GB2508556A

GB2508556A - Signal analyzing apparatus, signal analyzing method, and computer program

Info

Publication number: GB2508556A
Application number: GB1404450.7A
Authority: GB
Inventors: Toshiyuki Tanaka; Jun Ohkubo; Toshikazu Yurugi; Hiroyoshi Sawa; Seichi Sato
Original assignee: Horiba Ltd; Kyoto University NUC
Current assignee: Horiba Ltd; Kyoto University NUC
Priority date: 2011-08-19
Filing date: 2012-08-02
Publication date: 2014-06-04
Anticipated expiration: 2032-08-02
Also published as: GB2508556B; GB201404450D0

Abstract

Provided are a signal analyzing apparatus, a signal analyzing method and a computer program wherein an analysis that excludes the subjective of a user can be done and the performance of the analysis can be adjusted. A signal analyzing apparatus (1) generates an intensity distribution of a plurality of particular signals from a spectrum distribution on two-dimensional coordinates measured by a measuring device (3) of an EDX apparatus or the like, and classifies n-dimensional coordinate points on an n-dimensional space, which is defined by a combination of the intensities of n particular signals, into a plurality of clusters by use of an EM algorithm. Further, the signal analyzing apparatus (1) determines the points on the two-dimensional coordinates corresponding to the n-dimensional coordinate points included in each cluster, thereby generating the distribution of a respective spectrum having a respective different shape. The distribution of each spectrum having the respective different shape represents the distribution of material components that generates the spectrum having the respective shape. Thus, an analysis that excludes the subjective of a user can be done by use of the EM algorithm, and particular signals to be used for the analysis are selected, thereby allowing the performance of the analysis to be adjusted.

Description

I

Specification

SIGNAL ANALYSIS APPARATUS, SIGNAL ANALYSIS METHOD

AND COMPUTER PROGRAM

[Technical Field]

[00011 The present invention relates to a signal analysis apparatus, a signal analysis method and a computer program for obtaining, from signal distribution on a two-dimensional coordinate system, distribution of a portion where multiple signals have different combinations of intensities llBackgiound Arti [0002] An X-ray analysis is a method for directing radiation ray such as electronic beam or X-ray to a sample and analyzing components contained in the sample from the spectra of characteristic X-ray generated from the sample More specifically, radiation beam is directed to a sample while being scanned, characteristic X-ray from each point on the sample is detected, spectral distnbution in which the spectrum of characteristic X-ray is associated with each point on the sample is created, and components in the sample using the spectral distribution are analyzed As an example of an X-ray analysis using electronic beam as the radiation ray directed to the sample, Energy Dispersive X-ray Spectroscopy (EDX) is known Another example of an X-ray analysis using radiation ray thrected to a sample includes an X-ray fluorescence analysis Furthermore, an analysis method other than the X-ray analysis may be employed for creating spectral distribution For example, in the Raman spectroscopy, spectral thstribution may be created in which the spectrum of Raman scattered light is recorded for each point on an image corresponding to each point on a sample [00031 Since characteristic X-ray of a specific wavelength may be acquired from a specific element, thstribution of a specific element may be obtained by examining the signal intensity of the specific wavelength in the spectrum at each point on a sample Since a sample includes multiple elements, thstnbutions of multiple elements may be obtained from spectral distribution Normally, a sample includes more than one components, each of the components including more than one elements For example, m the case where a sample is a rock, the rock is constituted by multiple mineral components, each of which contains more than one elements As different components may contain the same element, the distribution of a component in a sample does not generally match with the distribution of an element therein.

[0004] Patent Document 1 describes a method of obtaining distributions of multiple elements from spectral distribution and obtaining distributions of a component in a sample from the distributions of multiple elements. In this method, two kinds of linear sums are calculated for values in the distributions of multiple elements using two appropriate sets of coefficents for each point, a scatter diagram is created in which the value-s of the linear sums for the points are two-dimensionally plotted, and the points gathered in the substantially same region on the scatter diagram are determined as the points included in the same component-For the calculation o-f the appropriate coefficients, principal component analysis is used.

13y associating a point on spectral distribution with a component determined as including the point, distribution of components in a sample may be shown. rp his method may be apphcable to spectral distribution obtained with an analysis method other than the X-ray analysis such as the llama ii spectroscopy.

[Frior Art Document] [Patent Document] [Patent Document ii Publication of Japanese Patent No.

[Summary of Invention]

[Problems to be Solved by Invention] iooo6 In the technique descri bed in Patent Document 1, the user classifies multiple points on the scatter diagram obtained by the principal component analysis, which causes such a problem that the user's subjective viewpoint affects the result of classification.

Though there is a method of automatically cIassiing the points based on the distance or the like on the scatter diagram, it is difficult to adjust the performance of the analysis.

[0007] rfhe present invention has been contrived in view of the circumstances described above, arid has an object of providing a signal analysis apparatus, a signal analysis method and a computer program that are able to perform an analysis without the effect of the users subjective viewpoint and to adjust; the performance of the analysis.

[Means for Solving Problems] [0008) A signal analysis apparatus obtaining distribution of a plurality of types of spectra having difierent combinations of intensities of a plurality of specific signals from spectral distribution in which a spectrum composed of one or more signals i determined for each point on a two-dimensional coordinate system, is characterized by comprising: means for generating intensity distribution of a plurality of specific signals from the spectral distribution; means for storing intensity distribution of N specific signals among the generated intensity distribution of a plurality of specific signals. where N is an integer larger than one, 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 fbr 5.

determrnmg the number of clusters used for classifying the generated N-thmensional coordinate points m accordance with positions on the N-dimensional space means for generating a probability distnbution model of an N-dimensional coordinate point included m each cluster, probability calculation means for performing processing of calculating a probability of including each of the generated N-dimensional coordinate points in each cluster, model update means for performing processing of updating a probability distribution model for each cluster so as to increase a likelihood of classification of N-dimensional coordinate points obtained from the calculated probability repeating means for making the probability calculation means and the model update means repeatedly perform processing; and means for generating, for each of the plurality of clusters, distribution of a plurality of types of spectra having different combinations of intensities of N specific signals by specifring distribution, in the spectral distribution, of points corresponding to N-dimensional coordmate points included in each cluster A signal analysis apparatus obtaimng, from intensity distribution of a plurality of signals measured from a same measuring object, distribution of a plurality of types of portions having different combinations of intensities of the plurality of signals to be measured among portions included rn the measuring object, is characterized by comprisin.g means for storing intensity (3 distribution of N signals, means for generating an Nthmensional coordinate point on an N-dimensional space defined by a combination of intensities of N signals for each point in the measuring object means for determining the number of a plurality of clusters used for classifying the generated N-dimensional coordinate points in accordance with positions on the N-dimensional space means for generating a probability distribution model of an N-dimensional coordinate point included in each cluster, probability calculation means for performing processing of calculating a probability of including each of the generated N-dimensional coordinate points in each clusters model update means for performing processing of updating a probability distribution model for each cluster so as to increase a likelihood of classification of N-dimensional coordinate points obtained from the calculated probability repeating means for making the probability calculation means and the model update means repeatedly perform processing and means for generating, for each of the plurality of clusters, distribution of a plurality of types of portions in the measuring object by specifring distribution, in the measuring object, of points corresponding to N-dimensional coordinate points included in each cluster.

[ooiol The signal analysis apparatus according to the present invention, is characterized in that the repeating means makes processing of making the probability calculation means and the

I

model update means repeatedly perform processing until a predetermined convergence condition is satisfied [00111 The signal analysis apparatus according to the present invention, is characterized in that the probability calculation means, the model update means and the repeating means perform processing m accordance with an Expectation-Maximization (EM) algorithm.

[00121 The signal analysis apparatus according to the present invention, is characterized in that means for collecting a plurahty of clusters with a distance between each other on the N-dimensional space being not more than a certain distance, among a plurality of clusters, into one cluster [00131 The signal analysis apparatus according to the present invention, is charactenzed in that means for accepting an initial value for the number of clusters [00141 A signal analysis method for obtaining, by a computer provided with an operation unit and a storage unit, distribution of a plurality of types of spectra having different combinations of intensities of a plurality of specific signals from spectral distribution in which a spectrum composed of one or more signals is determined for each point on a two-dimensional coordinate system, is characterized by comprising generating, by the operation unit.

intensity distribution of a plurality of specific signals from the spectral distribution; storing, by the storage unit, intensity distribution of N specific signals among the generated intensity distribution of t:he plurality of specific signals; generating, by the operation unit, 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: executing, by the operation unit, processing of determining the ] 0 number of a plurality of clusters used for classifying the generated plurality of N-dimensional coordinate points in accordance with positions on the N-dimensionai space: generating, by the operation unit, a probability distribution model of an N-dimensional coordinate point included in each cluster; executing, by the operation unit, probability calculation processing for calculating a probability of including each of the generated plurality of N-dimensional coordinate points in each cluster, executing. by the operation unit, model update processing for updating a probability distribution model for each clustei so as to increase a likelihood of élassiiication of N-dimensional coordinate points obtained from the calculated probability repeatedly executing. by the operation unit, the probability calculation processing and the model update processing; generating, by the operation unit, distribution of a plurality of types 4 spectra having different combinations of intensities of N specific signals by specifying distribution. in the spectral distribution, of points corresponding to N-dimensional coordinate points included in each cluster, 11w each of the plurality of clusters; and storing, by the storage Unit generated distribution of the plurality of types of spectra.

[0015] A computer program making a computer execute processing of obtaining distribution of a plurality of types of spectra having different combinations of intensities of a plurality o-f specific signals from spectral distribution in which a spectrum composed of one or more signals is determined for each point on a two-dimensional coordinate system, is characterized by making the computer execute processing inc]uding the steps of generating intensity distribution of a plurality of specific signals from the spectral distribul:ion 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 for which intensity distribution is generated, for each point included in the spectral distribution; determining the number of a plurality of clusters used for classif'ing the generated plurality of N-dimensional coordinate points in accordance with positions on the N-dimensional space' generating a probability distribution model of an N-dimensional coordinate point included in cacti cluster; executing probability calculation processing for calculating a probability of including each of tile generated plurality of N-dimensional coordinate points in each cluster; executing model update processing for updating a probability distribution model for each cluster so as to increase a likelihood of classification of N-dimensional coordinate points obtained from the calculated probabihty repeatedly executing the probability calculation processing and the model update processmg and generating, for each of the plurality of dusters, distribution of a plurality of types of spectra having different combinations of mtensitzes of N specific signals by specirng distribution, in the spectral distnbution, of points corresponding to N-dimensional coordinate points mcluded in each cluster [00161 In the present invention, intensity distribution of multiple specific signals is generated from the spectral distribution, an N-dimensional coordinate pomt on an N-dimensional space defined by a combination of intensities of N specific signals is generated, the N-dimensional coordinate points are classified into multiple clusters, and the distribution of spectra is generated for each cluster Distribution of spectra hanng a specific shape is obtained, which corresponds to the distribution or the hke of substance components containing multiple elements [00171 In the present invention, an N-dimensional coordinate point on an N-dimensional space, defined by the combination of intensities of N signals measured. from a same measuring object, is generated, the N-dimensional coordinate points are classified into multiple clusters, and the distribution of a part in the measuring object is generated for each cluster For the measuring object, the distribution of parts of multiple types in the measuring objects having different types of contained substance components, electronic states or the hke may be obtained [ooisl In the present invention, when the N-dimensional coordinate points are classified into multiple clusters, the processing in accordance with the EM algorithm is executed so as to precisely conduct a signal analysis [ooi] In the present invention, clusters located close to one another on the N-dimensional space are collected into one cluster Thus, an appropriate number of clusters may be obtained [00201 In the present invention, the initial value for the number of clusters may arbitrarily be designated By designating the number of clusters, the accuracy of processing, time required for processing or the like may be adjusted [Effects of Invention] [00211 According to the present invention, such beneficial effects may be presented that an analysis on signal distribution may be conducted without the effect of the user's subjective viewpoint, while the performance of the analysis may be adjusted by combining specific signals to be used in the analysis.

[Brief Description of Drawings]

[0022] Fig 1 is a block diagram illustrating a configuration of a signal analysis apparatus according to the present invention Fig 2 is a schematic characteristic view illustrating an example of a spectrum; Fig 3 is a flowchart illustrating a procedure of processing performed by the signal analysis apparatus according to Embodiment 1 Fig 4 is a flowchart illustrating a procedute of processing performed by the signal analysis apparatus according to Embodiment 1 Fig 5A is a schematic view illustrating an example of a signal distribution image Fig 5B is a schematic view illustrating an example of a signal distribution image, Fig SC is a schematic view illustrating an example of a signal distribution image Fig 5D is a schematic view illustrating an example of a signal distribution image Fig 6 is an example of a scatter diagram in which N-dimensional coordinate points are plotted on an N-dimensional coordinate system Fig. 7A is a schematic view ifiustrating an example of an image representing distribution of different types of spectra Fig. 7B is a schematic view illustrating an cxample of an image representing distribution of different types of spectra; Fig. 7C is a schematic view illustrating an example of an image representing distribution of different types of spectra; 3 Fig. S is a flowchart illustrating a procedure of processing performed by a signal analysis apparatus according to Emb)diflleflt 2: and Fig. 9 is a flowchart illustrating a procedure of processing performed by the signal analysis apparatus according to Embodiment 2.

[Mode for Carrying Out Invention]

[00231 The present invention wth specifically be described below with reference to the drawings illustrating the embodiments thereof.

Embodiment 1 Fig. 1 is a block djagram illustrating a configuration of a signal analysis apparatus 1 according to the present invention.

The signal analysis apparatus I is constituted with a general-purpose computer such as a personal computer (PC). The signal analysis apparatus 1 includes a CPU (operation unit) 11 performing arithmetic operations. a RAM 12 storing temporary information generated in association with the arithmetic operations, a drive unit 13 such as a CD-ROM drive reading information from a recording medium 2 such as an optical disk, and a non-volatile storage unit 14. The storage unit 14 may be, for example a hard disk. The PU 11 makes the drhe unit 13 read the computer program 21 of the present invention from the recordrng medium 2, and makes the storage unit 14 store the read computer program 21.

The Cpu 11 loads the computer program 21 to the RAM 12 from the storage unit 14 as needed, and the processing necessary for the signal analysis apparatus I is executed in accordance with the loaded computer program 21. Moreover, the sjgnal analysis apparatus I includes an input urnt 16 such as a keyboard, pointing device or the like through which information of various kinds of 1 0 processing instructions is input by the user operating it, and a display unit 17 such as a liquid-crystal display displaying various types of information.

[00241 Note that the computer program 21 may be downloaded to the signal analysis apparatus 1 from an external server apparatus (not illustrated) connected to the signal analysis apparatus I through a communication network (not illustrated) and stored in the storage unit 14. Moreover, the signal analysis apparatus I may also have a form of including an internal recording means such as a ROM in which the computer program 21 is recorded. instead of accepting the computer program 2:1 from the outside.

[00251 Moreover, the signal analysis apparatus I includes an interface unit 15 connected to a measurement device 3 for measuring two-dimensional spectral distribution. The measurement device 3 may be, for example, an EDX spectrometer, an X-ray fluorescence spectrometer or a Raman spectrometer The EDX spectrometer directs electronic beam to each point on a sample, detects characteristic X-ray generated from each point on the sample, and measures spectral distribution in which the spectra of characteristic X-ray obtained from the respective points are distributed on a two-dimensional coordinate system The X-ray fluorescence spectrometer directs X-ray to each point on a sample, detects X-ray fluorescence generated from each point on the sample, and measures spectral distribution in which the spectra of X-ray fluorescence obtained from the respective points are distributed on a two-dimensional coordinate system The Raman spectrometer directs light to each point on a sample and detects Raman scattered light generated from each point on a sample, and measures spectral distribution in which the spectra of Raman scattered light obtained from the respective points are distributed on the two-dimensional coordinate system The measurement apparatus 3 may be any other apparatus which can measure spectral distribution [0026] Fig 2 is a schematic characteristic view illustrating an example of a spectrum. In general, the spectrum is constituted by a combination of multiple signals In Fig 2, the horizontal ans indicates a wavelength while the vertical axis indicates the signal intensity at each wavelength In Fig 2, a peak of a signal included in the spectrum is indicated by an arrow. The signal included in the spectrum is identified by the wavelength. In the case of the spectrum of characteristic X-ray, each signal depends on an element contained in a sample The spectral distribution measured by the measurement apparatus 3 is constituted by spectra obtained for each point on the two-dimensional coordinate system corresponthng to the surface of the sample Each spectrum has a different combination of intensities of the contained signals and a different shape of the spectrum For example, a spectrum may be formed by a single signal, or may have zero signal intensity Note that the horizontal axis of a spectrum is not limited to the wavelength, and may also be energy, wave number oi the like Moreover, the horizontal axis of a spectrum is not limited to an absolute value, but may also be a relative value, such as a displacement from a certain wavelength [00271 The processing performed by the signal analysis apparatus 1 will now be described Figs 3 and 4 show a flowchart illustrating a procedure of processing performed by the signal analysis apparatus 1 according to Embodiment 1 The CPU 11 executes the processing described below in accordance with a computer program Spectral distribution data is input from the measurement device 3 to the interface unit 15, and the CPU 11 makes the storage unit 14 store the spectral distribution data (Si) The spectral distribution data is the data including the two-dimensional coordinates at each point on a sample and spectral data obtained from each point associated with each other The spectral data is the data including a wavelength or the like and signal intensity associated with each other The CPU 11 subsequently generates signal distribution data indicating intensity distribution of multiple specific signals from the spectral distribution data (S2) More specifically, at step S2, the CPU 11 reads out the signal intensity of a specific signal identified by a predetermined wavelength from the spectrum of each point, and generates signal distribution data in which the read-out signal intensity is associated with each point on the two-dimensional coordinate system in other words, the signal distribution data is the data including two-dimensional corn dinates at each point on a sample and signal intensity at a specific wavelength associated with each other The storage unit 14 stores multiple wavelengths in advance as the wavelengths of specific signals The CPU 11 generates signal distribution data for each of the multiple specific signals In other words, at step S2, multiple pieces of signal distribution data are generated Itis noted that the wavelengths of specific signals may be included in the computer program 21 Moreover, the specific signals may be identified by energy, wave number or the like Furthermore, a specific signal may be identified by a signal waveform in the spectrum, not by the position of a peak in the spectrum In addition, the signal analysis apparatus 1 may have a form in which externally-generated signal distribution data is input and the processing steps at and after step S3 are executed.

[0028] rube CPU 11 subsequently makes the display unit 17 display a signa] distribution image representing the intensity distribution of specific signals on I:he two-dimensional coordinate system based on the generated signal distribution data S3). Figs. 5A, 5B, 5C and SD are schematic views illustrating examples of signal distribution images. Jn Figs. 5A, 5B, 5C and 5D, four signal distribution images obtained from one spectral distribution are shown. The batched areas iii the drawings indicate the parts each having the intensity of a specific signal larger than zero. In a part where the intensity of a specific signal is larger than zero, the signal intensity differs for each point. The four signal distribution images shown in Figs. 5A, 5B, 5C and 51) represent the intensity distribution of different signals. The intensity distribution shown in Fig. 5A is set as the intensity distribution for a signal a, the intensity distribution shown in Fig. SB is set as the intensity distribution for a signal b, the intensity distribution shown in Fig. SC is set as-*th.e intensity distribution for a signal c, and the intensity distribution shown in Fig. 5D is set as the intensity distribution tbr a signa.l d -If the spectrum is of characteristic X-ray. the signal distribution image shows the density distribution for a specific element contained in a sample. The signal analysis apparatus I performs, at and after step 84, processing of obtaining the distribution of multiple types of spectra having different. combinations of intensities of multiple specific signals. The distribution of mu]tiple types of spectra corresponds 1:0 the distribution of multiple types of substance components with uifferent amounts of contained muitip]e specific elements in a sample.

[00291 The CPU 11 subsequently accepts selection of N specific signals frorn multiple specific signals for which the signal distribution images are displayed, in response to the user operating the input unit 16 (S4. Here. N is an integer larger than one. The cpu 11 accepts at step S4 selection of specific signals not less than two. For example, assume that the signals a and d are selecte& for which the signal distribution images are shown respectively in Figs. 5A and 51). It is noted that the CPU 1.1 may automatically and appropriately select specific signals. The CPU I I subsequently stores signal distribution data for the selected N signals in the storage unit 14 (55). rrhe CPU 11 subsequently generates N-dimensional data composed of the combination of intensities for the selected N specific signals (SB). More specifically, the CPU 11 generates an N-dimensional coordinate point on the N-dimensional space defined by the combination of intensiUes of the selected N specific signals, and generates N-dimensional data in which two-diinensjonal coordinates and N-dimensional coordinates for each point on the two-dimensional coordinate system are associated with each other.

[003 o] Fig. 6 is an example of a scatter diagram in which N-thmensional coordinate points are plotted on the N-dimensional coordinate system Fig 6 shows the case where the signals a and d are selected as specific signals and where N2 In Fig 6, the horizontal axis indicates the intensity of the signal a, while the vertical axis indicates the intensity of the signal d For each point on the twothmensional coordinate system corresponding to the surface of a sample, an Ndimensional coordinate point is plotted on the N-dimensional space The N-dimensional coordinate points may overlap with one another on the N-dimensional space It is noted that the signal analysis apparatus 1 may also have a form of accepting input of the N-dimensional data generated outside and executmg the processing at and after step S7 At and after step S7, the signal analysis apparatus 1 performs processing of classifying multiple N-dimensional coordinate points into multiple clusters with the Expectation-Maximization (EM) algorithm [00311 The CPU 11 accepts an initial value for the number of clusters in response to the user operating the input unit 16 (S7) The CPU 11 may perform, at step S7, processing of determining an appropriate numeric value as the initial value for the number of clusters. The CPU 11 subsequently performs initial setting for a probability distribution model of the N-dimensional coordinate points included in. each of the determined number of clusters (S8).

More specifically, the CPU 11 sets parameters for the probability distribution indicating the probability of including each point on the N-dimensional space in each cluster The parameters for probability distribution includes the center position on the N-dimensional space for each cluster As for the probability distribution, for example, Poisson mixture distribution or Gaussian mixture distribution used in the EM algorithm is used [00321 The CPU 11 subsequently calculates the probability of including each of N-dimensional coordinate points on the N-dimensional space in each cluster based on the probability distribution model for each cluster (59) The processing at step SB corresponds to the E (Expectation) step in the EM algorithm The CPU ii then performs processing of updating parameters for the probability distribution model for each cluster so as to raise the overall likelthood (Sm) More specifically, the parameters for probability distribution, such as the center position on the N-dimensional apace for each cluster, are updated The processing at step 510 corresponds to the M (Maximization) step in the EM algorithm [00331 The CPU 11 subsequently conducts a convergence test in the EM algonthm (Si i) As the indicator for convergence, an indicator generally used in the EM algorithm is employed, such as the value, the change amount or the change rate of a likelihood, the values, the change amounts or the change rate of the parameters for the probability distribution model. For example, the CPU ii determines that convergence has occurred when the amount of change in the likelihood is not larger than a predetermined value, and that convergence has not occurred when the amount of change in the likelihood is larger than the predetermined value It is noted that the signal analysis apparatus 1 may have a form of executing processing using, instead of the EM algorithm, an algonthm in the maximum likelihood estimation method or the maximum a posteriori estimation method For example, the signal analysis apparatus 1 may perform processing with an algorithm in the soft k-means clustering or NewtonRaphson method [00341 If no convergence has yet occurred at step Si 1 (S 11 NO), the CPU 11 returns the processing to step S9 If it is determined that convergence has occurred (Si 1 YES), the CPU ii determines whether or not clusters located close to each other with a distance not more than a predetermined distance on the N-thmensional space are present in the multiple cluster (S12) For example, at step 512, the CPU 11 calculates the Mahalanobis distance between the centers of two clusters, and makes a determination based on whether or not the calculated Mahalanobis distance is not more than a predetermined distance. Moreover, for example, the CPU ii calculates the inner product of vectors to the centers between the two clusters, and determines that the distance to each other is not more than a predetermined distance when the calculated inner product is closer to one compared to a predetermined threshold.

The CPU 11 executes the processing of determining the distance between two clusters for all the combinations of clusters At step SI 2, the CPU Ii may make a determination with a method other than the above When clusters located close to each other are present (S 12 YES), the CPU 11 combines such clusters (Si 3) More specifically, the CPU ii performs processing of determining that the range of the multiple clusters as a range of one new cluster Fig 6 shows the ranges of clusters with sohd lines In the example shown in Fig 6, four clusters are obtained [00351 After completing step 513, or when there are no clusters located close to each other at step Si2 (812 NO), the CPU ii independently generates distribution data of multiple types of spectra having thfferent combinations of intensities of multiple specific signals by speciing points on the two-dimensional coordinate system corresponding to Ndimensional points included m each cluster (514) The distribution data of each spectrum corresponds to data in which a two-dimensional coordinates at each point on a sample is associated with the data indicating presence/absence of a specific spectrum at each point The distribution data of a spectrum is generated for each of different types of spectra having different combinations of intensities of multiple specific signals The CPU ii subsequently makes the storage unft 14 store the generated distribution data of the independent spectrum (S is) and terminates the processing.

[00361 Figs 7A, 7B and 7C are schematic views showing examples of images representing the distribution of multiple types of spectra Fig 7A shows the distribution of spectra including the signal a but not including the signal d, Fig 7B shows the disLribution of spectra not including the signal a but including the signal d, and Fig 7C shows the distribution of spectra including both the signals a and d Accordingly, the two-dimensional distribution of multiple types of spectra having different combinations of intensities of multiple specific signals is obtained from the initial spectral distribution data If the spectra is of characteristic X-ray, the distnbution of different types of spectra corresponds to the distribution, in a sample, of multiple substance components having different amounts of contained multiple elements Assuming that the signal a corresponds to an element A, while the signal d corresponds to an element D, Fig 7A shows the distribution of substance components including the element A but not including the element ID In addition, Fig 7B shows the distribution of substance components not including the element A but including the element D, while Fig 7C shows the distribution of substance components including both the elements A and D [00371 Note that the spectral distribution obtained at step S14 is, in general, also the distribution of different types of spectra 26 having different combinations of intensities of multiple signals. It is thus possible, m the present invention, to obtain distribution other than the ones shown in Figs 7A, 713 and 7C For example, distribution of spectra having the different combinations of intensities of multiple signals from those in Figs 7A, 7B and 7C may also be obtained, such as the spectra with the signal a having the intensity of one and the signal d having the intensity of two, or the spectra with the signal a havmg the intensity of two and the signal d having the intensity of one Furthermore, since the clusters on the N-dimensional coordinate system have a certain degree of allowance, the combinations of intensities of signals included in each thstribution of spectra obtained at step S14 may also have an allowance to some extent It may, for example, also be possible to generate distribution of spectra with the signal a having the intensity not less than one but less than two and the signal d having the intensity less than one, distribution of spectra with the signal a having the intensity less than one and the signal d having the intensity not less than one but less than two, and distribution of spectra with both the signals a and d each having the intensity not less than two.

[0038] In the case where the signal analysis apparatus 1 uses the input signal distribution data to execute the processing at and after step S3, the CPU 11 likewise generates, at step S 14, distribution data indicating the distribution of multiple types of portions, on a sample, having different combinations of intensities of multiple s:ignals At step S15, the CPU 11 makes the storage umt 14 store the generated distribution data In this form also, distribution similar to the distribution shown in Figs 7A, 7B and 7C may be obtained Likewise, distribution of portions on a sample where the combinations of signal intensities are different from those in the examples of Figs 7A, 7B and 7C may also be obtained The combination of signal intensities included in each distribution may have a certain degree of allowance [00391 It is noted that the signal analysis apparatus 1 may also take a form of performing processing of determining the number of repetitions for the processing at steps S9 and 510, instead of making a determination on convergence In this form, the signal analysis apparatus 1 stores in the storage unit 14 a prescribed number of repetitions fox steps 59 and Sb in advance At step 511, the CPU 11 determines whether or not the number of repetitions for processing has reached a prescribed number, returns the processing to step S9 if the number of repetitions for processing has not yet reached the prescribed number, and proceeds the processing to step Si 2 if the number of repetitions for processing has reached the prescribed number As the prescribed number for repeating processing, a number at which the likehhood for the entire clusters have an empirically sufficient magnitude is determined. The prescribed number is, for example, one hundred times The signal analysis apparatus 1 may shorten the time for calculation by terminating the repetition for processing at the prescribed number irrespective of whether or not a convergence conthtion is satisfied Furthermore, the signal analysis apparatus] may also take a form of performing determination both on the convergence and the number of times, and may proceed to step S12 when the convergence condition is satisfied before the number of repetitions for processing reaches the prescribed number [0040] As has been described above, the signal analysis apparatus 1 generates intensity distribution of multiple specific signals from the spectral distribution measured by the measurement device 3 such as the EDX spectrometer, and classifies the N-dimensional coordmate points on the N-dimensional space defined by a combination of intensities of N specific signals into multiple clusters with the EM algonthm The points on the spectral distribution corresponding to the N-dimensional coordinate points included in the same cluster have substantially the same combination of intensities of multiple specific signals included in the spectra, so as to generate an approximately equal spectral shape The points on the spectral distribution corresponding to the N-dimensional coordinate points included in different clusters have different combinations of intensities of multiple specific signals included in the spectra., so as to generate different shapes of spectra.. By speciing points on the two-dimensional coordinate system corresponding to the N-dimensional coordinate points included in each cluster, distribution of spectra each having a different shape is independently generated. The distribution of spectra havin.g different shapes represent the distribution of substance components generating spectra having corresponding shapes. For example, the distribution of different types of components with different compositions that are inriuded in a sample measured by the EDX spectrometer may be obtained More specifically, in the case where the sample measured by the EDX spectrometr is a rock, the distribution of various types of mineral components included in the sample may be obtained. Also iii the case where the measurement device 3 is another device such as the Raman spectrometer, similarly, the signal analysis apparatus 1 is able to obtain the distribution of various types of substance components included in the sample.

[00411 In the present invention, the EM algorithm is used to automatically conduct clustering. Thus classifying of Ndimensiona] coordinate points is performed without the user's subjective vIewpoint, allowing a precise signal analysis not affected by the user's subjective viewpoint. Further in the preset invention, the cnstnbutjon of substance components may be obtained without identifying substance components contained in a sample. Further in the present invention, multiple specific signals to be used in the analysis may be selected By limiting signals to be analyzed, for example, such distribution may be obtained that the substance corn ponents not. necessary to be examined are excluded from the analysis objects and the substance components necessary to be examined are specifically be represented, allowing adjustment ol the analysis perfbrmance. It is also possible to shorten the time required for calculation. F'urther in the present invention, the initial value for the number of clusters may be designated. The performance of the analysis may be adjusted by designating the initial value for the number of clusters. For example. a detailed analysis may be possible by setting the initial value for the number of clusters to be large, while the type of substance components necessary for distribution may be limited by setting the initial value br the number of clusters to be small. Moreover, the time reqtiired br the analysis may also be adjusted. Further in the present invention, the distribution of an appropriate number of substance components may be obtained even in the case where the initial value for the number of clusters is too large, by collecting clusters located close to each other into one cluster. Moreover, the signal analysis app2.ratus I may also have a form of storing parameters for the EM algorithm in the storage unit 14 during the processing of the EM algorithm. In this form, it may be possible for the signal analysis apparatus I to shorten the processmg by the alreadystorod parameters when analyzing the spectral distribution obtained from a similar sample.

[00421 Embodiment 2 The structure of a signal analysis apparatus 1 according to Embodiment 2 is similar to that in Embodiment 1 Figs 8 and 9 are flowcharts illustrating procedures of processing performed by the signal analysis apparatus 1 according to Embodiment 2 A CPU Ii executes the processing below in accordance with a computer program The CPU 11 executes the processing at steps SI to 58 similar to that in Embodiment 1 After step 58 is terminated, the CPU 11 calculates the probability of including each N-dimensional coordinate point on the N-dimensional space in each cluster, based on a probabthty distribution model for multiple clusters (521) The CPU 11 subsequently performs processing of updating parameters for the probability distnbution model for each cluster so as to raise the overall likelihood (522) The CPU 11 then performs determination on convergence for the EM algorithm (523) If convergence has not yet occurred (S23 NO), the CPU 11 returns the processing to step 521 If it is determined that convergence has occurred (523 YES), the CPU 11 makes the storage unit 14 store the parameters for the probability distribution model for each cluster (S24) and terminates the processing As described above, the signal analysis apparatus 1 generates parameters for multiple clusters on the Ndimensionai space by the processing performed at steps Si to 88 and steps 521 to 524. As in Embodiment 1, the CPU ii may have a form of performing processing of determining the number of repetitions for the processing at steps S21 and 522, instead of making a determination on convergence.

[0043] Furthermore, the signal analysis apparatus] performs processing of generating thstribution data of multiple types of spectra having different combinations of intensities of multiple specific signals, based on the generated parameters for multiple clusters The CPU 11 first reads out parameters for the probability distribution model for multiple clusters, which are stored in a storage unit 1.4, onto a RAM 12 (S31) The CPU 11 then accepts a threshold for determining whether or not the clusters are located close to each other on the N-dimensional space in response to the user operating an input unit 16 (S32) At step S32, the CPU 11, for example, accepts input of a threshold value for the Mahalanobis distance between the centers of clusters or input of a threshold value for an mner product of vectors to the centers of clusters The CPU 11 subsequently determines, based on the accepted threshold, whether or not there are clusters located close to each other with a distance on the N-dimensional space not more than the distance corresponding to the threshold (S33) At step S33, for example, the CPU 11 calculates the Mahalanobis distance between the centers of clusters, and makes a determination based on whether or not the calculated Mahalanobis distance is not more than the accepted threshold For another example, the CPU 11 calculates an inner product of vectors to the centers of two clusters, and determines that the distance between the clusters is close when the calculated inner product is closer to one compared to the accepted threshold The CPU 11 executes the processing of determining the distance between two clusters for all the combinations of clusters At step S33, the CPU 11 may make a determination with a method other than above [0044] When there are clusters located close to each other (533 YES), the CPU 11 combines such clusters (534) After step 534 is terminated or when there are no clusters located close to each other at step 533 (533 NO), the CPU 11 independently generates the distribution data of multiple types of spectra having thiferent combinations of intensities of multiple specific signals, and makes the storage unit 14 individually store the distribution data of each of the spectra (535) The CPU 11 subsequently makes the display umt 17 display the distribution of multiple types of spectra based on the generated distribution data of multiple types of spectra (536) For example, the CPU 11 makes the display unit 17 display an image representing distribution of spectra as shown in Figs 7A to 7C After step 536 is terminated, the CPU 11 terminates the processing The signal analysis apparatus 1 repeats the processing of steps S31 to S36 in accordance with a processing instruction to be input to the input unit 16 by the user's operation [0045] As has been described above, in the present embodiment, the signal analysis apparatus 1 may repeat the processing of steps 531 to S36 several times based on the parameters obtained by the processing at steps Si to 58 and steps S21 to 524. The processing of steps 831 to 536 show thfferent results depending on a threshold for determining the distance between clusters For example, if the distance depending on the threshold is small, the number of clusters is increased, the type of spectra for which the distribution is obtained is increased, and the number of substance components in a sample for which the distribution is obtained is also increased On the contrary, if the distance depending on the threshold is large, the number of clusters is decreased, the type of spectra for which the distribution is obtained is decreased, and the number of substance components in a sample for which the distribution is obtained is also decreased Thus, there is a need for adjusting the threshold value to an appropriate value in order to obtain the distribution of an appropriate number of substance components By repeating the processing at steps 831 to S36 by the signal analysis apparatus 1 while changing a threshold to be input by the user, a result appropriate for the user may be obtained The processing procedures at steps Si to 88 and steps S21 to S24 are separated from the processing at steps S31 to S36 and are not repeated, thereby avoiding the processing with high load and increasing the processing efficiency in the signal analysis apparatus 1 Furthermore, the user repeats the operation of changing the input threshold after recognizing the processing result in accordance with the threshold, so that a signal analysis for spectral distribution may be conducted in real time using the signal analysis apparatus 1 [00461 While Embodiments Ii. and 2 showed examples where one measurement device 3 is connected to the signal analysis apparatus 1, the signal analysis apparatus 1 according to the present invention may also have a form in which more than one measurement devices 3 may be connected. Furthermore, the signal analysis apparatus 1 may also have a form of executing similar signal analysis processing using the distribution of signal intensities measured by the measurement devices 3 directed to measure the same sample, and obtaining the distribution of multiple types of portions having different combinations of signa intensities measured by multiple measurement methods among the portions included in the sample.

In this form, the signal analysis apparatus 1 may perform a detailed analysis thai; cannot be conducted by only using the measurement result from a single measurement device 3. For example, an analysis using the measurement results from the EDX spectrometer and Raman spectrometer i9 eonducled so as to obtain the distribution of the portions with a crystal structure which emits specific Raman scattered light among the substance components emitting a specific X-ray spectrum.

[00471 In addition, the signal analysis apparatus 1 is not limited to the form of accepting data from the measurement device 3 connected thereto, hut may also take a form of accepting input of the distribution of signal intensities measured by a measurement device not connected thereto and conducting a signal analysis. Moreover, the thstribution of signal intensities to be analyzed by the signal analysis apparatus 1 is not limited to the ones measured from a sample to be measured in a laboratory, but may be more general measurement data For example, according to the present invention, it is possible to obtam the distribution of celestial objects with larger emission intensities of both visible light and X-ray, from the result of astronomical observation with visible light and X-ray.

[Industrial Apphcabthtyl [00481 The present invention is used to obtain distribution of desired components in a measuring object, such as distribution of specific substance components, from the distribution of intensities of multiple signals obtained from the measuring object using a single measurement device such as the EDX spectrometer or multiple types of measurement devices

[Description of Reference Codes]

[0049] 1 signal analysis apparatus 11 CPU (operation unit) 12 RAM 14 storage unit 2 recording medium 21 computer program 3 measurement device