Spectrum baseline processing and linear fitting method based on pseudo Voigt model

Abstract

The invention discloses a baseline processing method for a spectrum based on a pseudo Voigt model, and relates to the technical field of spectral measurement analysis, spectral data is modeled through a Non-negative Matrix Factorization (Non-negative Matrix Factorization) method, meanwhile, a pseudo Voigt function spectral peak model is used, in the non-negative Matrix Factorization method, an independent normal noise model is assumed, and the spectral data are subjected to spectral data processing through a non-negative Matrix Factorization model. Therefore, the requirements of high-precision instruments and equipment are met, and the method is suitable for precision improvement of other spectral measurement methods. And the central peak value of the spectral line can be directly obtained. In addition, the pseudo Voigt method further provides the confidence coefficient of the number of peak values, and the number and accuracy of parameter extraction are greatly improved.

Description

Technical Field

[0001] The invention relates to the technical field of spectrum measurement, and in particular to a spectrum baseline processing method based on a pseudo-Voigt model. Background Art

[0002] With the advancement of spectral absorption technology and the improvement of laser equipment, this technology has been widely used in key fields such as industry, medical treatment and environmental protection. However, the demand for trace gas detection in these fields is extremely high, and conventional methods are difficult to meet. In recent years, due to the intensification of environmental pollution, global temperatures have risen year by year, and accurate detection of atmospheric components has become crucial. Spectral absorption technology has become one of the powerful tools for estimating the concentration of greenhouse gases in the atmosphere due to its high accuracy, and the research of related spectral instruments has therefore become a global focus. In addition, each pixel molecule in the atmosphere corresponds to a specific concentration, which is called "fractional abundance". They must all be non-negative values, and their sum must be equal to 1. When calculating reflectivity, it can be regarded as linear using the Lambert-Beer law. As for those nonlinear parts, they are generally omitted because of their small impact and the possibility of increasing the complexity of model construction. Now various research and other industries have high requirements for the sensitivity of detecting trace amounts of various substances, which are difficult to meet with general measurement methods. Therefore, it is urgent to improve this shortcoming. The present invention is to study and improve the existing algorithm deficiencies and provide a spectral signal processing method. Summary of the invention

[0003] The purpose of the present invention is to provide a baseline processing method for spectra based on the pseudo-Voigt model to improve the precision and accuracy, thereby meeting the needs of high-precision instruments and equipment, and being applicable to the precision improvement of other spectral measurement methods, and solving the problems raised in the above background technology. To achieve the above purpose, the present invention provides the following technical solutions: The present invention proposes a baseline processing method for spectrum based on pseudo-Voigt model, establishes pseudo-Voigt algorithm model, and applies conjugate prior The conditional distribution of the parameters is sampled by Gibbs sampling. In the first step, as in the setting of non-negative matrix factorization methods, an independent normal noise model is assumed with accuracy and mean , the mean is modeled by the sum of K pseudo-Voigt-shaped components and a background component. The second step is to define the Voigt function: . V is the wave number The center has parameters c, and The third step is to substitute the established Voigt function into the non-negative matrix factorization method. is the magnitude associated with a component and a particular observation; is the common background spectrum; and is the background amplitude associated with a particular observation. Therefore, the pseudo-Voigt line model is given by , : In the fourth step, use the following prior parameter function: where N+ represents a normal distribution truncated to a positive real number. Here is given a fuzzy uniform prior, is exponential, reflecting the expected small number of peaks that the observed spectra may contain, while and The parameters are given relatively flexible truncated normal priors: they must be positive, allowing their other hyperparameters to be chosen to determine the location and width of the spectral peaks, or to be set to ambiguous values ​​in the absence of prior information. The background component allows the selection of other hyperparameters based on prior information, all under independent and identical distribution: The conditional distribution of the weight of the pseudo-Voigt function is proportional to the product of the normal distribution and the exponential distribution. Therefore, the resulting distribution is a truncated normal distribution, which is positive, has a symmetrical center and height. In summary, the above steps can be integrated into the following formula: Likewise, the conditional distribution of the background signal is also a truncated normal distribution. Due to the symmetry of the likelihood function, The conditional distribution of is almost the same as described previously. The parameters of the pseudo-Voigt applied here are selected using the Metropolis-Hastings algorithm. For the noise precision parameter , and the corresponding standard results are also obtained, where is the shape parameter of the conjugate prior distribution, and is the rate parameter: The present invention has the following beneficial effects: The spectral data is modeled by the non-negative matrix factorization (Non-negative Matrix Factorization) method, and the pseudo-Voigt function spectral peak model is used. In the non-negative matrix factorization method, an independent normal noise model is assumed to improve the precision and accuracy, so as to meet the needs of high-precision instruments and equipment, and to improve the accuracy of other spectral measurement methods. The central peak of the spectral line can be directly obtained. In addition, the pseudo-Voigt method also provides the confidence of the number of peaks, which greatly improves the number and accuracy of parameter extraction. 1. Based on the basic method of the NMF model, it ensures that the results meet the advantages of non-negativity constraints, partial decomposition, easy solvability, stability and adaptability, and reduces the spatial dimension. 2. The basic function is replaced by the Voigt function, which can accurately depict the spectral line and has good flexibility, making it very suitable for the analysis of complex systems. In terms of spectral fitting and interpretation, the Voigt function shows significant advantages. 3. Combining these two model methods, not only the non-negativity and partial decomposition characteristics of NMF are retained, but also the accurate spectral line depiction ability and flexibility of the Voigt function are retained. 4. In the process of setting the model parameters, the meaning of each parameter is very clear, and these settings are also reflected in the sum formula of the pseudo-Voigt function. 5. By adopting the Metropolis-Hastings algorithm to select all parameters, this probability distribution sampling algorithm based on the MCMC method can more accurately resolve complex distributions. BRIEF DESCRIPTION OF THE DRAWINGS

[0004] Figure 1 Generate flow chart with test data; Figure 2 Test data wave number-measurement index diagram; Figure 3 The test data was restored by non-negative matrix decomposition and pseudo-Voigt processing, and the results were compared with the true underlying spectrum; Figure 4 The spectrum data itself is a sampling result wave number-measurement index diagram; Figure 5 Residual distribution line graph of spectral data sampling results; Figure 6 Peak diagram of spectral data after fitting with pseudo-Voigt model. DETAILED DESCRIPTION

[0005] The following embodiments of the present invention are described in further detail in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention. Example 1

[0006] like Figure 1-Figure 6 As shown, In practice, the proposed pseudo-Voigt method is based on the determinant, inspired by the pp volume in the following formula, that is, a specific volume regularization term (in the context of hyperspectral image decomposition, the volume regularization term is a technique used to encourage the sparsity of the solution, that is, to make the elements in the decomposed matrix as zero as possible. This regularization helps to ensure that the decomposed components (end members) and their concentrations (fractional abundances) are sparse to some extent, that is, as few different end members as possible are used to explain the changes in the data): The additive constraint on fractional abundance is modeled as a uniform prior on the unit simplex. For this purpose, a fast Gibbs sampling method is designed. Following the sparse non-negative matrix factorization model method, a similar algorithm is developed for learning the pseudo-Voigt model, which is the main content of the present invention. The main technical background of the present invention is based on the non-negative matrix factorization method (i.e. NMF), in which the spectrum is modeled as a scaled sum of K basis spectra learned from the observed data. The following is a brief introduction to the NMF method: use Represents the observed data: an array of positive real numbers, where is the wave number in the observed spectrum n The measured amplitude is Denote the number of observed wavelengths and n the number of observed spectra. Non-negative Matrix Factorization assumes that each observed spectrum can be decomposed into a weighted sum of constituent basis spectra. Using the normal observation noise model, the data array can be modeled as the product of two matrices S and A, where the K columns of S are the basis spectra and each column of A contains their amplitudes for a given observed spectrum. Assuming a standard shape parameter for noise accuracy is , the rate parameter is The conjugate Gamma prior distribution of , and independent exponential priors (independent and identically distributed) for the spectrum and its amplitude, set to and These priors reflect the constraint that the spectra and their amplitudes are non-negative, and correspond to a Bayesian sparse non-negative matrix factorization model. In the non-negative matrix decomposition method, a standard conjugate Gamma prior of noise accuracy is assumed. The name of this linear fitting method is tentatively named "Baseline processing and linear fitting of spectra based on pseudo-Voigt function". The present invention proposes a spectral signal processing method. Following the same method as NMF, the base spectrum is replaced by the Voigt function. We have developed a new algorithm for learning the Voigt model, which is part of the content of this patent technology: establishing a pseudo-Voigt algorithm model. We apply the conjugate prior The conditional distribution of the parameters is sampled by Gibbs sampling. In the first step, as in the setting of non-negative matrix factorization methods, we assume an independent normal noise model with accuracy and mean , the mean is modeled by the sum of K pseudo-Voigt-shaped components and a background component. The second step is to define the Voigt function: . V is the wave number The center has parameters c, and The third step is to substitute the established Voigt function into the non-negative matrix factorization method. is the magnitude associated with a component and a particular observation; is the common background spectrum; and is the background amplitude associated with a particular observation. Therefore, the pseudo-Voigt line model is given by , : In the fourth step, we use the following prior parameter function: where N+ represents a normal distribution truncated to a positive real number. Here is given a fuzzy uniform prior, is exponential, reflecting the expected small number of peaks that the observed spectra may contain, while and The parameters are given relatively flexible truncated normal priors: they must be positive, allowing their other hyperparameters to be chosen to determine the location and width of the spectral peaks, or to be set to ambiguous values ​​in the absence of prior information. The background component allows the selection of other hyperparameters based on prior information, all under independent and identical distribution: The conditional distribution of the weights of the pseudo-Voigt function is proportional to the product of the normal distribution and the exponential distribution. The resulting distribution is therefore a truncated normal distribution, positive, with a symmetrical center and height.

[0007] In summary, we can integrate the above steps into the following formula: Likewise, the conditional distribution of the background signal is also a truncated normal distribution. Due to the symmetry of the likelihood function, The conditional distribution of is almost the same as described previously. The parameters of the pseudo-Voigt applied here are selected using the Metropolis-Hastings algorithm. For the noise precision parameter , we also obtained the corresponding standard results, where is the shape parameter of the conjugate prior distribution, and is the rate parameter: Pseudo-Voigt fitting usually requires the help of computer algorithms and spectral analysis software. The pseudo-Voigt parameters obtained by fitting can provide detailed information about the molecular state and concentration, thereby improving the practicality of absorption spectroscopy technology in scientific research and technological applications. Therefore, using the pseudo-Voigt model as a constrained source separation model has become a more mature linear fitting processing method. The model can directly and reliably identify the off-axis integral cavity output spectral mode, and its overall performance is similar to that of the state-of-the-art non-negative matrix factorization method. However, the model provides a better explanation and is a step towards realizing the detection of gas molecule concentration using absorption spectroscopy in real environments. A Bayesian non-negative matrix factorization method based on volume prior is proposed for the inverse inference of gas concentration under spectral absorption technology for the analysis of high-resolution spectral images. At the same time, a similar algorithm is developed based on the model of sparse non-negative matrix factorization to deal with the pseudo-Voigt model. This pseudo-Voigt method performs well on simulated data, and its performance is comparable to that of state-of-the-art algorithms such as non-negative matrix factorization (NMF) and maximum likelihood method (MCR). The advantage of the pseudo-Voigt model is that it can be fitted with the center of the spectral peak as a model parameter without additional processing. In addition, another major advantage provided by the pseudo-Voigt model is that it can restore a spectrum with a Voigt shape, which means that the real spectral peak has been successfully restored. The spectrum generated by the non-negative matrix decomposition model requires additional processing to extract the same information. This method is applicable to the fitting and research of various types of spectral lines, and has a wide range of applications. The embodiments of the present invention are given for the sake of example and description, and are not exhaustive or limit the present invention to the disclosed form. Many modifications and changes are obvious to those of ordinary skill in the art. Selecting and describing embodiments is to better illustrate the principles and practical applications of the present invention, and to enable those of ordinary skill in the art to understand the present invention and design various embodiments with various modifications suitable for specific purposes.

Claims

1. A method for processing spectrum baseline based on pseudo-Voigt model, characterized by: The method comprises the following steps: S1. Assume an independent normal noise model with accuracy and mean , the mean is modeled by the sum of K pseudo-Voigt-shaped components and one background component; S2. Define the Voigt function: , where V is the wave number The center has parameters c, and The pseudo-Voigt shape component of ; S3, Substitute the established Voigt function into the non-negative matrix decomposition method, is the magnitude associated with a component and a particular observation; is the common background spectrum; and is the background amplitude associated with a particular observation; S4. Use the following a priori parameter function: , where N+ represents a normal distribution truncated to a positive real number.

2. The method for processing spectrum baseline based on the pseudo-Voigt model according to claim 1, characterized in that: Said is given a fuzzy uniform prior, is exponential, reflecting the expected small number of peaks that the observed spectra may contain, while and The parameters were given relatively flexible truncated normal prior values.

3. The method for processing spectrum baseline based on pseudo-Voigt model according to claim 1, characterized in that: The background component described allows the selection of other hyperparameters based on prior information, all of which are independent and identically distributed: , where the conditional distribution of the weights of the pseudo-Voigt function is proportional to the product of the normal distribution and the exponential distribution.

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