Spectral decomposition apparatus, spectral decomposition method, and program

Abstract

To highly accurately perform spectral decomposition on spectral data whose at least one end has been cut off.SOLUTION: A spectral decomposition device includes: a spectral input part configured to accept input of spectral data whose at least one end has been cut off; and a parameter estimation part configured to estimate a parameter for assigning a bell-shaped distribution, whose at least one end has been cut off, to the spectral data by performing Bayesian estimation using a Dirichlet process mixture model.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] This disclosure relates to a spectral decomposition apparatus, a spectral decomposition method, and a program. [Background technology]

[0002] There are techniques for decomposing complex spectra into multiple normal distributions. For example, Non-Patent Document 1 discloses a technique in which the parameters of each normal distribution are Bayesian-estimated for each number of normal distributions, and the spectrum is decomposed into the number of normal distributions that minimizes the Bayesian free energy.

[0003] By using a Dirichlet process mixture model, it is possible to simultaneously estimate the number of normal distributions and their parameters. For example, Non-Patent Document 2 discloses a technique for decomposing a complex probability density function into a simpler one by using Bayesian estimation with a Dirichlet process mixture model. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Kenji Nagata, Seiji Sugita, and Masato Okada, "Bayesian spectral deconvolution with the exchange Monte Carlo method", Neural Networks, vol. 28, pp. 82-89, 2012. [Non-Patent Document 2] Abhra Sarkar, Bani K. Mallick, John Staudenmayer, Debdeep Pati, and Raymond J. Carroll, "Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors", Journal of Computational and Graphical Statistics, vol. 23(4), pp. 1101-1125, 2014. [Overview of the project] [Problems that the invention aims to solve]

[0005] However, conventional techniques have the problem that they cannot resolve spectra with at least one end cut off with high precision. Spectra observed by measuring instruments may have at least one end cut off due to factors such as the observation range of the measuring instrument.

[0006] For example, the prior art disclosed in Non-Patent Document 1 is inefficient because it performs Bayesian estimation on the parameters of each normal distribution sequentially for each normal distribution, resulting in a large number of Bayesian estimations. For example, the prior art disclosed in Non-Patent Document 2 does not consider the decomposition of spectra that have been cut off at least one end.

[0007] In view of the technical challenges described above, this disclosure aims to resolve spectra with at least one end cut off with high precision. [Means for solving the problem]

[0008] This disclosure comprises the following configuration.

[0009] [1] A spectral input unit configured to accept spectral data with at least one end cut off, A parameter estimation unit configured to estimate parameters for assigning a fishing bell-shaped distribution with at least one end cut off to the spectrum data by performing Bayesian estimation using a Dirichlet process mixture model, A spectrum decomposition device comprising the above.

[0010] [2] The spectrum decomposition device according to [1] above, [[ID=�]] where the parameters include the height, position, and width of the peak of each fishing bell-shaped distribution. Spectrum decomposition device.

[0011] [3] The spectrum decomposition device according to [2] above, where the fishing bell-shaped distribution is a distribution symmetric about the center of the peak or a distribution asymmetric about the center of the peak. Spectrum decomposition device.

[0012] [4] The spectrum decomposition device according to [1] above, where the parameter estimation unit is configured to perform the Bayesian estimation by obtaining a posterior distribution by the Markov chain Monte Carlo method, the variational Bayesian method, or maximum a posteriori probability estimation. Spectrum decomposition device.

[0013] [5] The spectrum decomposition device according to [1] above, further comprising a decomposition result output unit configured to output a plurality of spectrum data representing components of the spectrum data based on the parameters. Spectrum decomposition device.

[0014] [6] The spectrum decomposition device according to [5] above, where the decomposition result output unit is further configured to output the parameters corresponding to each spectrum data. Spectrum decomposition device.

[0015] [7] The spectrum decomposition device according to [6] above, The decomposition result output unit is configured to further output the parameters calculated by the parameter estimation unit during the estimation process. Spectrum decomposition device.

[0016] [8] A computer A spectrum input procedure for receiving an input of spectrum data with at least one end cut off, A parameter estimation procedure for estimating parameters for assigning a cut-off bell-shaped distribution to the spectrum data by performing Bayesian estimation using a Dirichlet process mixture model, A spectrum decomposition method for executing the above.

[0017] [9] To a computer A spectrum input procedure for receiving an input of spectrum data with at least one end cut off, A parameter estimation procedure for estimating parameters for assigning a cut-off bell-shaped distribution to the spectrum data by performing Bayesian estimation using a Dirichlet process mixture model, A program for causing the above to be executed.

Advantages of the Invention

[0018] According to the present disclosure, spectrum data with at least one end cut off can be spectrally decomposed with high accuracy.

Brief Description of the Drawings

[0019] [Figure 1] It is a block diagram showing an example of the overall configuration of a spectrum decomposition system. [Figure 2] It is a block diagram showing an example of the hardware configuration of a computer. [Figure 3] It is a diagram showing an example of the functional configuration of a spectrum decomposition system. [Figure 4] It is a flowchart showing an example of the processing procedure of a spectrum decomposition method. [Figure 5]This figure shows an example of spectral data to be decomposed. [Figure 6] This figure shows an example of spectral data after scaling. [Figure 7] This figure shows an example of a bell-shaped distribution. [Figure 8] This figure shows an example of the process of folding a rod. [Figure 9] This is a flowchart showing an example of the parameter estimation process. [Figure 10] This figure shows an example of a convergence condition. [Figure 11] This figure shows an example of parameter estimation results. [Figure 12] This figure shows an example of parameter estimation results after scale restoration. [Figure 13] This figure shows an example of the decomposition results in the example. [Figure 14] This figure shows an example of the decomposition results in the example. [Modes for carrying out the invention]

[0020] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In this specification and drawings, components having substantially the same functional configuration are denoted by the same reference numerals, and redundant descriptions will be omitted.

[0021] [Embodiment] One embodiment of the present invention is a spectral decomposition system that decomposes input spectral data into its individual components. The spectral decomposition system in this embodiment takes spectral data with at least one end cut off as input and decomposes the spectral data into its individual components by assigning one or more bell-shaped distributions with at least one end cut off to each.

[0022] The spectral decomposition system in this embodiment simultaneously estimates the number of bell-shaped distributions to assign to the spectral data and the parameters of each bell-shaped distribution. Parameter estimation is performed using Bayesian estimation with a Dirichlet process mixture model.

[0023] An example of spectral data in this embodiment is a fluorescence spectrum obtained by irradiating a sample with ultraviolet or visible light and measuring the amount of light emitted by the sample. By decomposing the fluorescence spectrum into its constituent peaks, it is possible to analyze the state, concentration, or composition of the sample.

[0024] Another example of spectral data in this embodiment is an ultraviolet-visible absorption spectrum obtained by irradiating a sample with ultraviolet or visible light and measuring the amount of light absorbed by the sample. By decomposing the ultraviolet-visible absorption spectrum into its individual components, it is possible to analyze the state, concentration, or composition of the sample.

[0025] Another example of spectral data in this embodiment is a mass spectrum obtained by ionizing a sample and detecting molecules under a magnetic field. By decomposing the mass spectrum into its individual components, information regarding the structure of the sample molecules can be obtained and used for identifying existing substances or determining the structure of new substances.

[0026] <Overall Configuration of the Spectral Decomposition System> First, the overall configuration of the spectral decomposition system in this embodiment will be described with reference to Figure 1. Figure 1 is a block diagram showing an example of the overall configuration of the spectral decomposition system in this embodiment.

[0027] As shown in Figure 1, the spectral decomposition system 1 in this embodiment includes a spectral decomposition device 10, a measuring device 20, and a user terminal 30. The spectral decomposition device 10, the measuring device 20, and the user terminal 30 are connected via a communication network N1 such as a LAN (Local Area Network) or the Internet, enabling data communication.

[0028] The spectral decomposition device 10 is an information processing device such as a PC (Personal Computer), workstation, or server that decomposes spectral data generated by the measuring device 20. The spectral decomposition device 10 receives spectral data to be decomposed from the measuring device 20. The spectral decomposition device 10 then decomposes the received spectral data into its individual components and transmits the decomposition results to the user terminal 30.

[0029] The measuring device 20 is an instrument that measures a sample based on a predetermined method in response to user operation and generates spectral data. The measuring device 20 transmits the generated spectral data to the spectral decomposition device 10. An example of the measuring device 20 is a spectrofluorometer. Other examples of the measuring device 20 are an ultraviolet-visible spectrophotometer or a mass spectrometer.

[0030] The user terminal 30 is an information processing terminal such as a PC, tablet, or smartphone operated by the user. The user terminal 30 receives the decomposition results from the spectral decomposition device 10 and outputs them to the user.

[0031] The overall configuration of the spectral decomposition system 1 shown in Figure 1 is just one example, and various system configurations are possible depending on the application and purpose. For example, the spectral decomposition device 10 may be implemented using multiple computers, or it may be implemented as a cloud computing service. Alternatively, for example, the spectral decomposition system 1 may be implemented using a standalone information processing device that combines the functions that the spectral decomposition device 10, the measuring device 20, and the user terminal 30 should each have.

[0032] <Hardware configuration of the spectral decomposition system> Next, the hardware configuration of the spectral decomposition system 1 in this embodiment will be described with reference to Figure 2.

[0033] Computer Hardware Configuration In this embodiment, the spectral decomposition device 10 and the user terminal 30 are implemented, for example, by a computer. Figure 2 is a block diagram showing an example of the hardware configuration of the computer 500 in this embodiment.

[0034] As shown in Figure 2, the computer 500 includes a CPU (Central Processing Unit) 501, ROM (Read Only Memory) 502, RAM (Random Access Memory) 503, HDD (Hard Disk Drive) 504, input device 505, display device 506, communication interface 507, and external interface 508. The CPU 501, ROM 502, and RAM 503 form what is known as a computer. Each piece of hardware in the computer 500 is interconnected via a bus line 509. The input device 505 and display device 506 may also be used by connecting them to the external interface 508.

[0035] The CPU 501 is a processing unit that controls and implements the overall functions of the computer 500 by reading programs and data from storage devices such as the ROM 502 or HDD 504 onto the RAM 503 and executing processing.

[0036] ROM502 is an example of non-volatile semiconductor memory (storage device) that can retain programs and data even when the power is turned off. ROM502 functions as the main memory, storing various programs and data necessary for the CPU501 to execute the programs installed on HDD504. Specifically, ROM502 stores boot programs such as BIOS (Basic Input / Output System) and EFI (Extensible Firmware Interface) that are executed when the computer 500 starts up, as well as OS (Operating System) settings, network settings, and other data.

[0037] RAM503 is an example of volatile semiconductor memory (storage device) whose programs and data are erased when the power is turned off. RAM503 includes, for example, DRAM (Dynamic Random Access Memory) and SRAM (Static Random Access Memory). RAM503 provides a working area that is expanded when various programs installed on HDD504 are executed by CPU501.

[0038] HDD504 is an example of a non-volatile storage device that stores programs and data. The programs and data stored in HDD504 include the operating system (OS), which is the basic software that controls the entire computer 500, and applications that provide various functions on the OS. Note that computer 500 may use a storage device that uses flash memory as its storage medium (e.g., SSD: Solid State Drive) instead of HDD504.

[0039] The input device 505 includes a touch panel used by the user to input various signals, operation keys and buttons, a keyboard and mouse, and a microphone for inputting sound data such as voice.

[0040] The display device 506 consists of a display such as a liquid crystal or organic EL (Electro-Luminescence) that displays a screen, and a speaker that outputs sound data such as audio.

[0041] Communication I / F 507 is an interface that connects to a communication network and allows computer 500 to perform data communication.

[0042] External I / F 508 is an interface for external devices. Examples of external devices include the drive device 510.

[0043] The drive device 510 is a device for setting the recording medium 511. The recording medium 511 here includes media that record information optically, electrically, or magnetically, such as CD-ROMs, flexible disks, and magneto-optical disks. The recording medium 511 may also include semiconductor memory that records information electrically, such as ROMs and flash memory. This allows the computer 500 to read and / or write to the recording medium 511 via the external I / F 508.

[0044] The various programs to be installed on the HDD 504 are installed, for example, when the distributed recording medium 511 is set in a drive device 510 connected to an external I / F 508, and the various programs recorded on the recording medium 511 are read by the drive device 510. Alternatively, the various programs to be installed on the HDD 504 may be downloaded via the communication I / F 507 from a network other than the communication network and installed that way.

[0045] <Functional Configuration of the Spectral Decomposition System> Next, the functional configuration of the spectral decomposition system in this embodiment will be described with reference to Figure 3. Figure 3 is a block diagram showing an example of the functional configuration of the spectral decomposition system 1 in this embodiment.

[0046] ≪Functional Configuration of Spectral Decomposition Device≫ As shown in Figure 3, the spectral decomposition device 10 in this embodiment includes a spectral input unit 101, a scale conversion unit 102, a parameter estimation unit 103, a scale restoration unit 104, and a decomposition result output unit 105.

[0047] The spectral input unit 101, scale conversion unit 102, parameter estimation unit 103, scale restoration unit 104, and decomposition result output unit 105 are realized by a process in which a program, which is loaded from the HDD 504 shown in Figure 2 onto the RAM 503, is executed by the CPU 501.

[0048] The spectral input unit 101 receives spectral data to be decomposed (hereinafter also referred to as the "target spectrum") from the measuring device 20. In this embodiment, the target spectrum is assumed to be truncated at least one end. The target spectrum may be truncated at both ends. Furthermore, the truncation position (for example, the distance from the center of the peak) is not limited. In this specification, the center of the peak refers to the position of the local maximum intensity of the target spectrum before the spectral data is decomposed into its components. The center of the peak may also be the position of the local maximum intensity after smoothing or the like.

[0049] The scale conversion unit 102 converts the scale of the target spectrum received by the spectrum input unit 101 so that the integral value of the target spectrum becomes 1.

[0050] The parameter estimation unit 103 estimates parameters for assigning one or more bell-shaped distributions, each with at least one end cut off, to the target spectrum (hereinafter also referred to as the "transformed spectrum") that has been scaled by the scale transformation unit 102. The parameter estimation unit 103 estimates the parameters of each bell-shaped distribution by Bayesian estimation using a Dirichlet process mixture model.

[0051] The scale restoration unit 104 restores the scale of the parameters estimated by the parameter estimation unit 103 (hereinafter also referred to as "estimated parameters") to the scale of the target spectrum.

[0052] The decomposition result output unit 105 outputs the decomposition result of the target spectrum based on the parameters whose scale has been restored by the scale restoration unit 104 (hereinafter also referred to as "restored parameters"). Specifically, the decomposition result output unit 105 transmits the decomposition result of the target spectrum to the user terminal 30. The decomposition result output unit 105 may also display the decomposition result on the display device 506 provided in the spectrum decomposition device 10.

[0053] ≪Functional Configuration of the Measuring Device≫ As shown in Figure 3, the measuring device 20 in this embodiment includes a measuring unit 201 and a spectrum generation unit 202.

[0054] The measurement unit 201 measures the sample to be measured using a predetermined method. The measurement method can be any method that can generate the desired spectral data. One example of a measurement method in this embodiment is fluorescence spectroscopy for generating a fluorescence spectrum. Other examples of measurement methods in this embodiment include ultraviolet-visible spectroscopy for generating an ultraviolet-visible absorption spectrum or mass spectrometry for generating a mass spectrum.

[0055] The spectrum generation unit 202 generates a target spectrum based on the measurement results from the measurement unit 201. An example of spectral data in this embodiment is a fluorescence spectrum. Other examples of spectral data in this embodiment include ultraviolet-visible absorption spectra or mass spectra.

[0056] ≪Functional Configuration of User Terminal 30≫ As shown in Figure 3, the user terminal 30 in this embodiment includes a disassembly result display unit 301.

[0057] The disassembly result display unit 301 is realized by a process in which the program, which is loaded from the HDD 504 shown in Figure 2 onto the RAM 503, is executed by the CPU 501.

[0058] The decomposition result display unit 301 receives the decomposition result of the target spectrum from the spectrum decomposition device 10. The decomposition result display unit 301 displays the received decomposition result of the target spectrum on the display device 506.

[0059] <Processing procedure for spectral decomposition system> Next, the processing procedure of the spectral decomposition method performed by the spectral decomposition system 1 in this embodiment will be described with reference to Figure 4. Figure 4 is a flowchart showing an example of the processing procedure of the spectral decomposition method in this embodiment.

[0060] In step S1, the measuring unit 201 of the measuring device 20 measures the sample using a predetermined method in response to user operation. Next, the spectrum generation unit 202 of the measuring device 20 generates a target spectrum based on the measurement results from the measuring unit 201. Subsequently, the spectrum generation unit 202 transmits the generated target spectrum to the spectrum decomposition device 10.

[0061] In this embodiment, the target spectrum is, for example, a fluorescence spectrum measured from a sample using a spectrofluorometer. Since a spectrofluorometer measures light intensity in a region where the light energy falls within a predetermined observation range, the spectral data may be truncated at the upper and lower limits of the observation range.

[0062] In the spectral decomposition device 10, the spectral input unit 101 receives the target spectrum from the measuring device 20. Next, the spectral input unit 101 sends the received target spectrum to the scale conversion unit 102.

[0063] Here, the target spectrum in this embodiment will be described with reference to Figure 5. Figure 5 is a diagram showing an example of the target spectrum in this embodiment.

[0064] As shown in Figure 5, the target spectrum in this embodiment is observed in the range of 2.00 to 4.00 eV, with both ends truncated at the upper and lower limits of the observation range. In this embodiment, only one end of the target spectrum may be truncated, while the other end is in contact with the horizontal axis.

[0065] Let's return to Figure 4 for explanation. In step S2, the scale conversion unit 102 of the spectral decomposition device 10 receives the target spectrum from the spectral input unit 101. Next, the scale conversion unit 102 converts the scale of the target spectrum so that the integral value of the target spectrum becomes 1. Subsequently, the scale conversion unit 102 sends the converted spectrum to the parameter estimation unit 103.

[0066] Specifically, the scale conversion unit 102 first numerically integrates the target spectrum using the trapezoidal rule or Simpson's rule, etc. This gives the integral value S of the target spectrum. Next, the scale conversion unit 102 divides each value of the target spectrum by the integral value S of the target spectrum. After that, the scale conversion unit 102 stores the integral value S of the target spectrum in a storage unit implemented by RAM 503 or HDD 504, etc.

[0067] Here, the converted spectrum in this embodiment will be described with reference to Figure 6. Figure 6 is a diagram showing an example of the converted spectrum in this embodiment.

[0068] As shown in Figure 6, the converted spectrum has its light intensity reduced to the range of 0.0 to 0.8. In the target spectrum shown in Figure 5, the light intensity was in the range of 0 to 50. In the converted spectrum shown in Figure 6, the area of ​​the shaded region (i.e., the integral value of the converted spectrum) is 1.

[0069] Let's return to Figure 4 for explanation. In step S3, the parameter estimation unit 103 of the spectral decomposition device 10 receives the transformed spectrum from the scale transformation unit 102. Next, the parameter estimation unit 103 estimates parameters for assigning one or more bell-shaped distributions, each with at least one end truncated, to the transformed spectrum by Bayesian estimation using a Dirichlet process mixture model.

[0070] Here, the bell-shaped distribution in this embodiment will be explained with reference to Figure 7. Figure 7 is a diagram showing an example of the bell-shaped distribution in this embodiment.

[0071] An example of a bell-shaped distribution in this embodiment is a normal distribution. Figure 7(A) shows an example of a normal distribution. A normal distribution with at least one end truncated is called a truncated normal distribution.

[0072] The probability density function (Gaussian function) of the normal distribution is given by equation (1).

[0073]

number

[0074] Here, b is the reciprocal of the variance and μ is the peak position. The peak height of a normal distribution is given by a√(b / 2π).

[0075] Another example of a bell-shaped distribution in this embodiment is the Cauchy distribution. Figure 7(B) shows an example of the Cauchy distribution.

[0076] The probability density function (Lorentz function) of the Cauchy distribution is given by equation (2).

[0077]

number

[0078] Here, γ is a measure that gives the half-width at half maximum, and x0 is the peak position. The peak height of the Cauchy distribution is given by a / (πγ).

[0079] Another example of a bell-shaped distribution in this embodiment is the log-normal distribution. Figure 7(C) shows an example of a log-normal distribution.

[0080] The probability density function of the log-normal distribution is given by equation (3).

[0081]

number

[0082] The peak position of a log-normal distribution is e μ-σ^2 It is represented as follows.

[0083] As shown in FIG. 7, the bell-shaped distribution in the present embodiment may be a distribution symmetric about the center position of the peak, such as a normal distribution or a Cauchy distribution, or may be a distribution asymmetric about the center position of the peak, such as a lognormal distribution. The center position of the peak after decomposition is obtained as μ for each component as a result of decomposing the spectral data into each component.

[0084] ≪Parameter Estimation Processing≫ Here, the parameter estimation processing (step S3 in FIG. 4) in the present embodiment will be described in detail with reference to FIGS. 8 to 10.

[0085] Here, it will be described as assigning a truncated normal distribution as the bell-shaped distribution. In this case, the parameter estimation unit 103 uses the Dirichlet process mixture model to perform Bayesian estimation of the parameters {μ i , b i}, {ν i=1 K , {ν j}, α, and σ. j=1 K , α, and σ are estimated by Bayesian estimation.

[0086]

Equation

[0087] However, y s is the transformed spectrum. K is the maximum number of truncated normal distributions. Beta is the beta distribution. InvGamma is the inverse gamma distribution. Upper is the larger value of the horizontal axis value of the cut-off position of the transformed spectrum. Lower is the smaller value of the horizontal axis value of the cut-off position of the transformed spectrum.

[0088] Also, π i represents the mixing ratio of the truncated normal distributions. ν <00,00011>represents the ratio of each truncated normal distribution. C i is a normalization constant for normalizing the integral value of the truncated normal distribution to 1.

[0089] Equations (6) to (8) correspond to the rod-folding process in the Dirichlet process. Figure 8 shows an example of the rod-folding process. As shown in Figure 8, in the rod-folding process, a straight line of length 1 is ν i :1-ν i The process of dividing in the ratio ν is repeated. i This uses random numbers generated by the beta distribution Bata(1, α).

[0090] Note that α is a parameter that represents the shape of the beta distribution. The larger α, the smaller ν. i The likelihood of generating increases. As a result, the mixing ratio π i Many small components will be assigned to it.

[0091] Furthermore, σ is the standard deviation of the noise following a normal distribution.

[0092] Figure 9 is a flowchart showing an example of the parameter estimation process in this embodiment.

[0093] In step S3-1, the parameter estimation unit 103 determines the maximum number K of truncated normal distributions to assign. The maximum number K can be arbitrarily determined according to the shape of the target spectrum. The maximum number K can be set by the user or determined automatically.

[0094] In step S3-2, the parameter estimation unit 103 determines the prior distribution of the parameters. The prior distribution is expressed by equation (11).

[0095]

number

[0096] p(ν i ) and others are prior distributions for each parameter.

[0097] The parameter estimation unit 103 can simply determine its initial values ​​randomly. For example, α can be randomly obtained from the inverse gamma distribution InvGamma(1, 1). iμ is randomly selected from the beta distribution Beta(1, α). i This is obtained randomly from a normal distribution N(1.0, 1 / 5.0). i σ is randomly obtained from the gamma distribution Gamma(5.0, 0.04). σ is randomly obtained from the half-Cauchy distribution HalfCauchy(1.0).

[0098] In step S3-3, the parameter estimation unit 103 determines the convergence condition for terminating Bayesian estimation. The convergence condition can be any condition used in Bayesian estimation. In this embodiment, the convergence condition can be defined as, for example, that the maximum value of the posterior probability is no longer updated.

[0099] Here, the convergence conditions in this embodiment will be explained with reference to Figure 10. Figure 10 is a diagram showing an example of the convergence conditions in this embodiment.

[0100] Figure 10 is a graph showing the change in the maximum value of the log posterior probability at each step, with the horizontal axis representing the number of steps in Bayesian estimation (step) and the vertical axis representing the maximum value of the log posterior probability (log probability). In the example shown in Figure 10, the maximum value of the log posterior probability remains constant from around 16,000 steps onward. As described above, if the convergence condition is defined as the posterior probability no longer being updated, then it can be determined that convergence occurred at 16,000 steps.

[0101] Let's return to Figure 9 for explanation. In step S3-4, the parameter estimation unit 103 performs Bayesian estimation of the posterior distribution of the parameters. The posterior distribution of the parameters is expressed by equations (12) to (13).

[0102]

number

[0103] The posterior distribution of Bayesian estimation can be determined by any method. For example, the posterior distribution can be determined using Markov chain Monte Carlo, variational Bayesian methods, or maximum posterior probability estimation.

[0104] In step S3-5, the parameter estimation unit 103 determines whether the calculated posterior probability satisfies the convergence condition. If the convergence condition is met (YES), the parameter estimation unit 103 proceeds to step S3-6. If the convergence condition is not met (NO), the parameter estimation unit 103 repeats step S3-4.

[0105] In step S3-6, the parameter estimation unit 103 outputs the parameter estimation results. The parameter estimation results output by the parameter estimation unit 103 are sent to the scale restoration unit 104.

[0106] Here, the parameter estimation results in this embodiment will be explained with reference to Figure 11. Figure 11 is a diagram showing an example of the parameter estimation results in this embodiment.

[0107] Figure 11 shows a superimposed display of the truncated normal distribution with the estimated parameters and the transformed spectrum. As shown in Figure 11, three distributions D1 to D3 are assigned to the parameter estimation results. Distribution D1 is a truncated normal distribution with the left end truncated. Distribution D2 is a normal distribution with neither end truncated. Distribution D3 is a truncated normal distribution with the right end truncated.

[0108] Let's return to Figure 4 for explanation. In step S4, the scale restoration unit 104 of the spectrum decomposition device 10 receives the parameter estimation results from the parameter estimation unit 103. Next, the scale restoration unit 104 restores the scale of the parameter estimation results to the scale of the target spectrum. Subsequently, the scale restoration unit 104 sends the parameter estimation results after scale restoration to the decomposition result output unit 105.

[0109] Specifically, the scale reconstruction unit 104 first obtains the integral value S of the target spectrum stored in the memory unit. Next, the scale reconstruction unit 104 multiplies the parameter estimation result by the integral value S, as shown in equations (14) to (16).

[0110]

number

[0111] Here, the parameter estimation results after scale restoration in this embodiment will be explained with reference to Figure 12. Figure 12 is a diagram showing an example of the parameter estimation results after scale restoration in this embodiment.

[0112] Figure 12 shows the truncated normal distribution with scaled parameters superimposed on the target spectrum. As shown in Figure 12, in the parameter estimation results after scaled restoration, the distributions D1 to D3 are expanded to a range of 0 to 50 on the vertical axis. In the parameter estimation results before scaled restoration shown in Figure 11, the vertical axis was in the range of 0.0 to 0.8.

[0113] Let's return to Figure 4 for explanation. In step S5, the decomposition result output unit 105 of the spectral decomposition device 10 receives the parameter estimation results after scale restoration from the scale restoration unit 104. Next, the decomposition result output unit 105 generates the decomposition result of the target spectrum based on the parameters after scale restoration.

[0114] The decomposition results of the target spectrum include spectral data representing each component of the target spectrum (hereinafter also referred to as "component spectra"). The component spectra are represented by the truncated normal distributions included in the parameter estimation results and by normal distributions that have the same parameters representing the shape and are not truncated at both ends.

[0115] The decomposition result of the target spectrum may include the parameter estimation results output by the parameter estimation unit 103. Furthermore, the decomposition result of the target spectrum may include the intermediate parameters calculated by the parameter estimation unit 103.

[0116] Next, the decomposition result output unit 105 transmits the generated decomposition results to the user terminal 30. At the user terminal 30, the decomposition result display unit 301 receives the decomposition results from the spectral decomposition device 10. Then, the decomposition result display unit 301 displays the received decomposition results on the display device 506.

[0117] The decomposition result output unit 105 may also display the generated decomposition results on the display device 506 provided by the spectral decomposition device 10.

[0118] The decomposition result display unit 301 displays each component spectrum included in the decomposition result in a manner that allows comparison with the target spectrum. For example, the decomposition result display unit 301 may display the target spectrum and each component spectrum on a single graph using different line types. Alternatively, for example, the decomposition result display unit 301 may display the graph showing the target spectrum and the graphs showing each component spectrum side by side, either horizontally or vertically.

[0119] The decomposition result display unit 301 may display the position, height, and width of the peaks in each truncated normal distribution, corresponding to the target spectrum. The width of the truncated normal distribution may be, for example, the standard deviation (bandwidth) or the full width at half maximum (FWHM).

[0120] Furthermore, the decomposition result display unit 301 may display the position, height, and width of the peaks in each truncated normal distribution that were calculated during the estimation process.

[0121] Furthermore, if the target spectrum is decomposed using an asymmetrical bell-shaped distribution, such as a log-normal distribution, the decomposition result display unit 301 may display the total width of the asymmetrical bell-shaped distribution with at least one end cut off as the width of each distribution. In this case, the decomposition result display unit 301 may also display the width of the left side and the width of the right side of the peak in each distribution, respectively.

[0122] The information displayed by the decomposition result display unit 301 as the decomposition result is not limited to the above. Any information within the range of information obtained during the process of the spectral decomposition device 10 decomposing the target spectrum may be displayed.

[0123] <Effects of the Embodiment> The spectral decomposition system in this embodiment assigns one or more bell-shaped distributions, each with at least one end cut off, to spectral data with at least one end cut off by Bayesian estimation using a Dirichlet process mixture model.

[0124] By using a bell-shaped distribution with at least one end truncated, it is possible to assign a distribution with high accuracy even to spectral data with at least one end truncated. Furthermore, by using a Dirichlet process mixture model and Bayesian estimation, the number of bell-shaped distributions and the parameters of each bell-shaped distribution can be efficiently estimated.

[0125] Therefore, the spectral decomposition system of this embodiment can efficiently and accurately decompose spectral data in which at least one end has been cut off.

[0126] [Examples] To evaluate the resolution accuracy of the spectral decomposition system 1 in the above embodiment, a comparison was made between the decomposition results when a truncated normal distribution was assigned to the spectral data to be decomposed and when a normal distribution was assigned. Below, the evaluation results will be described using Example 1 as the case where a truncated normal distribution was assigned and Comparative Example 1 as the case where a normal distribution was assigned.

[0127] In this example, three Gaussian functions and a random number ε(x) following a normal distribution with mean 0 and variance 1 were mixed, and the spectral data f(x) obtained by cutting both ends was used for decomposition. The spectral data f(x) in this example is expressed by equations (17) to (18).

[0128]

number

[0129] Figure 13 shows an example of the disassembly results in this embodiment. Figure 13(A) shows the fitting accuracy of Example 1. Figure 13(B) shows the fitting accuracy of Comparative Example 1.

[0130] Figure 13 overlays the spectrum to be decomposed (thick solid line), the assigned distributions (dotted, dashed, and double-dotted lines), and the mixed distribution (thin solid line) resulting from the combination of the assigned distributions. A graph showing the residuals between the spectrum and the mixed distribution is also displayed at the top of the graph.

[0131] As shown in Figure 13, in Example 1 (Figure 13(A)), the average of the residuals is almost 0, indicating good fitting. On the other hand, in Comparative Example 1 (Figure 13(B)), the average of the residuals is a positive value, indicating poor fitting accuracy.

[0132] Figure 14 shows an example of the decomposition results in this embodiment. Figure 14(A) is a table showing the parameters of the normal distribution (i.e., the correct parameters) which are components of the spectrum to be decomposed. Figure 14(B) is a table showing the parameters estimated in Example 1. Figure 14(C) is a table showing the parameters estimated in Comparative Example 1.

[0133] As shown in Figure 14, in Example 1, all parameters are close to the correct parameters, indicating that the parameters were estimated with good accuracy. On the other hand, in Comparative Example 1, some parameters deviate from the correct parameters, resulting in poor parameter estimation accuracy. In particular, the deviation from the correct value is large in the value of b, which represents the width of the distribution.

[0134] As described above, this embodiment demonstrates that truncated spectral data can be decomposed with high accuracy by using a Dirichlet process mixture model to Bayesian estimate the parameters of the truncated normal distribution.

[0135] [supplement] Each of the embodiments described above can be implemented by one or more processing circuits. Hereinafter, "processing circuit" as used herein includes processors programmed to execute each function by software, such as processors implemented by electronic circuits, as well as devices such as ASICs (Application Specific Integrated Circuits), DSPs (Digital Signal Processors), FPGAs (Field Programmable Gate Arrays), and conventional circuit modules designed to execute each of the functions described above.

[0136] Although embodiments of the present invention have been described in detail above, the present invention is not limited to these embodiments, and various modifications or changes are possible within the scope of the gist of the present invention as described in the claims. [Explanation of Symbols]

[0137] 1. Spectral Decomposition System 10. Spectral decomposition device 101 Spectrum Input Section 102 Scale conversion section 103 Parameter Estimation Unit 104 Scale Restoration Section 105 Decomposition result output section 20 Measuring devices 201 Measuring section 202 Spectrum generation unit 30 User terminals 301 Decomposition result display section

Claims

1. A spectral input unit configured to accept spectral data with at least one end cut off, A scale conversion unit configured to convert the scale of the spectral data so that the integral value becomes 1, A parameter estimation unit is configured to estimate parameters for assigning a bell-shaped distribution, which is asymmetrical with respect to the center of the peak and has at least one end truncated, to the spectral data by Bayesian estimation using a Dirichlet process mixture model. A scale restoration unit is configured to restore the estimation results of the parameters to the scale of the spectral data received by the spectral input unit, Equipped with, The parameter estimation unit is configured to simultaneously estimate the number of bell-shaped distributions, the ratio of the bell-shaped distributions, and a normalization constant for normalizing the integral value of the bell-shaped distribution to 1. Spectral decomposition device.

2. A spectral decomposition apparatus according to claim 1, The aforementioned bell-shaped distribution is a log-normal distribution. Spectral decomposition device.

3. A spectral decomposition apparatus according to claim 1 or 2, The aforementioned parameters include the height, position, and width of the peaks in each bell-shaped distribution. Spectral decomposition device.

4. A spectral decomposition apparatus according to claim 1 or 2, The parameter estimation unit is configured to perform Bayesian estimation by obtaining the posterior distribution using Markov chain Monte Carlo method, variational Bayes method, or maximum posterior probability estimation. Spectral decomposition device.

5. A spectral decomposition apparatus according to claim 1 or 2, The system further includes a decomposition result output unit configured to output a plurality of spectral data representing the components of the spectral data based on the aforementioned parameters. Spectral decomposition device.

6. A spectral decomposition apparatus according to claim 5, The decomposition result output unit is configured to further output the parameters corresponding to each spectral data. Spectral decomposition device.

7. A spectral decomposition apparatus according to claim 6, The decomposition result output unit is configured to further output the parameters calculated by the parameter estimation unit during the estimation process. Spectral decomposition device.

8. Computers A spectral input procedure that accepts spectral data input with at least one end cut off, A scaling procedure for transforming the scale of the spectral data so that the integral value is 1, A parameter estimation procedure for estimating parameters to assign a bell-shaped distribution, which is asymmetrical with respect to the peak center and has at least one end truncated, to the spectral data by Bayesian estimation using a Dirichlet process mixture model, A scale restoration procedure for restoring the estimation results of the parameters to the scale of the spectral data received in the spectral input procedure, Execute, The parameter estimation procedure simultaneously estimates the number of bell-shaped distributions, the proportion of the bell-shaped distributions, and a normalization constant for normalizing the integral value of the bell-shaped distribution to 1. Spectral decomposition method.

9. On the computer, A spectral input procedure that accepts spectral data input with at least one end cut off, A scaling procedure for transforming the scale of the spectral data so that the integral value is 1, A parameter estimation procedure for estimating parameters to assign a bell-shaped distribution, which is asymmetrical with respect to the peak center and has at least one end truncated, to the spectral data by Bayesian estimation using a Dirichlet process mixture model, A scale restoration procedure for restoring the estimation results of the parameters to the scale of the spectral data received in the spectral input procedure, Make it run, The parameter estimation procedure simultaneously estimates the number of bell-shaped distributions, the proportion of the bell-shaped distributions, and a normalization constant for normalizing the integral value of the bell-shaped distribution to 1. program.

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