time is processed in this way, the estimation result is unreliable due to the influence of human subjective factors, and the automatic operation of the raman spectrometer is not facilitated.
Disclosure of Invention
In order to overcome the defect that the conventional Raman spectrum characteristic peak searching algorithm needs to manually set a threshold, the invention provides a Raman spectrum characteristic peak identification method based on robust noise variance estimation, which does not need to perform background removal processing on a Raman spectrum in advance, does not need to manually set any parameter, and can realize the automation of spectrum peak identification.
The technical scheme adopted by the invention for solving the technical problem is as follows: a Raman spectrum characteristic peak identification method based on robust noise variance estimation comprises the following steps:
(1) Determining a reference percentile and a percentile thereof by taking Gaussian noise with a mean value of 0 and a variance of 1 as a reference; carrying out forward difference operation and normalization on the Raman spectrum data, sequencing the normalized data from small to large, calculating percentiles of the data, then obtaining the percentile corresponding to the reference percentile through linear interpolation, and dividing the percentile by the reference percentile to obtain a series of noise standard deviations, and taking the median of the standard deviations as the noise estimation standard deviation sigma of the spectrum data;
(2) The peak value and the valley value of the Raman spectrum data are obtained through first-order derivation, each peak value is compared with the minimum valley value on the left side and the right side of the peak value, and if the noise standard deviation sigma is larger than r times (r is usually larger than or equal to 6), the peak value is considered as the characteristic peak of the Raman spectrum.
Further, the step (1) is specifically as follows:
(1.1) assume that the random variable ε obeys a mean of 0 and a variance σ 2 The probability density function of the gaussian distribution of (1) is:
it is known that percentile p (x) refers to the cumulative probability that a random variable epsilon is smaller than the percentile x, i.e.:
according to the definition of the error function:
the following can be obtained:
further, the following can be obtained:
taking Gaussian noise with mean value of 0 and variance of 1 as reference, and determining the percentage position p (x) is in the range of [0,0.5 ]]Taking m points in the range to form a percentile vector p 0 The percentile vector can be obtained
(1.2) respectively carrying out 1,2, …, n-order forward difference operation on the Raman spectrum data vector x and normalizing to obtain a difference data vector x 1 ,x 2 ,…,x n ；
(1.3) performing the following on i = 1:n:
(1.3.1) to x i Sorting according to the sequence from small to large;
(1.3.2) known x 0 Is m, j =1:m is operated as follows:
(1.3.2.1) hypothesis x i Is q, then x is ordered i Corresponding to each element in (1)Percentile vectorWherein τ =1,2, …, q,0<κ<, 1. Note p 0 (j) Is p 0 By the j-th element of (1) at p i P is obtained by linear interpolation between adjacent elements i ＝p 0 (j) And p i ＝1-p 0 (j) Corresponding to x i Are respectively a percentile x i,j And x' i,j ；
(1.3.2.2) calculation of x i At p i ＝p 0 (j) Standard deviation of time-dependent noise estimate
(1.3.3) taking σ i,j (j =1,2, …, m) as the median x i Is estimated as the standard deviation sigma of the noise i ；
(1.4) taking σ i The median of (i =1,2, …, n) is taken as the noise estimation standard deviation σ of the raman spectrum data vector x.
Further, the step (2) is specifically as follows:
(2.1) carrying out first-order derivation on the Raman spectrum data to obtain the peak value and the valley value of the Raman spectrum data, and forming a new vector z by the peak value and the valley value;
(2.2) determining whether the first element in z is a peak or a valley, i.e. whether z (1) is greater than z (2): if yes, k =0; if not, k =1, thus ensuring that the following cycle starts from one peak;
(2.3) the variables tempmax = min (z) and leftmin = x (1) are defined, tempmax representing the provisional peak and leftmin representing the left valley. If z has a length of l, when k < l, the following cycle is performed:
(2.3.1) k = k +1, and determines whether z (k) is greater than tempmax and leftmin + threshold: if yes, tempmax = z (k), wherein threshold = r σ represents a spectral peak judgment threshold (usually r ≧ 6);
(2.3.2) k = k +1, and determines whether tempmax is greater than z (k) + threshold: if yes, tempmax is a spectral characteristic peak, the position and the size of the characteristic peak are recorded, and then variables are reset to tempmax = min (z), leftmin = z (k); if not, judging whether z (k) is smaller than leftmin, and if so, then leftmin = z (k).
Through the process of the step (2.3), the position and size information of each characteristic peak can be extracted from the Raman spectrum data.
The invention has the beneficial effects that:
(1) The method is insensitive to baseline drift and outliers, can accurately estimate the noise statistical characteristics of the spectrum without manually selecting regions, and provides an objective and reasonable judgment threshold for characteristic peak identification;
(2) The automation of spectral peak identification can be realized without manually setting any parameter, and the background removal processing of the Raman spectrum is not required in advance, so that the loss of spectral information caused by the background removal operation is avoided, and the accuracy of spectral peak identification is high;
(3) The method has the advantages of simple calculation, low requirements on the storage space and the calculation capacity of the processor, and capability of being used on various hardware platforms including an embedded system.
Drawings
FIG. 1 is a general block diagram of the data processing of the present invention;
FIG. 2 is a detailed flow diagram of the data processing of the present invention;
FIG. 3 is a Raman spectrum of a PS plastic sample and a peak identification result thereof;
fig. 4 is a raman spectrogram of a PC acrylic sample and a peak recognition result thereof.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the drawings.
Conventional spectral peak identification methods generally include: baseline correction and spectral peak search, wherein the spectral peak search requires an operator to manually set a decision threshold. Experiments prove that different baseline correction algorithms and judgment threshold selection determine the spectrum peak identification result to a great extent. As shown in fig. 1, the spectral data in the invention is directly sent to the spectral peak identification unit without baseline correction, thereby avoiding the loss of spectral information caused by baseline correction; the spectral peak identification unit estimates the noise variance of the spectral data, the noise variance can be used as an evaluation basis for the quality of data collected by the spectrometer and can also be used as a judgment threshold of a rear-end spectral peak search algorithm, and the method is very visual and objective and greatly reduces the burden of operators.
As shown in fig. 2, the present invention provides a raman spectrum characteristic peak identification method based on robust noise variance estimation, which specifically includes the following steps:
1. assuming that the mean obedience of the random variable ε is 0 and the variance is σ 2 The probability density function of the gaussian distribution of (1) is:
the percentile p (x) is known to refer to the cumulative probability that the random variable epsilon is smaller than the percentile x, i.e.:
according to the definition of the error function:
the following can be obtained:
further, the method can be obtained as follows:
due to the inverse error function erf -1 (2 p-1) is an odd function, and the value range of 2p-1 is [ -1,1]So only the percentile x needs to be given in percentile 2 p-1E [ -1,0](i.e., p E [0,0.5)]) Values within the range can determine the complete profile.
The method takes Gaussian noise with the mean value of 0 and the variance of 1 as reference, and belongs to [0,0.5 ] in percentile p (x)]Taking m points in the range to form a percentile vector p 0 The percentile vector can be obtained
2. The Raman spectrum data vector x is respectively subjected to 1,2, …, n-order forward difference operation and normalization, and a difference data vector x can be obtained 1 ,x 2 ,…,x n ；
3. I =1:n is operated as follows:
3.1 pairs of x i Sorting according to the sequence from small to large;
3.2 known of x 0 Is m, j =1:m is operated as follows:
3.2.1 hypothesis x i Is q, then x is ordered i Percentile vector corresponding to each element in (1) Wherein τ =1,2, …, q,0<κ&And (lt) 1. Note p 0 (j) Is p 0 By the j-th element of (1) at p i Linear interpolation between adjacent elements to obtain p i ＝p 0 (j) And p i ＝1-p 0 (j) Corresponding to x i Are respectively a percentile x i,j And x' i,j ；
3.2.2 calculating x i At p i ＝p 0 (j) Standard deviation of time-dependent noise estimate
3.3 take σ i,j (j =1,2, …, m) as the median x i Is estimated as the standard deviation sigma of the noise i ；
4. Take sigma i The median of (i =1,2, …, n) is taken as the noise estimation standard deviation σ of the raman spectrum data vector x.
5. First order difference data vector x at step 2 above 1 Finding out data of positive and negative symbols jumping before and after, wherein the data correspond to Raman spectrum peaks or valleys, and forming a new vector z by the data;
6. determining whether the first element in z is a peak or a valley, i.e., whether z (1) is greater than z (2): if yes, k =0; if not, k =1, thus ensuring that the following cycle starts from one peak;
7. the variables tempmax = min (z) and leftmin = x (1) are defined for storing temporary peaks and left valleys, respectively. If z has a length of l, when k < l, the following cycle is performed:
7.1 k = k +1, and determines whether z (k) is greater than tempmax and leftmin + threshold: if yes, tempmax = z (k), wherein threshold = r σ represents a spectrum peak judgment threshold (usually, r is greater than or equal to 6);
7.2 k = k +1, and determines whether tempmax is greater than z (k) + threshold: if yes, tempmax is a spectral characteristic peak, the position and the size of the characteristic peak are recorded, and then variables are reset to tempmax = min (z), leftmin = z (k); if not, judging whether z (k) is smaller than leftmin: if yes, leftmin = z (k).
Through the process, the position and size information of each characteristic peak can be extracted from the Raman spectrum data, and then the judgment and identification of unknown samples can be realized by establishing a standard database for material identification and a search algorithm.
Example (b):
taking the data of the PS plastic and PC acrylic samples collected by the raman spectrometer as an example, the original spectra are shown in fig. 3 and 4, respectively. As can be seen from the figure, the two materials have different characteristic spectral lines, but the baseline generates a certain shift due to the influence of the fluorescence background.
Firstly, the robust noise variance estimation method provided by the invention is utilized to process the spectral data, and a percentile vector p is taken 0 = {0.05,0.10,0,15,0.20, …,0.40}, κ =0.5, raman spectral noise estimation standard deviation σ of PS plastic can be obtained 1 =38.9859, raman spectral noise estimation standard deviation σ of pc acrylic 2 =35.8535. In order to verify whether the noise standard deviation estimation results are reasonable, data in the range of 1600-2500 in fig. 3 and the range of 1700' 1 =38.1571, noise standard deviation calculation result of PC acrylic is σ' 2 =34.8209, which is substantially consistent with the robust noise variance estimation result proposed by the present invention. Then, r =6, that is, 6 times of noise estimation standard deviation is taken as a judgment threshold of a spectral peak, the spectrum is further processed by using the characteristic peak search algorithm provided by the present invention, the searched characteristic peak is marked in the spectrogram by a small circle, and the final result is shown in fig. 3 and fig. 4. According to the graph, the Raman spectrum characteristic peak identification method based on robust noise variance estimation can effectively identify the characteristic peak of each spectrum.
Claims (2)
1. A Raman spectrum characteristic peak identification method based on robust noise variance estimation is characterized by comprising the following steps:
(1) Determining a reference percentile and a percentile thereof by taking Gaussian noise with a mean value of 0 and a variance of 1 as a reference; carrying out forward difference operation and normalization on the Raman spectrum data, sequencing the normalized data from small to large, calculating percentiles of the data, then obtaining the percentile corresponding to the reference percentile through linear interpolation, and dividing the percentile by the reference percentile to obtain a series of noise standard deviations, and taking the median of the standard deviations as the noise estimation standard deviation sigma of the spectrum data;
(2) Obtaining peak values and valley values of Raman spectrum data through first-order derivation, comparing each peak value with the minimum valley values on the left side and the right side of the peak value, and if the noise standard deviation sigma is larger than r times, determining that the peak value is a characteristic peak of the Raman spectrum;
the step (1) is specifically as follows:
(1.1) assume that the random variable ε obeys a mean of 0 and a variance σ 2 The probability density function of the gaussian distribution of (1) is:
the percentile p (x) is known to refer to the cumulative probability that the random variable epsilon is smaller than the percentile x, i.e.:
according to the definition of the error function:
the following can be obtained:
further, the method can be obtained as follows:
taking Gaussian noise with mean value of 0 and variance of 1 as reference, and determining the percentage position p (x) is in the range of [0,0.5 ]]Taking m points in the range to form a percentile vector p 0 The percentile vector can be obtained
(1.2) respectively carrying out 1,2, …, n-order forward difference operation on the Raman spectrum data vector x and normalizing to obtain a difference data vector x 1 ,x 2 ,…,x n ；
(1.3) performing the following on i = 1:n:
(1.3.1) to x i Sorting according to the sequence from small to large;
(1.3.2) known x 0 Is m, j =1:m is operated as follows:
(1.3.2.1) hypothesis x i Is q, then x is ordered i The percentile vector corresponding to each element in (1)Wherein τ =1,2, …, q,0<κ&1; note p 0 (j) Is p 0 By the j-th element of (1) at p i Linear interpolation between adjacent elements to obtain p i ＝p 0 (j) And p i ＝1-p 0 (j) Corresponding to x i Are respectively a percentile x i,j And x' i,j ；
(1.3.2.2) calculation of x i At p i ＝p 0 (j) Standard deviation of time-dependent noise estimate
(1.3.3) taking σ i,j (j =1,2, …, m) as the median x i Is estimated as the standard deviation sigma of the noise i ；
(1.4) taking σ i The median of (i =1,2, …, n) is taken as the noise estimation standard deviation σ of the raman spectrum data vector x.
2. The method for identifying the Raman spectrum characteristic peak based on the robust noise variance estimation according to claim 1, wherein the step (2) is specifically as follows:
(2.1) carrying out first-order derivation on the Raman spectrum data to obtain the peak value and the valley value of the Raman spectrum data, and forming a new vector z by the peak value and the valley value;
(2.2) determining whether the first element in z is a peak or a valley, i.e. whether z (1) is greater than z (2): if yes, k =0; if not, k =1, thus ensuring that the following cycle starts from one peak;
(2.3) defining variables tempmax = min (z) and leftmin = x (1), tempmax representing a provisional peak and leftmin representing a left valley; if z has a length of l, when k < l, the following cycle is performed:
(2.3.1) k = k +1, and determines whether z (k) is greater than tempmax and leftmin + threshold: if yes, tempmax = z (k), wherein threshold = r σ represents a spectral peak judgment threshold;
(2.3.2) k = k +1, and determines whether tempmax is greater than z (k) + threshold: if yes, tempmax is a spectral characteristic peak, the position and the size of the characteristic peak are recorded, and then variables are reset to tempmax = min (z), leftmin = z (k); if not, judging whether z (k) is smaller than leftmin, if so, then leftmin = z (k);
through the process of the step (2.3), the position and size information of each characteristic peak can be extracted from the Raman spectrum data.
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| CN114166814A (en) * | 2021-05-25 | 2022-03-11 | 北京理工大学 | Raman spectrum peak identification method based on dual-scale correlation operation |
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