JP7390210B2 - Spectrum processing device and method - Google Patents

Description

The present invention relates to a spectrum processing apparatus and method, and in particular to estimation and removal of specific components included in a spectrum.

Examples of spectra to be subjected to spectral analysis include NMR (Nuclear Magnetic Resonance) spectra, X-ray spectra, spectral spectra, and mass spectra. Generally, a spectrum includes a waveform component of interest and a baseline component. The waveform component of interest typically includes one or more peaks, and is the original target of analysis. On the other hand, the baseline component is a component that is not originally an analysis target and is a component that exists over a wide range in frequency space (frequency domain).

For example, in observing an NMR spectrum, linking noise generated during the measurement stage, data loss after digital filter processing, signal components derived from molecular structure, etc. generate baseline components. A fluctuation, curvature, slope, etc. with a large period corresponding to the base in an NMR spectrum is a baseline component, or such a base itself is a baseline component.

Note that Patent Document 1 discloses a technique for correcting an NMR spectrum. Patent Document 1 does not describe estimation of a baseline component, particularly estimation of a baseline component based on a baseline model.

Japanese Unexamined Patent Publication No. 62-124450

In order to improve the accuracy of analysis of the waveform component of interest in the spectrum, a baseline component in the spectrum is estimated and removed from the spectrum prior to or concurrently with the spectrum analysis. When estimating the baseline component, the baseline component is fitted using a mathematical model. As functions that define the model, Nth-order polynomials, cosine functions, sine functions, spline functions, piecewise linear functions, and the like are known.

However, the task of appropriately selecting a function that defines a model and then providing appropriate parameters to that function is usually a heavy burden on the user, and it requires experience to do it properly. . If such work is not performed appropriately, the accuracy of estimating the baseline component will decrease, and as a result, the accuracy of spectrum analysis will decrease. Note that the baseline component may be estimated due to necessity other than the above.

When estimating the baseline component, it is necessary to identify a portion of the spectrum other than the portion where the waveform component of interest is dominant, that is, a portion where the baseline component is dominant. If the user identifies the information, the burden on the user increases and objectivity decreases.

An object of the present invention is to accurately estimate a baseline component included in a spectrum. Alternatively, it is an object of the present invention to estimate the baseline component and remove it from the spectrum without causing a significant burden on the user.

The spectrum processing device according to the present invention generates a baseline model by accepting a spectrum including a baseline component and applying a weight sequence consisting of a plurality of weights to a basis function sequence consisting of a plurality of basis functions. a determining means for determining, based on at least the spectrum, a sample point sequence that defines a sample portion in the spectrum and a sample portion in the baseline model; a search means for searching for an optimal weight sequence so that a fitting condition for fitting the sample portion is satisfied; and a subtraction means for subtracting an optimal baseline model generated based on the optimal weight sequence from the spectrum. It is characterized by including the following.

The spectral processing method according to the present invention generates a baseline model by applying a weight sequence consisting of a plurality of weights to a basis function sequence consisting of a plurality of basis functions, and generates a baseline model based on at least the spectrum. and fitting conditions for determining a sample point sequence that defines a sample part in the baseline model and fitting the sample part in the baseline model to the sample part in the spectrum, and the Lp norm of the weight sequence (where p≦ 1) search for an optimal weight sequence so that the Lp norm condition that reduces Features.

According to the present invention, a baseline component included in a spectrum can be estimated with high accuracy. Alternatively, according to the present invention, the baseline component can be estimated and removed from the spectrum without causing a large burden on the user.

FIG. 2 is a conceptual diagram showing a spectrum processing method according to an embodiment. FIG. 1 is a block diagram showing a spectrum processing device according to an embodiment. 3 is a flowchart showing a spectrum processing method according to the first embodiment. FIG. 3 is a diagram showing the effects of the spectrum processing method according to the first example. 7 is a flowchart showing a spectrum processing method according to a second embodiment. FIG. 7 is a diagram showing the effects of the spectrum processing method according to the second example. 7 is a flowchart showing a spectrum processing method according to a third embodiment. 12 is a flowchart showing a sample point sequence determination method according to a third embodiment. FIG. 7 is a diagram showing the effects of the sample point sequence determination method according to the third embodiment. FIG. 7 is a diagram showing the effects of the spectrum processing method according to the third example.

Hereinafter, embodiments will be described based on the drawings.

(1) Details of Embodiment A spectrum processing device according to an embodiment includes an accepting means, a generating means, a determining means, a searching means, and a subtracting means. The accepting means is a means for accepting a spectrum including a baseline component. The determining means generates a baseline model by applying a weight sequence consisting of a plurality of weights to a basis function sequence consisting of a plurality of basis functions. The determining means determines a sample point sequence defining a sample portion in the spectrum and a sample portion in the baseline model, based at least on the spectrum. The search means searches for an optimal weight sequence so that a fitting condition for fitting the sample portion in the baseline model to the sample portion in the spectrum is satisfied. The subtraction means subtracts an optimal baseline model generated based on the optimal weight sequence from the spectrum.

According to the above configuration, an optimal weight sequence that defines an optimal baseline model is automatically searched, and a sample point sequence is automatically improved in the process of the search. Therefore, it is possible to reduce the burden on the user and to objectively estimate the baseline component.

In determining the sample point sequence, the spectrum and a baseline model may be compared. According to the comparison, it is possible to increase the possibility of identifying a portion where the baseline component is dominant while avoiding a portion where the waveform component of interest is dominant. Alternatively, a portion of the spectrum where the waveform component of interest exists may be specified, and the sample point sequence may be determined based on portions other than the specified portion. Alternatively, the sample point sequence may be determined by identifying a flat portion in the spectrum.

When searching for an optimal weight sequence, only the fitting condition may be considered, but the fitting condition and other conditions may also be considered. Other conditions include the Lp norm condition, which will be described later. The spectrum is, for example, an NMR spectrum. The above processing may be applied to other spectra. The plurality of means described above correspond to the plurality of functions performed by the processor in the embodiment.

In the embodiment, the search means searches for an optimal weight sequence so that the fitting condition and the Lp norm condition for reducing the Lp norm (where p≦1) of the weight sequence are satisfied. As a result, the weight sequence gradually becomes sparse in the process of searching for the optimal weight sequence. That is, the proportion of 0 weights or weights close to 0 in the weight sequence increases. As a result, the number of basis functions constituting the baseline model in the basis function sequence gradually decreases. As a result, it becomes easier to construct a baseline model using a small number of basis functions representing the basic properties of the baseline component as a broadband component.

When searching for an optimal weight sequence based only on fitting conditions, it becomes easy to give weights widely and evenly to the multiple basis functions that make up the basis function sequence, and as a result, in some cases, excessive fitting may occur. It becomes more likely to occur. On the other hand, by introducing an Lp norm condition (specifically, an Lp norm minimization condition) in addition to the fitting condition, the problem of excessive fitting becomes less likely to occur.

In general, increasing the number of basis functions constituting a basis function sequence causes problems such as slow convergence of solutions. According to the above configuration, even if the basis function sequence is composed of a large number of basis functions, only a small number of basis functions are actually given significant weight, so it can be expected that the solution converges quickly. Conversely, according to the above configuration, the basis function sequence can be composed of more basis functions. In that case, it is possible to obtain good fitting results even for the baseline component having a special shape.

Note that each basis function corresponds to an element constituting the baseline model. Weights define the degree of contribution of each basis function. The optimal solution does not have to be an optimal solution in a strict sense, but may be one that is considered to be an optimal solution in terms of calculation. For example, the solution at the time when the search end condition is satisfied becomes the optimal solution.

Regarding the Lp norm, the effect of increasing the sparsity of the norm calculation target is recognized when p is 1 or less, and generally, the smaller p is, the greater the effect is. Therefore, the value of p may be changed depending on the content of the baseline component. P is defined as a value between 0 and 1.0, but if p is 0 (that is, when using the L0 norm), the solution may become unstable depending on the situation, so set p to a value larger than 0. is desirable.

In an embodiment, the determining means determines the sample point sequence based on the spectrum and the baseline model. In the process of searching for the optimal weight sequence, the sample point sequence and baseline model become better.

In the embodiment, the determining means obtains a residual sequence by comparing the spectrum and a baseline model, and determines a sample point sequence based on the residual sequence. The residual sequence corresponds to a residual spectrum described later. In the embodiment, the determining means determines the sample point sequence based on a plurality of residuals satisfying a predetermined condition among the residual sequences. In that case, for example, a residual that is less than or equal to 0 may be specified, or an absolute value of the residual that is within a threshold value may be specified. In the embodiment, the determining means generates a histogram based on the residual sequence and determines the sample point sequence based on the histogram. A histogram shows the statistical characteristics of a sample portion. Based on the assumption that the histogram corresponding to the part of the spectrum where the baseline component is dominant has a constant distribution, residuals that deviate from the constant distribution are identified, and sampling point candidates are narrowed down based on this identification. You may be

The program according to the embodiment has an acceptance function, a generation function, a determination function, a search function, and a subtraction function. The acceptance function is a function that accepts a spectrum containing a baseline component. The generation function is a function that generates a baseline model by applying a weight sequence consisting of a plurality of weights to a basis function sequence consisting of a plurality of basis functions. The determining function is a function of determining, based at least on the spectrum, a sample point sequence that defines the sample portion in the spectrum and the sample portion in the baseline model. The search function optimizes the fitting condition to fit the sample part in the baseline model to the sample part in the spectrum, and the Lp norm condition to make the Lp norm (however, p≦1) of the weight sequence small. This is a function to search for a weight sequence. The subtraction function is a function that subtracts the optimal baseline model generated based on the optimal weight sequence from the spectrum. The program is installed on the information processing device via a portable storage medium or via a network. The concept of an information processing device includes a computer, a spectrum generation device, a spectrum measurement device, and the like.

The spectrum processing method according to the embodiment includes a generation step, a determination step, and a search step. The generation step is a step of generating a baseline model by applying a weight sequence consisting of a plurality of weights to a basis function sequence consisting of a plurality of basis functions. The determining step is a step of determining, based at least on the spectrum, a sample point sequence that defines a sample portion in the spectrum and a sample portion in the baseline model. The search process is performed optimally so that the fitting condition for fitting the sample portion in the baseline model to the sample portion in the spectrum and the Lp norm condition for reducing the Lp norm (however, p≦1) of the weight sequence are satisfied. This is the process of searching for a weight sequence. A baseline component included in the spectrum is estimated as an optimal baseline model based on the optimal weight sequence.

(2) Details of Embodiment FIG. 1 shows a spectrum processing method according to an embodiment. Specifically, a spectral processing algorithm is shown executed by the processor. Reference numeral 100 indicates an acceptance process, which corresponds to an acceptance means. Reference numeral 102 indicates a generation step, which corresponds to a generation means. Reference numeral 104 indicates a determining step, which corresponds to determining means. Reference numeral 106 indicates a search step, which corresponds to a search means. Reference numeral 108 indicates a subtraction step, which corresponds to a subtraction means.

The accepted NMR spectrum (hereinafter simply referred to as "spectrum") y is the processing target. The horizontal axis f is the frequency axis, and the vertical axis is the intensity axis. The spectrum y consists of N (N is an integer of 2 or more, for example, several hundred or several thousand) intensities arranged on the frequency axis, and is treated as a vector in arithmetic processing.

The spectrum y includes a waveform component of interest a and a baseline component b. In the illustrated example, the waveform component a of interest consists of a plurality of peaks. The baseline component b is a component other than the waveform component of interest a, is a broadband component, and corresponds to the base of the spectrum y. Prior to analyzing the spectrum y, it is required to remove the baseline component b contained therein in advance. The spectral processing algorithm removes the baseline component b from the spectrum y.

In the generation step 102, the baseline model Ax is generated by applying the weight sequence x to the basis function sequence A, specifically, by multiplying the basis function sequence A by the weight sequence x. The basis function sequence A consists of K (K is an integer of 2 or more, for example, several to several dozen) basis functions. Usually, various types of functions with various degrees are prepared as basis functions (model elements). For example, N-order polynomials from 1st to 10th orders, cosine functions from 1st to 20th orders, sine functions from 1st to 20th orders, etc. are prepared. The basis function sequence A may include an exponential function, a logarithmic function, a spline function, a piecewise linear function, and the like. In the illustrated example, the N basis functions are arranged in the n-axis direction, and each basis function has a waveform on the frequency axis. Each basis function is treated as a vector for calculation purposes.

The weight sequence x is composed of K weights arranged in the n-axis direction. Each weight is a factor by which its corresponding function is multiplied. If a weight is 0, the corresponding function is effectively excluded from the components of the baseline model. The weight sequence x is treated as a vector in calculation processing. In searching for the optimal baseline model that approximates the baseline component b, the weight sequence x is repeatedly updated so that the evaluation value J, which will be described later, is minimized. The weight sequence x at the time when the search end condition is satisfied becomes the optimal weight sequence, and the baseline model Ax at that time becomes the optimal baseline model.

In the determination step 104, a sample point sequence I is determined. The sample point sequence I consists of M sample points (M is an integer of 2 or more, for example, several % to 100% of N) arranged in the frequency axis direction. It is treated as a vector in arithmetic processing. Each sampling point is a sampling point selected from among all observation points. A sample matrix S _I required for vector calculation is defined from the sample point sequence I. The sample matrix S _I defines the sample portion S _I y in the spectrum y and the sample portion S _I Ax in the baseline model Ax. A plurality of sample points constituting the sample point sequence I are gradually selected so that the sample point sequence I is concentrated not in the part where the waveform component of interest a is dominant but in the part where the baseline component b is dominant. .

More specifically, in the determination step 104, the spectrum y and the baseline model Ax are compared, and a residual spectrum (residual sequence) corresponding to the difference between the two is calculated. By individually evaluating the N residuals constituting the residual spectrum, M sample points constituting the sample point sequence I are selected. In the embodiments to be described later, the value of M usually becomes gradually smaller.

Note that a portion in the spectrum y where the waveform component of interest a is dominant may be specified, and the sample point sequence I may be determined based on portions other than that portion. A flat portion in the spectrum y may be specified, and the sample point sequence I may be determined based on the flat portion. The sample point sequence I may be determined by other methods. In the embodiment, since the spectrum y and the baseline model Ax are compared, the sample point sequence I is naturally improved as the baseline model Ax is improved.

In an embodiment, a decision step 104 is performed during the initial decision. Thereafter, as described below, in the process of repeatedly updating the weight sequence x, if the evaluation value J is minimized and the search end condition is not satisfied, the determination step 104 is executed. Note that the determining step 104 may be executed each time the number of calculations of the evaluation value J reaches a certain value C (C is an integer of 2 or more). Alternatively, the determination step 104 may be executed each time the evaluation value J is calculated.

なお、ｙはＮ×１ベクトルであり、Ｓ_ＩはＭ×Ｎ行列であり、ＡはＮ×Ｋ行列であり、Ｌｐノルムは以下の（２）式で定義される。

上記（１）式において、第１項は、標本部分間の残差スペクトルのＬ２ノルムを最小化する条件を規定しており、すなわち、フィッティング条件を規定している。残差スペクトルは、スペクトルｙにおける標本部分Ｓ_ＩｙからベースラインモデルＡｘにおける標本部分Ｓ_ＩＡｘを減算することにより求められる。２つの標本部分Ｓ_Ｉｙ及びＳ_ＩＡｘが相互に完全に一致した場合、Ｌ２ノルムは０となる。 In the search step 106 (see particularly reference numeral 106A), the weight sequence x is gradually improved so that the evaluation value J is minimized. The evaluation value J is defined by the following equation (1).

Note that y is an N×1 vector, S _I is an M×N matrix, A is an N×K matrix, and the Lp norm is defined by the following equation (2).

In the above equation (1), the first term defines the condition for minimizing the L2 norm of the residual spectrum between sample parts, that is, defines the fitting condition. The residual spectrum is obtained by subtracting the sample portion S _I Ax in the baseline model Ax from the sample portion S _I y in the spectrum y. If the two sample parts S _I y and S _I Ax perfectly match each other, the L2 norm will be zero.

In the above equation (1), the second term defines an Lp norm condition that minimizes the Lp norm (where p≦1) of the weight sequence x. As the Lp norm of the weight sequence x becomes smaller, the sparsification of the weight sequence x is promoted. That is, among the K weights forming the weight sequence x, the weights having a value of 0 or a value close to 0 increase. With the promotion of sparsification, the number of basis functions that substantially define the baseline model gradually decreases. Typically, only a small number of prescribed functions representing the main components in the baseline component b remain, and the others are excluded. As a result, overfitting is prevented or reduced. Note that λ is a coefficient that adjusts the effect of the first term and the effect of the second term.

As mentioned above, 0≦p≦1, and when seeking the stability of the solution, 0<p≦1. When p is less than or equal to 1, the sparsity of the solution increases in the process of searching for a solution using the Lp norm. In the embodiment, this property is effectively utilized in the search for the optimal solution for the weight sequence x. Generally, p is 1, but if the sparsity of the weight sequence is expected to be high, p may be set to, for example, 0.75 or 0.5.

The evaluation value J makes it possible to simultaneously consider the fitting condition as the first condition and the Lp norm condition as the second condition. However, other calculation formulas may be used as long as the sample portion S _I Ax in the baseline model Ax can be fitted to the sample portion S _I y in the spectrum y.

Based on the above equation (1), the weight sequence x is gradually updated by applying a known optimal solution search method such as the gradient method (see reference numeral 106B), and the weight sequence x is gradually improved. . In the process, the sample point sequence I is also improved step by step. The weight sequence x at the time when the search end condition is satisfied is set as the optimal weight sequence x, and the baseline model Ax at that time is set as the optimal baseline model Ax. The search for the optimal solution may be terminated when the evaluation value J becomes less than a certain value, when the number of calculations of the evaluation value J reaches a certain value, etc.

In the subtraction step 108, the optimal baseline model Ax is subtracted from the spectrum y when the search end condition is satisfied (see reference numeral 106C). This subtraction generates a spectrum yc from which the baseline component b has been removed. The spectrum yc becomes the analysis target. The subtraction is expressed by the following equation (3).

In FIG. 2, an NMR measurement system is shown. In the illustrated configuration example, the NMR measurement system includes an NMR measurement device 30 and a spectrum processing device 32. Spectral data is transferred from the NMR measurement device 30 to the spectrum processing device 32. The transfer takes place, for example, via a network or via a storage medium.

Although the details are not shown in FIG. 2, the NMR measuring device 30 is composed of a spectrometer and a measuring section. The measuring section is composed of a static magnetic field generator, a probe, and the like. The static magnetic field generator has a bore as a vertical through hole, into which a probe insertion section is inserted. A detection circuit for detecting an NMR signal from a sample is provided within the head of the insertion section. A spectrometer is composed of a control section, a transmitting section, a receiving section, and the like. The transmitter generates a transmit signal according to the transmit pulse sequence, and the transmit signal is sent to the probe. As a result, the sample is irradiated with electromagnetic waves. The NMR signal from the sample is then detected at the probe. A received signal generated by the detection is sent to the receiving section. In the receiving section, an NMR spectrum is generated by FFT calculation on the received signal. The NMR spectrum is sent to spectrum processing device 32 as required. The spectrum processing device 32 may be incorporated into the NMR measuring device 30.

The spectrum processing device 32 as an information processing device includes a CPU 50, a memory 56, an input device 52, a display device 54, and the like. A spectrum processing program 58 and a spectrum analysis program 60 are stored on the memory 56 . The spectrum processing program 58 is a program that executes the spectrum processing algorithm shown in FIG. The spectrum analysis program 60 is a program for analyzing the spectrum after preprocessing. These programs 58 and 60 are executed in the CPU 50.

The CPU 50 functions as an accepting means, a generating means, a determining means, a searching means, and a subtracting means. The input device 52 includes a keyboard, a pointing device, and the like, and is used to specify a value to be substituted for p, a coefficient λ, an end condition, and the like. For example, the iterative process may be terminated when the amount of change in the solution becomes 0.1% or less. The display 54 is constituted by, for example, an LCD, and the spectrum is displayed there.

The first to third embodiments will be described below. In the first to third embodiments, the sample point sequence I is determined using different methods. The other parts are basically the same in all embodiments.

FIG. 3 shows a spectrum processing method according to the first embodiment. In S10, the weight sequence x is initialized. For example, random values are given to the K weights that make up the weight sequence x. In S12A, the sample point sequence I is initialized. Specifically, a residual spectrum (residual sequence) is obtained by subtracting the baseline model Ax from the spectrum y, and observation points that have produced a residual of 0 or less are identified based on the residual spectrum. . Observation points that produce a residual of 0 or less are determined as a sample point sequence I. However, in S12A, all observation points consisting of N observation points may be determined as the sample point sequence I.

In S16, an evaluation value J is calculated. In S18, it is determined whether the evaluation value J has become the minimum (or a value that can be considered the minimum) under the current sample point sequence I. If it is determined that the evaluation value J is not the minimum, the weight column x is updated in S20. Thereafter, the evaluation value J is calculated again in S16. Minimization of the evaluation value J may be determined when the change in the evaluation value J becomes equal to or less than a certain value.

If it is determined in S18 that the evaluation value J has become the minimum, it is determined in S22 whether the search end condition is satisfied. For example, when the evaluation value J becomes a value less than a threshold value, when the change in the evaluation value J becomes less than a certain value, when the number of calculations of the evaluation value J reaches a certain number, etc., the search end condition is set. considered to be satisfied.

If it is determined that the search end condition is not satisfied, the sample point sequence I is updated in S24A. Specifically, in the same manner as described above, a residual spectrum is calculated, and residuals of 0 or less are identified. Observation points that produce a residual of 0 or less are determined as a sample point sequence I. After that, the steps after S16 are executed. As is clear from the content of FIG. 3, the determination of the sample point sequence I is repeated until the search end condition is satisfied. If it is determined in S22 that the search end condition is satisfied, the optimal baseline model Ax (that is, the estimated baseline component) is subtracted from the spectrum in S28.

FIG. 4 shows the effect of the first embodiment. A10 in the first stage indicates the input spectrum. The second stage shows the first minimization process (processing to minimize the weight sequence), the third stage shows the second minimization process, and the fourth stage shows the third minimization process. The minimization process is shown, and the fifth stage shows the sixth minimization process.

In each row, on the left side, a sample point sequence is shown as a series of a plurality of observation points (see A20, A30, A40, A50). In each row, the estimated baseline model is shown in the center (see A22, A32, A42, and A52). In each stage, on the right side, the residual spectrum generated by the subtraction is shown (see A24, A34, A44, A54). The baseline model is improved by repeating the estimation process. Finally, the baseline component contained in the spectrum has been effectively removed.

According to the first embodiment, the portion corresponding to the bottom of the spectrum tends to become the sample portion. As a result, there is a tendency for the number of sample points to become extremely small. Therefore, the first embodiment is considered to work effectively for metabolomics data and the like.

FIG. 5 shows a spectrum processing method according to a second embodiment. In FIG. 5, the same steps as those shown in FIG. 3 are given the same reference numerals, and their explanations will be omitted.

In S12B, the sample point sequence I is initialized. Specifically, the residual spectrum (residual sequence) is obtained by subtracting the baseline model Ax from the spectrum y, and the absolute value of the residual within a threshold value (residual absolute value) is calculated based on the residual spectrum. The observation point that caused the occurrence is identified. Observation points that produce residual absolute values within the threshold are determined as sample point sequence I. However, in S12B, all observation points consisting of N observation points may be determined as the sample point sequence I.

In S24B, the sample point sequence I is updated. Specifically, in the same manner as described above, a residual spectrum is calculated, and a residual absolute value within a threshold value is specified based on the residual spectrum. Observation points that produce residual absolute values within the threshold are determined as sample point sequence I. In the second embodiment, regardless of the positive or negative sign, a portion that causes a small residual error is determined to be a sample portion, and a portion that causes a large residual error is determined to be a non-sampled portion. For example, the absolute value of the maximum value of the spectrum may be used as the reference value, and 0.1% of the reference value may be set as the threshold value.

FIG. 6 shows the effect of the second embodiment. B10 in the first stage shows the input spectrum. The second stage shows the first minimization process, the third stage shows the second minimization process, the fourth stage shows the third minimization process, and the fifth stage shows the third minimization process. The ninth stage shows the ninth minimization process.

In each row, on the left side, a sample point sequence is shown as a series of a plurality of observation points (see B20, B30, B40, and B50). In each row, the estimated baseline model is shown in the center (see B22, B32, B42, and B52). In each stage, on the right side, the residual spectrum generated by the subtraction is shown (see B24, B34, B44, B54). The baseline model is improved by repeating the minimization process that involves updating the sample point sequence I. Finally, the baseline component contained in the spectrum has been effectively removed.

According to the second embodiment, it becomes easier to employ many sample points. Therefore, it becomes easier to obtain stability of the calculation results. However, it is necessary to appropriately set the threshold value.

FIG. 7 shows a spectrum processing method according to a third embodiment. In FIG. 7, the same steps as those shown in FIG. 3 are given the same reference numerals, and their explanations will be omitted.

In S12C, a sample point sequence I is initially determined. In that case, sample points (observation points) are selected so that the histogram, which will be described in detail below, approaches a predetermined distribution (normal distribution) (so that the histogram is normalized). However, in S12C, all observation points may be initially determined as the sample point sequence I.

In S24C, as in S12C, sample points (observation points) are selected so that the histogram approaches a predetermined distribution (normal distribution) (so that the histogram is normalized).

Hereinafter, based on FIG. 8, a method for determining a sample point sequence in the third embodiment will be described. In S30, all observation points are provisionally determined as sample point candidates. In S32, the baseline model is subtracted from the spectrum, thereby obtaining a residual spectrum. A histogram is then generated from the residual spectrum. That is, the number (frequency) is counted for each size of the residual, and a histogram (residual histogram) is generated from the result. In S34, a known chi-square test is applied to the histogram. The test determines whether the histogram follows a certain distribution (chi-square distribution).

If it is determined in S36 that the histogram does not follow a certain distribution, that is, if it is determined to be false, then in S38 bins (bars as histogram elements) that satisfy the exclusion condition are excluded from the histogram. Specifically, the bins furthest from the histogram center are excluded. This corresponds to excluding one or more observation points (that is, one or more sample point candidates). The step S38 is a step of modifying the histogram, particularly a step of making the histogram closer to a normal distribution.

As a result of the above test, if it is determined in S36 that the histogram follows a certain distribution, that is, if it is determined to be true, then in S40 the sample point candidates at that point become a sample point sequence.

FIG. 9 shows the effect of the sample point determination method according to the third embodiment. C10 in the first stage indicates all sample point candidates corresponding to the entire spectrum. The second row shows the results of the first histogram correction, the third row shows the results of the second histogram correction, and the fourth row shows the results of the sixth histogram correction. In each row, the determined sample point sequence is shown on the left (see C20, C30, C40) and the corrected histogram is shown on the right (see C22, C32, C42). ). Note that the scales of the three horizontal axes are different. As the number of repetitions of histogram correction increases, the sample point sequence becomes better.

FIG. 10 shows the effect of the spectrum processing method according to the third example. D10 in the first stage indicates the input spectrum. The second stage shows the first minimization process, the third stage shows the second minimization process, the fourth stage shows the third minimization process, and the fifth stage shows the third minimization process. The ninth stage shows the ninth minimization process. In each row, on the left side, a sample point sequence is shown as a series of a plurality of sample points (see D20, D30, D40, D50). In each row, the estimated baseline model is shown in the center (see D22, D32, D42, and D52). In each stage, the residual spectrum generated by the subtraction is shown on the right side (see D24, D34, D44, D54). The baseline model is improved by repeating the estimation process. Finally, the baseline component contained in the spectrum has been effectively removed.

The embodiment to be adopted may be selected depending on the properties of the spectrum and the method of analyzing the spectrum. For example, if a broad signal component is regarded as a baseline component and the signal component is to be removed, the first embodiment may be adopted. If sufficient accuracy in estimating the weight sequence can be ensured, the second embodiment or the third embodiment may be adopted.

The third embodiment is based on the assumption that the histogram of the baseline component in the spectrum follows a normal distribution. As described above, as the process is repeated, the number of sample points decreases and the histogram approaches a normal distribution. According to the third embodiment, the optimal solution can be stably derived as in the second embodiment. In the third embodiment, since it is not necessary to set a threshold value, it can be pointed out that compared to the second embodiment, it is possible to point out the advantage that a relatively good solution can be easily obtained without depending much on the situation or environment.

100 acceptance process (acceptance means), 102 generation process (generation means), 104 determination process (determination means), 106 search process (search means), 108 subtraction process (subtraction means).

Claims (7)

means for accepting a spectrum including a baseline component;
Generating means for generating a baseline model by applying a weight sequence consisting of a plurality of weights to a basis function sequence consisting of a plurality of basis functions;
determining means for obtaining a residual sequence by comparing the spectrum and the baseline model, and determining , based on the residual sequence, a sample point sequence that defines a sample portion in the spectrum and a sample portion in the baseline model;
searching means for searching for an optimal weight sequence so that a fitting condition for fitting the sample portion in the baseline model to the sample portion in the spectrum is satisfied;
subtraction means for subtracting an optimal baseline model generated based on the optimal weight sequence from the spectrum;
including;
In the process of searching for the optimal weight sequence, the determination of the sample point sequence by the determining means is repeated,
In the process of searching for the optimal weight sequence, the sample point sequence and the baseline model are improved;
A spectrum processing device characterized by: The spectrum processing device according to claim 1,
The search means searches for the optimal weight sequence so that the fitting condition and the Lp norm condition for reducing the Lp norm (where p≦1) of the weight sequence are satisfied.
A spectrum processing device characterized by: The spectrum processing device according to claim 2,
In the process of searching for the optimal weight sequence, the weight sequence gradually becomes sparse.
A spectrum processing device characterized by: The spectrum processing device according to claim 1 ,
The determining means determines the sample point sequence based on a plurality of residuals satisfying a predetermined condition in the residual sequence.
A spectrum processing device characterized by: The spectrum processing device according to claim 1 ,
The determining means is
generating a histogram based on the residual sequence;
determining the sample point sequence based on the histogram;
A spectrum processing device characterized by: the ability to accept spectra containing baseline components;
A function to generate a baseline model by applying a weight sequence consisting of multiple weights to a basis function sequence consisting of multiple basis functions;
A function of obtaining a residual sequence by comparing the spectrum and the baseline model, and determining a sample point sequence that defines a sample portion in the spectrum and a sample portion in the baseline model based on the residual sequence ;
The fitting condition for fitting the sample portion in the baseline model to the sample portion in the spectrum and the Lp norm condition for reducing the Lp norm (however, p≦1) of the weight sequence are satisfied. A function to search the weight column,
a function of subtracting an optimal baseline model generated based on the optimal weight sequence from the spectrum;
including;
In the process of searching for the optimal weight sequence, the determination of the sample point sequence is repeated,
In the process of searching for the optimal weight sequence, the sample point sequence and the baseline model are improved;
A program characterized by: Generate a baseline model by applying a weight sequence consisting of multiple weights to a basis function sequence consisting of multiple basis functions,
determining a residual sequence by comparing the spectrum and the baseline model; based on the residual sequence, determining a sample point sequence that defines a sample part in the spectrum and a sample part in the baseline model;
The fitting condition for fitting the sample portion in the baseline model to the sample portion in the spectrum and the Lp norm condition for reducing the Lp norm (however, p≦1) of the weight sequence are satisfied. Search the weight sequence,
A spectrum processing method that estimates a baseline component included in the spectrum as an optimal baseline model based on the optimal weight sequence,
In the process of searching for the optimal weight sequence, the determination of the sample point sequence is repeated,
In the process of searching for the optimal weight sequence, the sample point sequence and the baseline model are improved;
A spectral processing method characterized by:

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