Method for generating synthetic spectral data

Abstract

A computer-implemented method for synthesizing spectral data, comprising the steps of:-acquiring (110) a set of spectral data using a spectroscopy method, each spectral data associating a spectrum with a sample having a given chemical composition,-determining (130) a theoretical model of the distribution of the intensities of the spectrum for each wavelength channel of the spectrum, -generating (140) a set of resultant spectral data (150) by generating a randomly rendered intensity for each wavelength channel of the spectrum according to the probability distribution of the theoretical model.

Description

Technical Field

[0001] The present invention relates to the field of analysis of spectral data, i.e. data having a plurality of intensity values ​​in various wavelength channels or spectral bands. The data may be multispectral or hyperspectral data, where the number of spectral bands varies from tens to hundreds and the data originate from emission or absorption spectra of chemical species comprising thousands of wavelength channels. The present invention is applicable to any type of spectral analysis, as long as a large number of copies of the input data are necessary and these copies are not readily available in large quantities. The present invention is particularly, but not exclusively, applicable to quantitative analysis (e.g. determination of concentration) or for classifying a sample for which the spectral data are measured.

[0002] More specifically, the present invention relates to a method for synthesizing synthetic spectral data so as to provide learning data for a machine learning engine for analyzing species associated with the spectral data, particularly but not exclusively, for quantitative or qualitative analysis of chemical species.

[0003] One possible application of the invention involves determining the concentration of chemical elements or classifying samples based on spectral data, such as acquired by Laser Induced Breakdown Spectroscopy (LIBS) technology. The invention is not limited to this particular technology and can be applied to any type of spectroscopic technology that produces multispectral or hyperspectral data or spectral data on the emission or absorption of chemical species.

[0004] The present invention is applicable to any type of spectral analysis. In fact, the present invention can be used in the context of quantitative analysis, which includes, for example, predicting the quantity characterizing the sample to be analyzed. It is also applicable to qualitative analysis, such as segmenting or identifying scenes or graphs using techniques that produce multispectral or hyperspectral images or spectra of chemical species, which are obtained using spectroscopic techniques (such as LIBS, etc.). In addition, it can also be applied to generate samples for super-resolution and other unsupervised learning techniques. The difference is only the nature of the variables to be predicted or processed, which are, for example, continuous in terms of quantification (e.g., the concentration of a species), discrete in terms of classification (e.g., class or species labels), or of the same type as the input data for unsupervised analysis (e.g., the intensity values ​​of the spectral bands of pixels in image super-resolution). Background Art

[0005] In the context of spectral data, various processing methods are used for various types of analysis. In particular, multivariate deep learning methods, mainly based on artificial neural networks, have been explored and used, for example, for quantitative analysis (calibration, regression) or for classification of samples. Examples of such methods are described in references [1]-[3]. However, these algorithms are generally characterized by their ability to learn based on a very large number of realizations (spectra), which limits their use when the available data set contains a limited number of realizations.

[0006] Unlike the most widely used approach based on fully connected neural networks proposed in [4], recent developments in spectral signature analysis have led to the introduction of architectures inspired by convolutional neural network-based object detection and image classification algorithms (see, for example, [5] and [6]). Although all neural network models present the same problem, this type of architecture is specifically designed to learn the model based on training data, which requires a lot of implementation in order for the model to correctly learn to associate input data with output data, for example in the context of supervised learning. As an example, a standard dataset for image processing contains 10 4 to 10 6 The number of training data is often as small as 100 samples (see ), while conventional LIBS datasets contain tens or hundreds of spectra (see [7]), or thousands to tens of thousands of LIBS maps (see [8]). This observation is also true for other types of spectra.

[0007] Acquiring large amounts of spectral data is a problem to be solved. For example, in the context of LIBS spectroscopy, the collection of large numbers of spectra can be prevented by damaging the surface of the sample or by too small an available surface area or even by simple time reasons (e.g., not being able to probe a given area quickly enough).

[0008] Besides LIBS spectroscopy, the lack of training spectral data may also be attributed to the high cost of obtaining a sufficient amount of labeled data for learning.

[0009] Therefore, there is a need to substantially increase the amount of learning data available for spectral data.

[0010] The lack of implementations in the context of spectral analysis has rarely been addressed in the literature. Some of the work reviewed below aims to enrich the information provided to the architecture (e.g. neural network) or focus only on arbitrarily relevant parts of the information, but from the perspective of deep learning techniques, the lack of a large number of different implementations (i.e. spectra) may still lead to problems of overfitting or poor generalization performance.

[0011] In general, data augmentation and synthesis are methods used in the context of deep learning, for example in the context of computer vision. The basic idea is to create an oversampling of the input data in a non-trivial way. Conventionally, with data augmentation, the learning data is enriched with transformations (rotations, magnifications, reflections, etc.) of the training data in order to produce new implementations in most deep learning applications such as image classification, time series, natural language processing, etc. (see, for example, [9],

[10] ,

[12] , and

[18] ). This process makes it possible to produce an arbitrary number of examples that are directly based on the distribution of the training data (except for constraints related to the size or form of the data). The effect is to regularize and stabilize the learning, resulting in models that generalize better in the context of classification or for regression tasks. The synthesis of new data is often used in image processing (e.g., super-resolution)

[11] . In addition, the development of deep learning models on smaller datasets (especially spectral datasets) or in the context of single-shot learning in computer vision is a highly topical problem.

[0012] For example, reference [2] relates to a “data enhancement” method for LIBS technology that uses time-resolved spectra of chemical elements for multivariate analysis using shallow neural networks. In other words, for each pit on the surface, instead of a single spectral feature, multiple spectra are recorded at different times of laser emission. Then, for each pit, a cascade of these spectra is used as a representative of the measurement, which now has an additional time direction and is therefore called a “time-resolved spectrum”. The data set used for the analysis of the neural network thus consists of a collection of time-resolved spectra. Here, the term data “enhancement” is not used correctly. In fact, the number of implementations is not really increased, but the amount of information in a given implementation is increased. It can be said that the quality of the data has certainly been enhanced, even if no new data has been generated. The analysis proposed in reference [3] uses the same type of time-resolved data without explicitly mentioning “data enhancement”.

[0013] The methods described in references

[13] and

[14] use deep learning methods based on convolutional neural networks to analyze LIBS data. However, the problem of data enhancement is not addressed therein. Recently, the authors in

[15] introduced data enhancement techniques derived directly from standard deep learning image processing methods. Their analysis is again based on convolutional neural networks and focuses on basic two-dimensional maps with a spatial resolution of 150 μm between the pits. Starting from the maps obtained based on the intensities of preselected lines, they use slicing, rebinning, image filters (e.g., adding Gaussian noise and median filters) and reflections to generate additional learning data to classify the samples. It should be noted that in this case the authors do not directly use the spectral information contained in the original data, but rather they extract the maps in order to exploit the spatial information therein. The enhancement is then performed directly on the maps. In the context of image classification, and for the purposes shown by the authors, the techniques used in the article can improve the generalization ability of the classifier network. However, for more general purposes, the use of slicing and reassembling to generate new images does not directly modify the data associated with each pixel (i.e., associated with each pit), but rather reassembles them via the map: this data augmentation technique results in an oversampling of the data collected in the intensity map, rather than the production of a spectrum. For example, other types of analysis, such as multivariate regression for quantitative analysis, may not benefit greatly from this treatment, as it may be considered a simple duplication of the input data to the regression network (although it may result in a slight performance improvement). Furthermore, very small basis maps, where only a small number of laser shots are performed, may only slightly benefit from this, as the number of relevant transformations is significantly reduced.

[0014] The review article

[16] presents the concept of data augmentation by suggesting generating an arbitrary number of spectra by adding random noise to each experimental spectrum. However, the implementation of this technique is not shown in the article, and no definition of random noise is proposed.

[0015] Other analyses described in Ref.

[17] use various types of LIBS spectral data, for example only considering specific wavelength channels for analysis in order to reduce the size of the training data relative to the size of the neural network model. This approach makes it possible to use simplified versions of the input data, where it is assumed that relevant information has been extracted beforehand to improve the analysis. However, due to the limited amount of available data, this can still lead to problems of overfitting and poor generalization, and performance can be reduced due to information loss caused by the prior selection of the input data.

[0016] In the context of the analysis of multispectral or hyperspectral images, one can also mention traditional data augmentation methods, which are usually defined for tasks such as object detection or semantic segmentation (e.g., Ref. [9] gives examples and a full literature of the prior art). However, in this context, the purpose of the analysis is different and is usually limited to scene classification or characterization (similarly, these techniques have also been applied in the context of LIBS spectroscopy in

[15] , as mentioned above). Summary of the invention

[0017] The present invention aims to overcome the limitations of the prior art by providing a method for synthesizing spectral data that allows better exploitation of deep learning algorithms and, more generally, any algorithm that requires a large amount of input spectral data. This provision allows for more efficient algorithms that are able to reduce prediction uncertainty and build reliable models but require a large amount of learning data.

[0018] The present invention proposes a method for synthesizing spectral data, which can be used for learning as regularization and oversampling of training data, or directly as learning data. The synthesis method according to the present invention is based on experimental data for modeling signal distribution.

[0019] This distribution can then be used to generate an arbitrary number of spectra that statistically represent the real data. This new dataset can be used to train deep learning algorithms that require large amounts of data: since these data model the true distribution, the algorithm maintains its predictive power and its accuracy on new data experimentally acquired using spectroscopy methods.

[0020] Compared to some techniques from the prior art, the present invention focuses on generating an arbitrary number of truly different training spectral data, statistically representing the experimental data set, without placing constraints on the number of wavelength channels or spectral bands contained in the spectrum.

[0021] The present invention proposes a technique different from the prior art for synthesizing an arbitrary number of spectra. Since adding random noise directly to a limited number of spectra can modify the learned distribution (that is, it can change the nature of the distribution considering the relatively small number of implementations), the spectra are first modeled based on a known or estimated statistical distribution (for example, using a kernel density estimation method), and then the spectra are generated according to their statistical distribution so as to expand the feature space of the input data, that is, to cover a larger part of the domain of the distribution. In this way, the generated data set always has a statistical representation of the original data of an arbitrary large number of copies. Random noise (which is, for example, Gaussian or uniform in nature) can then be added separately to each synthetic copy in order to improve the generalization ability of the algorithm. The use of synthetic data provides a sufficiently large amount of input data so that the addition of noise is negligible on average without any overall effect on the data distribution. In contrast, adding noise to a limited number of data may significantly change the nature of the data and interfere with the learning of the algorithm. Generation based on statistical distributions ensures that each copy is a different representation of the training data, thereby giving the algorithm the ability to learn a larger number of features, and the number of copies is large enough to ensure that the learned distribution is statistically representative of the sample being analyzed.

[0022] Unlike the prior art, the present invention proposes an enhanced method that is directly linked to the properties of the spectral features in order to solve the problem of the number of spectra available for learning. Since no prior knowledge about the type of spectral data is required (e.g., it can be estimated), the same principles presented here can be extended to any type of multi-spectral or hyper-spectral data without having to be linked to LIBS technology.

[0023] The invention relates to a method for modeling the spectral distribution synthesized from real data in comparison with experimental data. The invention also provides a step of adding random noise from the synthesized data, which is different from adding noise directly to the original data. This technique makes it possible to generate an arbitrary amount of data that effectively represents a sample, and then modify the spectral intensity without changing the original distribution of the experimental data on average (in application, it only consists of a few implementations and does not represent the real distribution of the data).

[0024] Unlike usual data augmentation techniques in computer vision, any transformation (shift, translation, reflection, expansion) applied to spectral data will of course change the physical significance of the spectrum: for example, a wavelength shift of an emission line assigned to one element may cause it to be assigned to another element. The present invention proposes to generate new learning spectra, that is, to synthesize learning data using a theoretical model of the real data distribution. In other words, spectral profiles experimentally obtained using spectroscopic methods are used to generate spectra that have the same distribution on average for each wavelength channel. This method makes it possible to solve the problem of the number of implementations (spectral features) without distorting the physical content of the spectrum. Spectra are generated using random extraction based on this distribution: this method can also cover a larger part of the space in which the original data is defined (for example, in the context of spectral data, the wavelength space).

[0025] A subject of the present invention is a computer-implemented method for synthesizing spectral data, comprising the following steps:

[0026] - using spectroscopic methods to obtain a set of spectral data, each of which associates a spectrum with a sample of a given chemical composition,

[0027] - determining a theoretical model of the distribution of the intensity of the spectrum for each wavelength channel of the spectrum,

[0028] - A set of synthetic spectral data is generated by generating randomly drawn intensities according to the probability distribution of the theoretical model for each wavelength channel of the spectrum.

[0029] According to a particular aspect of the invention, the theoretical model is based on a probability distribution according to a Poisson distribution parameterized by the intensities measured on the acquired spectra.

[0030] According to a particular aspect of the invention, the set of spectral data comprises a plurality of spectral measurements of the same sample, and the method comprises the step of determining an average spectrum of the set of measurements.

[0031] According to a particular aspect of the invention, synthetic spectral data are generated by adding noise values ​​to randomly drawn intensities, the noise values ​​being drawn according to a uniform distribution within an interval centered around the intensity and having a parameterizable width.

[0032] According to a particular aspect of the invention, synthetic spectral data are generated by adding noise values ​​to randomly drawn intensities, the noise values ​​being drawn according to a normal distribution centered about the intensity, whose standard deviation is a modifiable parameter.

[0033] According to a particular aspect of the invention, the spectral data are acquired by laser induced breakdown spectroscopy.

[0034] According to a particular aspect of the invention, the spectral data are derived from emission or absorption spectra of chemical species.

[0035] Another subject of the invention is a method for quantitative or qualitative analysis of spectral data, comprising the following steps:

[0036] - generating a set of synthetic spectral data by executing the method for synthesizing spectral data according to the present invention,

[0037] - Train a machine learning model based on the generated synthetic spectral data,

[0038] -Use the trained model to perform quantitative or qualitative analysis of spectral data.

[0039] Another subject of the present invention is a computer program comprising instructions for executing the method according to the present invention when the program is executed by a processor, and also comprises a processor-readable recording medium on which is recorded the program comprising instructions for executing the method according to the present invention when the program is executed by a processor. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Other features and advantages of the present invention will become more apparent from the following description read in conjunction with the following drawings.

[0041] Figure 1 shows an example of spectral data characterizing a sample containing various chemical species,

[0042] Figure 2 A diagram showing steps for implementing a method for generating synthetic spectral data according to the present invention,

[0043] Figure 3 A flowchart showing the steps of a method for implementing machine learning of a spectral data analysis model according to the present invention is shown,

[0044] Figure 4 The quantile-quantile plots of the real and synthetic distributions of the cement sample with NaCl added (Type I) are shown,

[0045] Figure 5a An example of an average spectrum is shown, Figure 5b shows a diagram of the results obtained by the present invention using Gaussian modeling, Figure 5c shows a diagram of the results obtained by the present invention using "top hat" kernel based modeling, Figure 5a-5c A comparative diagram of the results obtained by the present invention using Gaussian modeling and modeling based on a "top hat" kernel is shown. DETAILED DESCRIPTION

[0046] The LIBS technique allows material analysis by laser ablation and spectroscopy. The data acquired via this technique are spectral data corresponding to an emission spectrum for each point of the area, the emission spectrum comprising atomic lines that are characteristic of the elementary chemical composition of the sample.

[0047] LIBS spectral data are obtained by focusing a laser beam on a point of the surface to be analyzed. The emission of the plasma generated by this focus is collected and processed by spectroscopy to obtain the spectrum of atomic lines. This process is iterated for each point of the area to be analyzed.

[0048] Figure 1 An example of a spectrum of atomic lines 101 obtained for a sample having a specific chemical composition is shown by way of illustration. Figure 1 In , spectral features of certain chemical elements (Ca, Al) corresponding to atomic lines in a given wavelength channel have been identified.

[0049] As explained in the foregoing, the present invention is intended to be based on Figure 1 One or more measurements of spectral data of the type described are used to generate synthetic spectral data.

[0050] exist Figure 2 The method according to the invention is described in .

[0051] A first step 110 consists in acquiring spectral data by means of an appropriate acquisition device, depending on the intended application. If the present application relates to, for example, a qualitative or quantitative analysis of a sample of material, the data are spectral data and are acquired, for example, by means of a spectrometric device, such as a laser-induced breakdown spectrometric device, or a device based on mass spectrometry coupled to laser ablation or ion beam or X-ray beam or synchrotron radiation induced or charged particle beam induced spectrometric techniques, or Raman or IR spectrometry. If the present application relates to a method for mapping a geographical area, multispectral or hyperspectral data are acquired, for example, by means of a multispectral or hyperspectral imaging sensor on a satellite payload. The present invention is more generally applicable to any other multispectral or hyperspectral data acquisition device, which makes it possible to generate a spectrum within a given wavelength range for a given sample.

[0052] The first step 110 may include measuring a single spectrum per sample or multiple spectra per sample.

[0053] In an optional step 121, the measured spectral data are preprocessed in order to estimate and correct any offset linked to the acquisition, to normalize the various measured spectra so that they are uniform with respect to each other and to eliminate blind spots if they exist. In other words, each measured spectrum can be normalized in various ways, such as using known emission / absorption lines or wavelength bands, using maximum intensity or using other methods. If multiple spectra are used that are assumed to represent the measurement, it is also possible to focus on a specific wavelength channel, taking into account the average intensity and discarding from the data set the spectra containing outliers for this channel. This preprocessing makes it possible to use only the spectra that are most representative of the sample, without having to model defects at the same time.

[0054] If multiple spectral measurements are made on the same sample, the spectra are averaged in step 122. In other words, multiple spectra representing the same sample can be used to model the distribution (for example, after multiple laser irradiations on the same sample in the context of the LIBS technique). The spectra used to generate the synthetic data are averaged in order to obtain a more accurate representation of the analyzed sample. In other words, instead of using a single spectrum as a representative of the sample, the spectral measurement can be replicated multiple times and synthesized using the average spectrum obtained from the sample. Taking into account possible average differences on the surface, this method makes it possible to have a more accurate representation of the sample. However, it should be noted that this implementation of the present invention is more specifically applicable to spectral data without the concept of an image, that is, to data where the spectral measurement can be repeated without changing the physical significance of the data (each spectrum must represent the same distribution). Applying this implementation to a multi-spectral or hyper-spectral map means that there are multiple implementations of the same image so that the contribution of a single pixel can be averaged. This application is not possible for the LIBS technique because the destructive nature of the interaction of the laser with the surface does not allow the measurement to be reproduced at the same location. On the other hand, for example, using a track mapping method to acquire a multi-spectral or hyper-spectral image makes it possible to replicate the same image multiple times.

[0055] In any case, experimental measurements of the spectrum were obtained.

[0056] Next, a model for the distribution of intensity values ​​of the spectral lines is determined based on experimental measurements (step 130 ).

[0057] In the case of spectral data acquired using the LIBS acquisition method, the main source of noise at low intensities and signal at high intensities are the photons that have hit the detector. Therefore, the distribution modeled on the photon counts can be used to estimate the actual distribution of the spectral data.

[0058] Therefore, the distribution model used is based on the formula Denotes the Poisson probability distribution of , where k is the variable of the distribution, which here is the intensity of the spectral line, and l is the parameter of the Poisson distribution.

[0059] If l n represents the parameter of the Poisson distribution of wavelength channel n, then this parameter also corresponds to the expected mean of the distribution of channel n. Therefore, in the context of the present invention, for each wavelength channel n, l is applied n =I n , that is, the peak of the probability distribution of the synthetic spectrum in channel n is equal to the intensity I recorded for the channel in the experimental spectrum n , which experimental spectrum is considered to model the synthetic spectrum (the spectrum provided at the input of step 130 , possibly averaged in step 122 ).

[0060] Next, in step 140, new synthetic spectrum data is generated based on the model obtained in step 130 for each wavelength channel n. The new synthetic spectrum is obtained by determining each intensity of the spectrum of each wavelength n by random drawing according to the intensity distribution model obtained in step 130. The random draw is calculated by inverting the cumulative distribution function and by using it to represent a random variable uniformly distributed in the interval [0,1] in the probability space. Therefore, any number of spectra having the same properties as the experimental spectrum 110 can be generated statistically.

[0061] As an illustrative example, Figure 4 The quantile-quantile plot of the real and synthetic distributions of cement samples with NaCl addition (Type I) is shown. The data was synthesized by modeling the strength using a Poisson distribution. The plot shows points aligned on the bisector of the first quadrant: the observed quantiles effectively overlap with the quantiles of the experimental distribution.

[0062] A set of synthetic spectral data 150 is then obtained, the number of which is larger than the number that could be realized experimentally. This set of synthetic data 150 can then be used as a learning set, which includes spectra that simultaneously represent the same distribution of the input data and different realizations of the experimental measurements (i.e., new data, independent of the experimental data).

[0063] In a variant embodiment of the present invention, instead of using a Poisson distribution to model the intensity of each wavelength channel, the distribution of the intensity of the spectrum can be modeled using, for example, a nonparametric kernel density estimation (KDE) method, as described, for example, in the reference M. Rosenblatt "Remarks on Some Nonparametric Estimates of a Density Function" Ann. Math. Statist. 27 (3) 832-837, September, 1956. In this variant, the kernel function K (z, h) is used to use a certain number of realizations (experimental spectra) To estimate the density f(*) of a random variable x (intensity, in the case of a spectrum). For each value of x use the function to estimate the form of f(x). The parameter a represents the bandwidth, which can be adapted by Improve the estimate of f(x).

[0064] The function f(x) can be estimated by various choices of the kernel K. In some variations that can be used for spectral analysis, one can choose (a "Gaussian" kernel) or for example K(x,h)∝θ(hx) (called a "top-hat" kernel), where θ is the Heaviside function. The choice of a usually depends on the type of data to be modeled: a smaller bandwidth allows a better fit of the kernel's profile to the data when there is a risk of generating oversampling effects. To choose a, for example, a quantile-quantile plot can be used to compare the distribution of the real data and the use of a spectral intensity density estimator. The distribution of synthetic data.

[0065] Figure 5a , Figure 5b and Figure 5c A comparison of the modeling of a cement sample (type I) using a Gaussian kernel and a "top hat" kernel with the addition of NaCl analyzed using the LIBS technique is shown. The average spectrum is 500 Figure 5a The various spectra 501, 502, 503, 504 obtained for the Gaussian kernel are shown in Figure 5b In Figure 5c Various spectra 510, 520, 530, 540 obtained for a "top hat" core are shown in FIG. Figure 5a-5c A comparison of the modeling of cement samples (type I) using Gaussian and "top hat" kernels with the addition of NaCl analyzed using the LIBS technique is shown. The average spectrum is represented as 500 in the figure.

[0066] Various spectra 501, 502, 503, 504 obtained for a Gaussian kernel are shown on the left side of the figure. Various spectra 510, 520, 530, 540 obtained for a "top hat" kernel are shown on the right side of the figure.

[0067] For each spectrum, the associated quantile-quantile plot is also shown.

[0068] In general, the data is best reproduced using low bandwidth values, as the quantiles align on the bisectors of the plot. Higher values ​​of a show the deviation of the quantiles at low and high intensities. This comparison also shows that the "top hat" kernel fits the data better for high values ​​of h. On the other hand, at low values ​​of a, the Gaussian kernel fits the data better.

[0069] In a variant embodiment, the synthetic distribution of the data can be made more realistic by adding an additional random noise source for each wavelength channel during the generation 140 of the synthetic data. Such a source is modeled as a difference in the number of photons reaching the detector.

[0070] Then, the spectral intensity with respect to wavelength is given by Given, where, for each wavelength channel n, Follow the parameter I nx Poisson distribution (That is, ), where I n is the experimentally recorded intensity for the channel (possibly averaged in step 122) and corresponds to The expected mean of the distribution of ), m is the noise parameter, which is chosen so that are numbers uniformly distributed in the interval [-m,m].

[0071] In a variant embodiment, it is possible to define Where m is the noise parameter, which is chosen so that N m is based on a centered at 1 and with standard deviation m (i.e. ) is a number distributed according to the normal law.

[0072] In a variant embodiment, the generated synthetic spectral data 150 may be added (step 160 ) to the measured input data 110 in order to construct a set of training data.

[0073] Alternatively, it is also possible to use only synthetic spectra 150 as a learning set, since the number of generated spectra is usually so much larger than the number of experimental data that the latter becomes statistically negligible.

[0074] A set of data obtained using the method according to the present invention can be used to train a machine learning engine, such as Figure 3 An example is shown in .

[0075] Synthetic spectral data are generated in step 301 based on the first training spectral data measured in step 300, and then used as learning data to train an analysis model in step 302. The analysis model may be aimed at quantitative analysis, such as estimating the concentration of chemical species in a sample based on analysis of its spectrum, or qualitative analysis, such as classifying the spectrum according to the type of sample.

[0076] The machine learning model is based, for example, on one or more convolutional neural networks or any other equivalent machine learning algorithm. The learning data can be used to perform oversampling and / or regularization of deep learning methods. References [9],

[10] ,

[12] illustrate various learning methods suitable for qualitative or quantitative analysis of spectral data.

[0077] Once the model has been trained, it can be used in step 303 to perform qualitative or quantitative analysis on new spectral data measured in step 304 .

[0078] The steps of the present invention may be implemented as a computer program including instructions for executing the present invention. The computer program may be recorded on a processor-readable recording medium.

[0079] References to computer programs that implement any of the above functions when executed are not limited to applications running on a single host computer. Instead, the terms computer program and software are used here in a general sense to refer to any type of computer code (e.g., application software, firmware, microcode, or any other form of computer instructions) that can be used to program one or more processors to implement various aspects of the technology described herein. Computing means or resources can be particularly distributed (cloud computing), possibly using peer-to-peer technology. The software code can be executed on any suitable processor (e.g., a microprocessor) or processor core or a group of processors that are provided in a single computing device or distributed between multiple computing devices (e.g., accessible in the environment of the device). The executable code of each program that allows a programmable device to implement a process according to the present invention can be stored in, for example, a hard drive or a read-only memory. Typically, one or more programs can be loaded into one of the storage devices of the device before being executed. The central processing unit can control and direct the execution of the instructions of one or more programs according to the present invention or part of the software code, wherein these instructions are stored in a hard drive or a read-only memory or other storage element described above.

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Claims

1. A computer-implemented method for synthesizing spectral data, comprising the following steps: - using a spectroscopic method to acquire (110) a set of spectral data, each spectral data associating a spectrum with a sample having a given chemical composition, each spectrum having a plurality of intensities associated with a wavelength channel, - determining (130) a theoretical model of the distribution of the intensity of the spectrum for each wavelength channel of the spectrum, - generating (140) a set of synthetic spectral data (150) by generating randomly drawn intensities for each wavelength channel of the spectrum according to the probability distribution of the theoretical model.

2. The method for synthesizing spectral data according to claim 1, wherein: The theoretical model is based on a probability distribution according to a Poisson distribution parameterized by the intensities measured on the acquired spectra.

3. A method for synthesizing spectral data according to any one of the preceding claims, wherein: The set of spectral data comprises a plurality of spectral measurements for the same sample, and the method comprises the step of determining an average spectrum of the set of measurements (122).

4. A method for synthesizing spectral data according to any one of the preceding claims, wherein: The synthetic spectral data is generated (140) by adding to the randomly drawn intensities noise values ​​drawn according to a uniform distribution within an interval centered about the intensities and having a parameterizable width.

5. A method for synthesizing spectral data according to any one of claims 1 to 3, wherein: The synthetic spectral data is generated (140) by adding a noise value to the randomly drawn intensities, the noise value being drawn according to a normal distribution centered about the intensities, the standard deviation of the noise value being a modifiable parameter.

6. A method for synthesizing spectral data according to any one of the preceding claims, wherein: The spectral data is acquired (110) via laser induced breakdown spectroscopy.

7. A method for synthesizing spectral data according to any one of the preceding claims, wherein: The spectral data is derived from the emission or absorption spectrum of the chemical species.

8. A method for quantitative analysis or qualitative analysis of spectral data, comprising the following steps: - generating (301) a set of synthetic spectral data by performing a method for synthesizing spectral data according to any one of the preceding claims, - training (302) a machine learning model based on the generated synthetic spectral data, - Using (303) the trained model to perform a quantitative analysis or a qualitative analysis (304) of the spectral data.

9. A computer program comprising instructions for implementing the method of any one of claims 1 to 7 when the computer program is executed by a processor.

10. A processor-readable recording medium having recorded thereon a program including instructions for implementing the method according to any one of claims 1 to 7 when the program is executed by a processor.

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