JPWO2013027553A1 - Signal analysis apparatus, signal analysis method, and computer program - Google Patents

Abstract

Provided are a signal analysis device, a signal analysis method, and a computer program that can perform analysis without subjecting a user's subjectivity and can adjust the performance of the analysis. The signal analyzer 1 generates an intensity distribution of a plurality of specific signals from a spectrum distribution on a two-dimensional coordinate measured by a measuring apparatus 3 such as an EDX apparatus, and n defined by a combination of the intensity of n specific signals. The n-dimensional coordinate points on the dimensional space are classified into a plurality of clusters by the EM algorithm. In addition, the signal analysis device 1 specifies points on the two-dimensional coordinates corresponding to the n-dimensional coordinate points included in each cluster, thereby generating individual spectrum distributions having different shapes. Distributions of spectra having different shapes represent distributions of substance components that generate spectra of the respective shapes. The analysis that excludes the user's subjectivity is possible by the EM algorithm, and the performance of the analysis can be adjusted by selecting a specific signal used for the analysis.

Description

  The present invention relates to a signal analysis apparatus, a signal analysis method, and a computer program for obtaining a distribution of a portion having a different combination of signal intensity from a signal distribution on a two-dimensional coordinate system.

  X-ray analysis is a method of irradiating a sample with radiation such as an electron beam or X-ray, and analyzing components contained in the sample from the spectrum of characteristic X-rays generated from the sample. In particular, the sample is irradiated while scanning with a radiation beam, characteristic X-rays from each point on the sample are detected, and a spectrum distribution is created in which the spectrum of the characteristic X-ray is associated with each point on the sample. Is used to analyze the components in the sample. As an example of X-ray analysis using an electron beam as radiation irradiated to a sample, Energy Dispersive X-ray Spectroscopy (EDX) is known. As an example of X-ray analysis using X-rays as radiation irradiated to a sample, there is fluorescent X-ray analysis. Moreover, there is an analysis method that can create a spectrum distribution as an analysis method other than the X-ray analysis. For example, in Raman spectroscopic analysis, a spectrum distribution in which the spectrum of Raman light is recorded for each point on the image corresponding to each point on the sample can be created.

  Since characteristic X-rays of a specific wavelength can be obtained from a specific element, the distribution of the specific element can be obtained by examining the signal intensity of the specific wavelength in the spectrum at each point on the sample. Since the sample includes a plurality of elements, a distribution of a plurality of elements can be obtained from the spectral distribution. In general, a sample includes a plurality of components, and each component includes a plurality of elements. For example, when the sample is a rock, the rock is composed of a plurality of mineral components, and each mineral component contains a plurality of elements. Since the same element may be contained even if the components are different, the distribution of the components in the sample and the distribution of the elements generally do not match.

  Patent Document 1 describes a method of obtaining a plurality of element distributions from a spectrum distribution and obtaining a component distribution in a sample from the plurality of element distributions. This method calculates the linear sum of values at multiple element distributions using appropriate coefficients for each point, creates a scatter plot that plots the linear sum values at each point in two dimensions, and It is determined that points gathered in substantially the same region on the figure are included in the same component. Principal component analysis is used to calculate appropriate coefficients. By associating the points on the spectrum distribution with the components determined to include each point, the distribution of the components in the sample can be known. This method can also be applied to a spectral distribution obtained by an analysis method other than X-ray analysis such as Raman spectroscopy.

Japanese Patent No. 3461208

  The technique described in Patent Document 1 has a problem that the user performs the task of classifying a plurality of points on the scatter diagram obtained by the principal component analysis, so that the subjectivity of the user affects the classification result. In addition, although there is a method of automatically classifying based on the distance on the scatter diagram, there is a problem that it is difficult to adjust the performance of analysis.

  The present invention has been made in view of such circumstances, and an object of the present invention is to perform a signal analysis that excludes the subjectivity of the user and adjust the analysis performance. To provide an analysis method and a computer program.

  The signal analysis apparatus according to the present invention is a distribution of a plurality of types of spectra having different combinations of intensities of a plurality of specific signals from a spectrum distribution in which a spectrum composed of one or a plurality of signals is determined for each point on a two-dimensional coordinate system. In the signal analysis apparatus for obtaining the above, means for generating an intensity distribution of a plurality of specific signals from the spectrum distribution, and n specific signals (n is an integer of 2 or more) among the generated intensity distributions of the plurality of specific signals Means for storing the intensity distribution, means for generating an n-dimensional coordinate point in an n-dimensional space defined by a combination of intensities of n specific signals for each point included in the spectrum distribution, and a plurality of generated Means for determining the number of a plurality of clusters for classifying the n-dimensional coordinate points according to the position in the n-dimensional space, and a probability distribution model of the n-dimensional coordinate points included in each cluster A probability calculating means for performing processing for calculating a probability that each of the plurality of generated n-dimensional coordinate points is included in each cluster, and likelihood of classification of the plurality of n-dimensional coordinate points obtained from the calculated probability A model updating unit that performs processing for updating the probability distribution model of each cluster, a repeating unit that causes the probability calculating unit and the model updating unit to repeatedly perform the processing, and a plurality of clusters for each cluster. Means for generating a distribution of a plurality of types of spectra having different combinations of intensities of n specific signals by specifying a distribution in the spectrum distribution of points corresponding to n-dimensional coordinate points included in It is characterized by.

  The signal analysis apparatus according to the present invention includes a plurality of types in which combinations of intensities of the plurality of signals measured in a portion included in the measurement object are different from intensity distributions of the plurality of signals measured from the same measurement object. In the signal analysis apparatus for obtaining the distribution of the portion of n, on the n-dimensional space defined by the combination of means for storing the intensity distribution of n signals and the intensity of n signals for each point in the measurement object means for generating n-dimensional coordinate points, means for determining the number of clusters for classifying the generated plurality of n-dimensional coordinate points according to positions in the n-dimensional space, and n-dimensional coordinates included in each cluster Means for generating a probability distribution model of points, probability calculating means for performing processing for calculating the probability that each of the generated n-dimensional coordinate points is included in each cluster, and a plurality of n-dimensional coordinates obtained from the calculated probabilities A model updating unit that performs a process of updating the probability distribution model of each cluster so that the likelihood of the classification of points becomes larger, a repeating unit that causes the probability calculating unit and the model updating unit to repeatedly execute the process, and a plurality of Means for generating distributions of the plurality of types of portions in the measurement object by specifying distributions in the measurement object of points corresponding to n-dimensional coordinate points included in each cluster for each cluster of It is characterized by providing.

  The signal analyzing apparatus according to the present invention is characterized in that the repetitive unit causes the probability calculating unit and the model updating unit to repeatedly execute processing until a predetermined convergence condition is satisfied.

  The signal analysis apparatus according to the present invention is characterized in that the probability calculation means, the model update means, and the repetition means execute processing according to an EM (Expectation-maximization) algorithm.

  The signal analysis apparatus according to the present invention further includes means for combining a plurality of clusters whose distances in the n-dimensional space are equal to or less than a specific distance among the plurality of clusters into one cluster.

  The signal analyzing apparatus according to the present invention further includes means for receiving an initial value of the number of clusters.

  According to the signal analysis method of the present invention, a computer including a calculation unit and a storage unit is used to calculate the intensity of a plurality of specific signals from a spectrum distribution in which a spectrum including one or a plurality of signals is determined for each point on a two-dimensional coordinate system. In a signal analysis method for obtaining a distribution of a plurality of types of spectra having different combinations, a calculation unit generates an intensity distribution of a plurality of specific signals from the spectrum distribution, and n of the generated intensity distributions of the plurality of specific signals An intensity distribution of a specific signal is stored in a storage unit, and an n-dimensional coordinate point on an n-dimensional space defined by a combination of n specific signal intensities is generated by an arithmetic unit for each point included in the spectrum distribution. And processing for determining the number of the plurality of clusters for classifying the generated plurality of n-dimensional coordinate points according to the position in the n-dimensional space, Probability distribution model of n-dimensional coordinate points to be generated is generated by the calculation unit, probability calculation processing for calculating the probability that each of the generated n-dimensional coordinate points is included in each cluster is executed by the calculation unit, and the calculated probability In order that the likelihood of classification of a plurality of n-dimensional coordinate points obtained from the above becomes larger, a model update process for updating the probability distribution model of each cluster is executed by the arithmetic unit, and the probability calculation process and the model update process are performed. Repeatedly executed by the calculation unit, and by specifying the distribution in the spectrum distribution of the points corresponding to the n-dimensional coordinate points included in each cluster for each of a plurality of clusters, the combinations of the strengths of the n specific signals are different. A plurality of types of spectrum distributions are generated by a calculation unit, and the generated plurality of types of spectrum distributions are stored in a storage unit.

  The computer program according to the present invention obtains a distribution of a plurality of types of spectra having different combinations of intensities of a plurality of specific signals from a spectrum distribution in which a spectrum composed of one or a plurality of signals is determined for each point on a two-dimensional coordinate system. In a computer program that causes a computer to execute the processing to be obtained, the computer generates an intensity distribution of a plurality of specific signals from the spectrum distribution, and a plurality of identifications that generate an intensity distribution for each point included in the spectrum distribution. A step of generating n-dimensional coordinate points on the n-dimensional space defined by a combination of intensities of n specific signals among the signals, and the generated plurality of n-dimensional coordinate points according to positions on the n-dimensional space. Determining the number of multiple clusters to be classified, and n-dimensional coordinate points included in each cluster A step of generating a rate distribution model, a step of calculating a probability that each of the plurality of generated n-dimensional coordinate points is included in each cluster, and a plurality of n-dimensional coordinate points obtained from the calculated probabilities A step of performing a model update process for updating the probability distribution model of each cluster, a step of repeating the probability calculation process and the model update process, and a plurality of clusters for each cluster so that the likelihood of classification becomes larger. Generating a distribution of a plurality of types of spectra having different combinations of intensities of n specific signals by specifying a distribution of the points corresponding to the included n-dimensional coordinate points within the spectrum distribution. It is made to perform.

  In the present invention, an intensity distribution of a plurality of specific signals is generated from the spectrum distribution, an n-dimensional coordinate point on an n-dimensional space defined by a combination of the intensity of n specific signals is generated, and the n-dimensional coordinate point is Classify into multiple clusters and generate spectral distribution for each cluster. A spectrum distribution having a specific shape corresponding to the distribution of substance components including a plurality of elements is obtained.

  In the present invention, an n-dimensional coordinate point on an n-dimensional space defined by a combination of n signal intensities is generated from an intensity distribution of a plurality of signals measured from the same measurement object, and the n-dimensional coordinate point is generated. Are classified into a plurality of clusters, and a distribution of a portion in the measurement target is generated for each cluster. With respect to the measurement object, a distribution of a plurality of types of parts in the measurement object with different types of substances or electronic states contained therein can be obtained.

  In the present invention, when the n-dimensional coordinate points are classified into a plurality of clusters, the signal analysis is accurately performed by executing processing according to the EM algorithm.

  In the present invention, a plurality of clusters close to each other in the n-dimensional space are combined into one cluster. For this reason, an appropriate number of clusters can be obtained.

  In the present invention, the initial value of the number of clusters can be arbitrarily specified. By specifying the number of clusters, the processing accuracy and processing time are adjusted.

  According to the present invention, it is possible to analyze a signal distribution that excludes the user's subjectivity, and it is possible to adjust the analysis performance by combining specific signals used for the analysis.

It is a block diagram which shows the structure of the signal analyzer of this invention. It is a typical characteristic figure showing an example of a spectrum. 4 is a flowchart illustrating a procedure of processing performed by the signal analysis device according to the first embodiment. 4 is a flowchart illustrating a procedure of processing performed by the signal analysis device according to the first embodiment. It is a schematic diagram which shows the example of a signal distribution image. It is a schematic diagram which shows the example of a signal distribution image. It is a schematic diagram which shows the example of a signal distribution image. It is a schematic diagram which shows the example of a signal distribution image. An example of a scatter diagram in which n-dimensional coordinate points are plotted on n-dimensional coordinates is shown. It is a schematic diagram which shows the example of the image showing distribution of multiple types of spectrum. It is a schematic diagram which shows the example of the image showing distribution of multiple types of spectrum. It is a schematic diagram which shows the example of the image showing distribution of multiple types of spectrum. 10 is a flowchart illustrating a procedure of processing performed by the signal analysis device according to the second embodiment. 10 is a flowchart illustrating a procedure of processing performed by the signal analysis device according to the second embodiment.

Hereinafter, the present invention will be specifically described with reference to the drawings showing embodiments thereof.
(Embodiment 1)
FIG. 1 is a block diagram showing a configuration of a signal analysis apparatus 1 according to the present invention. The signal analyzer 1 is configured using a general-purpose computer such as a personal computer (PC). The signal analysis apparatus 1 includes a CPU (arithmetic unit) 11 that performs calculation, a RAM 12 that stores temporary information generated along with the calculation, and a drive such as a CD-ROM drive that reads information from a recording medium 2 such as an optical disk. Unit 13 and a non-volatile storage unit 14. The storage unit 14 is, for example, a hard disk. The CPU 11 causes the drive unit 13 to read the computer program 21 of the present invention from the recording medium 2 and stores the read computer program 21 in the storage unit 14. The CPU 11 loads the computer program 21 from the storage unit 14 to the RAM 12 as necessary, and executes processing necessary for the signal analyzer 1 according to the loaded computer program 21. The signal analyzer 1 also includes an input unit 16 such as a keyboard or a pointing device for inputting information such as various processing instructions operated by the user, and a display unit 17 such as a liquid crystal display for displaying various information. And.

  The computer program 21 may be downloaded to the signal analysis device 1 from an external server device (not shown) connected to the signal analysis device 1 via a communication network (not shown) and stored in the storage unit 14. Further, the signal analysis apparatus 1 may be configured such that it does not accept the computer program 21 from the outside, but has a recording means such as a ROM in which the computer program 21 is recorded.

  The signal analysis device 1 also includes an interface unit 15 connected to the measurement device 3 that measures a two-dimensional spectral distribution. The measuring device 3 is, for example, an EDX device, a fluorescent X-ray measuring device, a Raman spectroscopic device, or the like. The EDX device irradiates each point on the sample with an electron beam, detects characteristic X-rays generated from each point on the sample, and distributes the characteristic X-ray spectrum obtained from each point on a two-dimensional coordinate system. Measure the spectral distribution. The X-ray fluorescence measuring apparatus irradiates each point on the sample with X-rays, detects the X-ray fluorescence generated from each point on the sample, and the spectrum of the fluorescent X-ray obtained from each point is a two-dimensional coordinate system. Measure the spectral distribution distributed above. The Raman spectrometer irradiates each point on the sample with light, detects the Raman light generated from each point on the sample, and the spectrum of Raman light obtained from each point is distributed on a two-dimensional coordinate system. Measure the distribution. The measuring device 3 may be another device as long as it can measure the spectral distribution.

  FIG. 2 is a schematic characteristic diagram showing an example of a spectrum. In general, a spectrum is composed of a combination of a plurality of signals. The horizontal axis in FIG. 2 is the wavelength, and the vertical axis is the signal intensity at each wavelength. In FIG. 2, the peak of one signal included in the spectrum is indicated by an arrow. The signal contained in the spectrum is identified by wavelength. In the case of a characteristic X-ray spectrum, each signal is attributed to an element contained in the sample. The spectrum distribution measured by the measuring device 3 is composed of spectra obtained for each point on the two-dimensional coordinate system corresponding to the surface of the sample. Each spectrum has a different combination of intensity of signals contained therein, and has a different spectrum shape. For example, some spectra may consist of a single signal and some may have zero signal strength. The horizontal axis of the spectrum is not limited to the wavelength, and may be energy or wave number. Further, the horizontal axis of the spectrum is not limited to an absolute value, and may be a relative value such as a wavelength shift from a specific wavelength.

  Next, processing performed by the signal analysis device 1 will be described. 3 and 4 are flowcharts showing a procedure of processing performed by the signal analyzing apparatus 1 according to the first embodiment. CPU11 performs the following processes according to a computer program. Spectral distribution data is input from the measuring device 3 to the interface unit 15, and the CPU 11 stores the spectral distribution data in the storage unit 14 (S1). The spectrum distribution data is data in which two-dimensional coordinates of each point on the sample are associated with spectrum data obtained from each point. The spectrum data is data in which the wavelength and the like are associated with the signal intensity. Next, the CPU 11 generates signal distribution data indicating the intensity distributions of a plurality of specific signals from the spectrum distribution data (S2). Specifically, in step S2, the CPU 11 reads the signal intensity of the specific signal identified with a predetermined wavelength from the spectrum of each point, and corresponds the read signal intensity to each point on the two-dimensional coordinate system. Generated signal distribution data. That is, the signal distribution data is data in which the two-dimensional coordinates of each point on the sample are associated with the signal intensity at a specific wavelength. The storage unit 14 stores a plurality of wavelengths as specific signal wavelengths in advance, and the CPU 11 generates signal distribution data for each of the plurality of specific signals. That is, in step S2, a plurality of signal distribution data are generated. Note that the wavelength of the specific signal may be included in the computer program 21. The specific signal may be identified by energy or wave number. Further, the specific signal may be identified not from the position of the peak in the spectrum but from the signal waveform in the spectrum. Further, the signal analysis device 1 may be configured to receive externally generated signal distribution data and execute the processing after step S3.

  Next, the CPU 11 displays a signal distribution image representing the intensity distribution of the specific signal on the two-dimensional coordinate system on the display unit 17 based on the generated signal distribution data (S3). 5A, 5B, 5C, and 5D are schematic diagrams illustrating examples of signal distribution images. 5A, 5B, 5C, and 5D show four signal distribution images obtained from one spectral distribution. The hatched portion in the figure indicates a portion where the intensity of the specific signal is greater than zero. Even within the portion where the intensity of the specific signal is greater than 0, the signal intensity differs at each point. The four signal distribution images shown in FIGS. 5A, 5B, 5C, and 5D represent different signal intensity distributions. The intensity distribution shown in FIG. 5A is the intensity distribution of signal a, the intensity distribution shown in FIG. 5B is the intensity distribution of signal b, the intensity distribution shown in FIG. 5C is the intensity distribution of signal c, and the intensity distribution shown in FIG. Let d be the intensity distribution. When the spectrum is a characteristic X-ray spectrum, the signal distribution image shows the concentration distribution of the specific element contained in the sample. In step S4 and subsequent steps, the signal analyzer 1 performs a process of obtaining a plurality of types of spectrum distributions having different combinations of intensities of a plurality of specific signals. The distribution of the plurality of types of spectra corresponds to the distribution in the sample of the plurality of types of substance components having different contents of the plurality of specific elements.

  Next, the CPU 11 accepts selection of n specific signals from among the plurality of specific signals displaying the signal distribution image by the user operating the input unit 16 (S4). n is an integer of 2 or more, and the CPU 11 accepts selection of two or more specific signals in step S4. For example, assume that signals a and d whose signal distribution images are shown in FIGS. 5A and 5D are selected. Note that the CPU 11 may automatically select a specific signal appropriately. Next, the CPU 11 stores the selected n signal distribution data in the storage unit 14 (S5). Next, the CPU 11 generates n-dimensional data composed of combinations of the strengths of the selected n specific signals (S6). Specifically, the CPU 11 generates, for each point on the two-dimensional coordinate system, an n-dimensional coordinate point on the n-dimensional space defined by a combination of the intensity of the selected n specific signals, and the two-dimensional coordinate N-dimensional data in which two-dimensional coordinates and n-dimensional coordinates of each point on the system are associated is generated.

  FIG. 6 shows an example of a scatter diagram in which n-dimensional coordinate points are plotted on n-dimensional coordinates. FIG. 6 shows a case where n = 2 in which signals a and d are selected as specific signals. The horizontal axis in FIG. 6 indicates the intensity of the signal a, and the vertical axis indicates the intensity of the signal d. For each point on the two-dimensional coordinate system corresponding to the surface of the sample, an n-dimensional coordinate point is plotted on the n-dimensional space. The n-dimensional coordinate points may overlap on the n-dimensional space. Note that the signal analysis device 1 may be configured to receive n-dimensional data generated externally and execute the processes in and after step S7. The signal analyzing apparatus 1 performs a process of classifying a plurality of n-dimensional coordinate points into a plurality of clusters by an EM (Expectation-maximization) algorithm after step S7.

  Next, the CPU 11 accepts an initial value of the number of clusters when the user operates the input unit 16 (S7). In step S7, the CPU 11 may perform processing for determining an appropriate numerical value as the initial value of the number of clusters. Next, the CPU 11 performs initial setting of the probability distribution model of the n-dimensional coordinate points included in the clusters for each of the determined number of clusters (S8). Specifically, the CPU 11 sets a probability distribution parameter indicating the probability that each point on the n-dimensional space is included in each cluster. The probability distribution parameter includes the center position of each cluster in the n-dimensional space. As the probability distribution, a probability distribution such as a mixed Gaussian distribution or a mixed Poisson distribution used in the EM algorithm is used.

  Next, the CPU 11 calculates the probability that each n-dimensional coordinate point in the n-dimensional space is included in each cluster based on the probability distribution model of each cluster (S9). The process of step S9 corresponds to the E (Expectation) step in the EM algorithm. Next, the CPU 11 performs a process of updating the probability distribution model parameters of each cluster so as to increase the overall likelihood (S10). Specifically, parameters of probability distribution such as the center position of each cluster in the n-dimensional space are updated. The process of step S10 corresponds to the M (maximization) step in the EM algorithm.

  Next, the CPU 11 determines whether the EM algorithm has converged (S11). As the convergence index, an index generally used in the EM algorithm, such as a likelihood value, a change amount or a change rate, or a parameter value of the probability distribution model, a change amount or a change rate, is used. For example, the CPU 11 determines that the likelihood has converged when the likelihood change amount is less than or equal to a predetermined value, and determines that the likelihood has not yet converged when the likelihood change amount is greater than the predetermined value. Note that the signal analysis device 1 may be configured to execute processing using a maximum likelihood method or a maximum posterior probability estimation method algorithm other than the EM algorithm in steps S9, S10, and S11. For example, the signal analysis device 1 may perform processing using an algorithm of soft k-means clustering or Newton-Raphson method.

  If it has not converged at step S11 (S11: NO), the CPU 11 returns the process to step S9. If it is determined that they have converged (S11: YES), the CPU 11 determines whether there are a plurality of clusters in which the distance between each other in the n-dimensional space is close to a predetermined distance or less. Is determined (S12). For example, in step S12, the CPU 11 calculates a Mahalanobis distance between centers between two clusters, and determines based on whether the calculated Mahalanobis distance is equal to or less than a predetermined value. Further, for example, the CPU 11 calculates the inner product of the vectors to the center between the two clusters, and determines that the mutual distance is equal to or less than the predetermined distance when the calculated inner product is closer to 1 than the predetermined threshold. CPU11 performs the process which determines the distance between two clusters about the combination of all the clusters. In step S <b> 12, the CPU 11 may make a determination by other methods. When there are a plurality of clusters close to each other (S12: YES), the CPU 11 combines the plurality of clusters close to each other (S13). Specifically, the CPU 11 performs processing for determining a plurality of cluster ranges as a new one cluster range. In FIG. 6, the cluster range is indicated by a solid line. In the example shown in FIG. 6, four clusters are obtained.

  After step S13 is completed or when there is no cluster close to each other in step S12 (S12: NO), the CPU 11 specifies a point on the two-dimensional coordinate system corresponding to the n-dimensional coordinate point included in each cluster. Thus, distribution data of a plurality of types of spectra having different combinations of intensities of a plurality of specific signals are individually generated (S14). The distribution data of each spectrum is data in which two-dimensional coordinates of each point on the sample are associated with data indicating the presence or absence of a specific spectrum at each point. The spectrum distribution data is generated for each of a plurality of types of spectra having different combinations of intensities of a plurality of specific signals. Next, the CPU 11 stores the generated individual spectrum distribution data in the storage unit 14 (S15), and ends the process.

  FIG. 7A, FIG. 7B, and FIG. 7C are schematic diagrams illustrating examples of images representing a plurality of types of spectrum distributions. FIG. 7A represents a spectrum distribution including the signal a and not including the signal d, and FIG. 7B represents a spectrum distribution including the signal d but not the signal a. FIG. 7C shows the distribution of the spectrum including both the signal a and the signal d. In this way, a two-dimensional distribution of a plurality of types of spectra having different combinations of intensities of a plurality of specific signals is obtained from the initial spectrum distribution data. When the spectrum is a characteristic X-ray spectrum, the distribution of the plurality of types of spectra corresponds to the distribution of the plurality of substance components having different contents of the plurality of elements in the sample. Assuming that the signal a corresponds to the element A and the signal d corresponds to the element D, FIG. 7A represents the distribution of material components that include the element A but not the element D. FIG. 7B shows the distribution of the substance component that does not contain the element A and contains the element D, and FIG. 7C shows the distribution of the substance component that contains both the element A and the element D.

  Note that the spectrum distribution obtained in step S14 is generally a distribution of a plurality of types of spectrums having different combinations of the intensity of a plurality of signals. Therefore, in the present invention, the distribution is shown in FIGS. 7A, 7B, and 7C. It is also possible to obtain a distribution other than the distribution. For example, a combination of a plurality of signal intensities such as a spectrum in which the intensity of the signal a is 1 and the intensity of the signal d is 2 or a spectrum in which the intensity of the signal a is 2 and the intensity of the signal d is 1 is shown in FIGS. It is also possible to obtain a spectrum distribution different from the example of FIG. 7C. Further, since the clusters on the n-dimensional coordinates have a certain extent, the combinations of the signal intensities included in the distributions of the respective spectra obtained in step S14 may have a certain width. For example, a spectrum distribution in which the intensity of the signal a is 1 or more and less than 2 and the intensity of the signal d is less than 1, a distribution of a spectrum in which the intensity of the signal a is less than 1 and the intensity of the signal d is 1 or more and less than 2, and the signal a It is also possible to generate a spectral distribution in which the intensity of the signal d is 2 or more.

  In the case where the signal analysis apparatus 1 is configured to execute the processing after step S3 using the input signal distribution data, the CPU 11 similarly differs in the combination of the intensity of the plurality of signals in step S14. Distribution data indicating the distribution of a plurality of types of parts on the sample is generated. In step S <b> 15, the CPU 11 stores the generated distribution data in the storage unit 14. Also in this embodiment, a distribution similar to the distribution shown in FIGS. 7A, 7B, and 7C can be obtained. Similarly, it is possible to obtain distributions of portions on the sample whose signal intensity combinations are different from those in the examples of FIGS. 7A, 7B and 7C. There may be some width.

  The signal analyzing apparatus 1 may be configured to perform a process of determining the number of repetitions of the processes of steps S9 and S10 instead of performing the convergence determination in step S11. In this embodiment, the signal analyzing apparatus 1 stores in advance the predetermined number of repetitions of steps S9 and S10 in the storage unit 14. In step S11, the CPU 11 determines whether or not the number of process repetitions has reached a predetermined number. If the number of process repetitions has not yet reached the predetermined number, the process returns to step S9, where the number of process repetitions is determined. If the predetermined number of times has been reached, the process proceeds to step S12. As the predetermined number of repetitions of processing, the number of times that the likelihood of the entire plurality of clusters is sufficiently large from experience is determined. The predetermined number of times is 100, for example. The signal analyzer 1 can shorten the calculation time by ending the repetition of the process a predetermined number of times regardless of whether or not the convergence condition is satisfied. In addition, the signal analysis device 1 performs both the convergence determination and the number determination, and performs a process of proceeding to step S12 when the convergence condition is satisfied before the number of repetitions of the process reaches the predetermined number. Also good.

  As described above, the signal analyzing apparatus 1 generates an intensity distribution of a plurality of specific signals from the spectrum distribution measured by the measuring apparatus 3 such as an EDX apparatus, and is defined by a combination of the intensity of n specific signals. The n-dimensional coordinate points on the n-dimensional space are classified into a plurality of clusters by the EM algorithm. At points on the spectrum distribution corresponding to the n-dimensional coordinate points included in the same cluster, the combinations of the intensities of a plurality of specific signals included in the spectrum are substantially the same, and the spectrum shapes are approximately the same. At points on the spectrum distribution corresponding to n-dimensional coordinate points included in different clusters, combinations of intensities of a plurality of specific signals included in the spectrum are different, and the shapes of the spectra are different from each other. By specifying points on the two-dimensional coordinate system corresponding to the n-dimensional coordinate points included in each cluster, spectrum distributions having different shapes are generated individually. The distribution of spectra having different shapes represents the distribution of substance components that generate spectra of the respective shapes. For example, a distribution of a plurality of types of components having different compositions contained in a sample measured with an EDX apparatus can be obtained. More specifically, when the sample measured by the EDX apparatus is rock, distribution of various mineral components contained in the sample can be obtained. Even when the measuring device 3 is another device such as a Raman spectroscopic device, the signal analyzing device 1 can similarly obtain the distribution of various substance components contained in the sample.

  In the present invention, clustering is automatically performed by the EM algorithm. For this reason, n-dimensional coordinate points are classified without user's subjectivity, and accurate signal analysis is possible without being influenced by the user's subjectivity. In the present invention, the distribution of the substance component can be obtained without identifying the substance component contained in the sample. In the present invention, it is possible to select a plurality of specific signals used in the analysis. By limiting the signal to be analyzed, it is possible to adjust the analysis performance, such as obtaining a distribution specialized for the substance component that needs to be examined by excluding the substance component that does not need to be examined from the analysis object. . In addition, the calculation time required for analysis can be shortened. In the present invention, it is possible to specify an initial value of the number of clusters. By increasing the initial value of the number of clusters, detailed analysis becomes possible, and by reducing the initial value of the number of clusters, the types of substance components that need to be distributed can be limited. The performance of the analysis can be adjusted by specifying the value. In addition, the time required for analysis can be adjusted. In the present invention, a plurality of clusters close to each other are combined into one, so that an appropriate number of substance component distributions can be obtained even when the initial number of clusters is too large. The signal analysis device 1 may be configured to store the parameters of the EM algorithm in the storage unit 14 during the processing of the EM algorithm. In this embodiment, when analyzing the spectrum distribution obtained from the similar sample, the signal analyzer 1 may be able to shorten the processing by using the stored parameters.

(Embodiment 2)
The configuration of the signal analyzing apparatus 1 according to the second embodiment is the same as that of the first embodiment. 8 and 9 are flowcharts showing a procedure of processing performed by the signal analyzing apparatus 1 according to the second embodiment. CPU11 performs the following processes according to a computer program. CPU11 performs the process of step S1-S8 similar to Embodiment 1. FIG. After step S8 ends, the CPU 11 calculates the probability that each n-dimensional coordinate point on the n-dimensional space is included in each cluster based on the probability distribution model of a plurality of clusters (S21). Next, the CPU 11 performs a process of updating the probability distribution model parameters of each cluster so as to increase the overall likelihood (S22). Next, the CPU 11 determines whether the EM algorithm has converged (S23). If it has not converged yet (S23: NO), the CPU 11 returns the process to step S21. When it determines with having converged (S23: YES), CPU11 memorize | stores the parameter of the probability distribution model of each cluster in the memory | storage part 14 (S24), and complete | finishes a process. As described above, the signal analysis device 1 generates parameters of a plurality of clusters in the n-dimensional space by the processes of steps S1 to S8 and steps S21 to S24. As in the first embodiment, the CPU 11 may perform a process of determining the number of repetitions of the processes in steps S21 and S22 instead of performing the convergence determination in step S23.

  In addition, the signal analysis device 1 performs processing for generating distribution data of a plurality of types of spectra having different combinations of intensities of a plurality of specific signals based on the generated parameters of the plurality of clusters. First, the CPU 11 reads out the parameters of the probability distribution models of the plurality of clusters stored in the storage unit 14 into the RAM 12 (S31). Next, the CPU 11 accepts a threshold value for determining whether or not the distance between the clusters in the n-dimensional space is close by the user operating the input unit 16 (S32). In step S32, the CPU 11 receives, for example, a threshold value of the Mahalanobis distance between the centers of the clusters or a threshold value of the inner product of the vectors to the centers between the clusters. Next, based on the received threshold value, the CPU 11 determines whether or not there are a plurality of clusters in which the distance between each other in the n-dimensional space is close to a distance corresponding to the threshold value or less. Is determined (S33). In step S33, for example, the CPU 11 calculates the Mahalanobis distance between the centers of the clusters, and determines based on whether the calculated Mahalanobis distance is equal to or less than the accepted threshold. Further, for example, the CPU 11 calculates the inner product of the vectors to the center between the two clusters, and determines that the mutual distance is close when the calculated inner product is closer to 1 than the accepted threshold. CPU11 performs the process which determines the distance between two clusters about the combination of all the clusters. In step S <b> 33, the CPU 11 may make a determination by other methods.

  When there are a plurality of clusters close to each other (S33: YES), the CPU 11 combines the plurality of clusters close to each other (S34). After step S34 is completed, or when there are no clusters close to each other in step S33 (S33: NO), the CPU 11 individually generates distribution data of a plurality of types of spectra having different combinations of a plurality of specific signal intensities, Individual spectrum distribution data is stored in the storage unit 14 (S35). Next, the CPU 11 displays a plurality of types of spectrum distributions on the display unit 17 based on the generated distribution data of the plurality of types of spectra (S36). For example, the CPU 11 displays an image representing a spectrum distribution as shown in FIGS. 7A to 7C. After step S36 ends, the CPU 11 ends the process. The signal analyzer 1 repeats the processes of steps S31 to S36 in response to a processing instruction input to the input unit 16 by a user operation.

  As described above, in the present embodiment, the signal analyzing apparatus 1 can repeat the processes of steps S31 to S36 a plurality of times based on the parameters obtained by the processes of steps S1 to S8 and steps S21 to S24. . In the processing of steps S31 to S36, the results differ depending on the threshold value for determining the distance between the clusters. For example, when the distance according to the threshold is small, the number of clusters increases, the number of spectrum types from which distribution is obtained increases, and the number of substance components from which the distribution in the sample is obtained increases. On the contrary, when the distance according to the threshold is large, the number of clusters decreases, the number of spectrum types from which the distribution is obtained decreases, and the number of substance components from which the distribution in the sample is obtained decreases. For this reason, in order to obtain a distribution of an appropriate number of substance components, there is a need to adjust the threshold value to an appropriate value. An appropriate result for the user can be obtained by repeating the processes of steps S31 to S36 in the signal analyzer 1 while changing the threshold value input by the user. Since the processes of steps S1 to S8 and steps S21 to S24 are separated from the processes of steps S31 to S36 and are not repeated, a process with a high load is avoided and the processing efficiency of the signal analyzer 1 is high. Become. The user can perform signal analysis of the spectrum distribution in real time using the signal analyzer 1 by repeating the operation of changing the threshold after confirming the processing result according to the input threshold.

  In the first and second embodiments, a configuration in which one measurement device 3 is connected to the signal analysis device 1 is shown. However, the signal analysis device 1 of the present invention has a configuration in which a plurality of measurement devices 3 can be connected. It may be. In addition, the signal analyzer 1 executes the same signal analysis process using the intensity distribution of the signals measured by the plurality of measuring devices 3 with the same sample as the measurement object, and within the portion included in the sample The form which calculates | requires distribution of several types of parts from which the combination of the intensity | strength of the signal measured by a several measuring method differs may be sufficient. In this embodiment, the signal analysis device 1 can perform detailed analysis that cannot be performed only by using the measurement result obtained by the single measurement device 3. For example, by performing analysis using the measurement results of the EDX apparatus and the Raman spectroscopic apparatus, the distribution of the portion having the crystal structure that generates specific Raman light among the material components that generate specific X-ray spectra is obtained. be able to.

  The signal analysis device 1 is not limited to a mode in which data is received from the connected measurement device 3, but is a mode in which signal intensity distribution measured by a measurement device that is not connected is input to perform signal analysis. May be. The signal intensity distribution that can be analyzed by the signal analyzer 1 is not limited to that measured from a sample that can be measured in a laboratory, and may be more general measurement data. For example, according to the present invention, it is also possible to determine the distribution of celestial bodies having high emission intensity of both visible light and X-rays from the observation results of celestial objects with visible light and X-rays.

  The present invention relates to a desired component in a measurement target, such as a distribution of a specific substance component, from an intensity distribution of a plurality of signals obtained from the measurement target using a single measurement device such as an EDX device or a plurality of types of measurement devices. Used to obtain the distribution of.

1 Signal Analyzer 11 CPU (Calculation Unit)
12 RAM
14 Storage Unit 2 Recording Medium 21 Computer Program 3 Measuring Device

Claims (8)

In a signal analyzer for obtaining a distribution of a plurality of types of spectra having different combinations of intensities of a plurality of specific signals from a spectrum distribution in which a spectrum composed of one or a plurality of signals is determined for each point on a two-dimensional coordinate system,
Means for generating an intensity distribution of a plurality of specific signals from the spectral distribution;
Means for storing intensity distributions of n specific signals (n is an integer of 2 or more) among the generated specific signal intensity distributions;
Means for generating an n-dimensional coordinate point on an n-dimensional space defined by a combination of intensities of n specific signals for each point included in the spectral distribution;
Means for determining the number of a plurality of clusters for classifying the generated plurality of n-dimensional coordinate points according to positions in the n-dimensional space;
Means for generating a probability distribution model of n-dimensional coordinate points included in each cluster;
A probability calculating means for performing a process of calculating the probability that each of the plurality of generated n-dimensional coordinate points is included in each cluster;
Model updating means for performing processing for updating the probability distribution model of each cluster so that the likelihood of classification of a plurality of n-dimensional coordinate points obtained from the calculated probabilities becomes larger;
Repetitive means for causing the probability calculating means and the model updating means to repeatedly execute processing;
By identifying the distribution in the spectrum distribution of the points corresponding to the n-dimensional coordinate points included in each cluster for each of the plurality of clusters, the distribution of a plurality of types of spectra with different combinations of n specific signal intensities can be obtained. And means for generating the signal analysis device. A signal analyzer that obtains distributions of a plurality of types of different combinations of intensity of the plurality of signals measured in a portion included in the measurement object from intensity distributions of the plurality of signals measured from the same measurement object In
means for storing an intensity distribution of n signals;
Means for generating an n-dimensional coordinate point on an n-dimensional space defined by a combination of n signal intensities for each point in the measurement object;
Means for determining the number of a plurality of clusters for classifying the generated plurality of n-dimensional coordinate points according to positions in the n-dimensional space;
Means for generating a probability distribution model of n-dimensional coordinate points included in each cluster;
A probability calculating means for performing a process of calculating the probability that each of the plurality of generated n-dimensional coordinate points is included in each cluster;
Model updating means for performing processing for updating the probability distribution model of each cluster so that the likelihood of classification of a plurality of n-dimensional coordinate points obtained from the calculated probabilities becomes larger;
Repetitive means for causing the probability calculating means and the model updating means to repeatedly execute processing;
Means for generating a distribution of the plurality of types of portions in the measurement object by specifying a distribution in the measurement object of points corresponding to n-dimensional coordinate points included in each cluster for each of a plurality of clusters; A signal analyzing apparatus comprising:   The signal analysis apparatus according to claim 1, wherein the repetitive unit performs a process of causing the probability calculation unit and the model update unit to repeatedly execute a process until a predetermined convergence condition is satisfied.   The signal analysis apparatus according to claim 3, wherein the probability calculation unit, the model update unit, and the repetition unit execute processing according to an EM (Expectation-maximization) algorithm. 5. The apparatus according to claim 1, further comprising means for combining a plurality of clusters whose distances in the n-dimensional space are equal to or less than a specific distance among the plurality of clusters into one cluster. Signal analysis device according to. The signal analysis apparatus according to claim 1, further comprising a unit that receives an initial value of the number of clusters. From a spectrum distribution in which a spectrum composed of one or a plurality of signals is determined for each point on a two-dimensional coordinate system by a computer having a calculation unit and a storage unit, a plurality of types of spectra having different combinations of specific signal intensities In the signal analysis method for obtaining the distribution,
From the spectrum distribution, the calculation unit generates an intensity distribution of a plurality of specific signals,
The intensity distribution of n specific signals among the generated intensity distributions of the specific signals is stored in the storage unit,
For each point included in the spectral distribution, an n-dimensional coordinate point on an n-dimensional space defined by a combination of n specific signal intensities is generated by an arithmetic unit,
A process for determining the number of a plurality of clusters for classifying the generated plurality of n-dimensional coordinate points according to positions in the n-dimensional space is executed by the arithmetic unit,
Generate a probability distribution model of n-dimensional coordinate points included in each cluster in the calculation unit,
Probability calculation processing for calculating the probability that each of the plurality of generated n-dimensional coordinate points is included in each cluster is executed by the arithmetic unit,
In order to increase the likelihood of classification of a plurality of n-dimensional coordinate points obtained from the calculated probabilities, a model update process for updating the probability distribution model of each cluster is executed in the arithmetic unit,
The probability calculation process and the model update process are repeatedly executed by a calculation unit,
By identifying the distribution in the spectrum distribution of the points corresponding to the n-dimensional coordinate points included in each cluster for each of the plurality of clusters, the distribution of a plurality of types of spectra with different combinations of n specific signal intensities can be obtained. Generated by the calculation unit,
A signal analysis method, wherein the generated distribution of the plurality of types of spectra is stored in a storage unit. A computer that causes a computer to execute a process for obtaining a distribution of a plurality of types of spectra having different combinations of intensities of a plurality of specific signals from a spectrum distribution in which a spectrum of one or a plurality of signals is determined for each point on a two-dimensional coordinate system In the program
On the computer,
Generating an intensity distribution of a plurality of specific signals from the spectral distribution;
For each point included in the spectral distribution, generating an n-dimensional coordinate point on an n-dimensional space defined by a combination of intensities of n specific signals among a plurality of specific signals that generated the intensity distribution;
Determining a number of a plurality of clusters for classifying the generated plurality of n-dimensional coordinate points according to positions on the n-dimensional space;
Generating a probability distribution model of n-dimensional coordinate points included in each cluster;
Performing a probability calculation process for calculating a probability that each of the plurality of generated n-dimensional coordinate points is included in each cluster;
Performing model update processing for updating the probability distribution model of each cluster so that the likelihood of classification of a plurality of n-dimensional coordinate points obtained from the calculated probabilities becomes greater;
Repeating the probability calculation process and the model update process;
By identifying the distribution in the spectrum distribution of the points corresponding to the n-dimensional coordinate points included in each cluster for each of the plurality of clusters, the distribution of a plurality of types of spectra with different combinations of n specific signal intensities can be obtained. A computer program for executing a process including the step of generating.

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