CN113673409A - Automatic convergence spectrum correction method and device for spectrum analysis - Google Patents

Automatic convergence spectrum correction method and device for spectrum analysis Download PDF

Info

Publication number
CN113673409A
CN113673409A CN202110939238.0A CN202110939238A CN113673409A CN 113673409 A CN113673409 A CN 113673409A CN 202110939238 A CN202110939238 A CN 202110939238A CN 113673409 A CN113673409 A CN 113673409A
Authority
CN
China
Prior art keywords
spectrum
baseline
correction
spectral
spectral analysis
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202110939238.0A
Other languages
Chinese (zh)
Inventor
刘中辉
叶坚
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Point Beautiful Napper Shanghai Biomedical Technology Co ltd
Original Assignee
Point Beautiful Napper Shanghai Biomedical Technology Co ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Point Beautiful Napper Shanghai Biomedical Technology Co ltd filed Critical Point Beautiful Napper Shanghai Biomedical Technology Co ltd
Priority to CN202110939238.0A priority Critical patent/CN113673409A/en
Publication of CN113673409A publication Critical patent/CN113673409A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/02—Preprocessing
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
    • G01J3/28—Investigating the spectrum
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

Abstract

The invention relates to the field of spectral analysis baseline correction, in particular to an automatic convergence spectrum correction method and device for spectral analysis. The invention provides an automatic convergence spectrum correction method for spectrum analysis, which comprises the following steps: step S1, acquiring an original spectrum y and setting a smooth parameter lambda; step S2, weighting matrix WtCarrying out initialization; step S3, calculating a fitting spectrum baseline z according to a Whitchman algorithmt(ii) a Step S4, judging whether a cutoff condition is met, if the cutoff condition is not met, entering step S5, and if the cutoff condition is met, entering step S6; step S5, calculating and updating the weight matrix WtProceeding to step S3;and step S6, outputting the spectrum baseline, and obtaining final spectrum correction data according to the spectrum baseline correction. The invention improves the effectiveness and stability of spectrum baseline fitting and improves the reliability of spectrum data analysis and interpretation.

Description

Automatic convergence spectrum correction method and device for spectrum analysis
Technical Field
The invention relates to the field of spectral analysis baseline correction, in particular to an automatic convergence spectrum correction method and device for spectral analysis.
Background
Spectroscopy, the subject of which is the study of the interaction of light with substances, is the generation of spectra by the interaction of electromagnetic or non-electromagnetic radiation with substances, with the aid of which it is possible to carry out theoretical studies and quantitative and qualitative analyses of substances.
Besides the information of the substance, background and random noise exist in the spectrum. Background noise, also known as baseline, interferes with the analysis and interpretation of the target signal, so spectral background signal subtraction, i.e. spectral correction, is the essential work for the basis of spectral analysis.
The baseline is usually a smooth curve independent of the target substance, and fitting and correcting of the baseline are performed manually or by a program. The algorithm of automatic baseline processing mainly comprises polynomial fitting, a punishment least square method, a wavelet transformation method, a derivative method and the like.
An adaptive weight iterative Penalized Least square method (airPLS) is a widely applied automatic baseline processing algorithm in the prior art. The airPLS spectral baseline fitting algorithm is derived from Whittaker (Whitcker) smoothing algorithm.
Whittaker in 1919 proposed a method for solving a fitted smooth curve by controlling the degree of fit and the degree of smoothness of the fitted curve, the degree of fit of the method is defined by the difference between the fitted spectrum and the original spectrum, the degree of smoothness is defined by the difference between adjacent elements of the fitted curve itself, and fitted smooth curves of different degrees of smoothness are obtained by controlling the smoothness parameters, see P EDINBURGH MATH SOC,1922,41: 63-75. DOI: 10.1017/S0013091500077853.
Eilers further studied the Whittaker smoothing algorithm and introduced a weight matrix for the need to fit a smooth curve when the raw spectral data was partially defective or non-uniform, see ANAL CHEM,2003,75(14): 3631-3636. DOI:10.1021/AC 034173T.
Zhimin Zhang et al define the weight matrix according to the characteristics of baseline fitting and generalize the smoothing algorithm into a baseline fitting algorithm by iteratively optimizing the weight matrix, see ANALYST,2010,135(5):1138.DOI: 10.1039/B922045C.
The invention CN202010191859.0 discloses a method, a system and a detection method for correcting a spectrogram baseline in tea near infrared spectrum analysis, and introduces a weighting function based on airPLS algorithm in order to solve the baseline fitting problem of multi-peak overlapping spectrum.
The automatic baseline fitting processing algorithm in the prior art generally has the following problems:
1) the condition of failure of baseline fitting is easy to occur, namely the intensity of a spectral peak is overestimated, even the algorithm generates a spectral peak which does not exist in an original spectrum, and the problem is caused to the analysis and the interpretation of spectral data;
2) the iterative optimization process is divergent, namely in the baseline iterative optimization process, the baseline difference of adjacent iterative times is increased along with the increase of the iterative times, so that the problem of uncontrollable quality of a fitted baseline is easily caused;
3) the weight range is not limited, and overlarge weight is easy to occur in the optimization process of the baseline, so that the matrix calculation is unstable, and the crash of a program or equipment is caused;
4) due to the fact that the iterative optimization process is divergent, the iterative cut-off condition can be defined only through the difference between the correction spectrum and the original spectrum, and the threshold value of the iterative cut-off condition changes along with the difference of the original spectrum, the effectiveness and consistency of the cut-off condition of the fitted spectrum baseline cannot be guaranteed, and the quality of the fitted spectrum baseline cannot be guaranteed.
Disclosure of Invention
The invention aims to provide an automatic convergence spectrum correction method and device for spectrum analysis, and solves the problem that the effectiveness and stability of a fitting baseline in the prior art are poor.
In order to achieve the above object, the present invention provides an automatic convergence spectrum correction method for spectrum analysis, comprising the steps of:
step S1, acquiring an original spectrum y and setting a smooth parameter lambda;
step S2, weighting matrix WtInitializing to obtain an initialization weight momentMatrix of
Figure BDA0003214093660000021
Step S3, calculating a fitting spectrum baseline z according to the Whittaker algorithmt；
Step S4, judging whether a cutoff condition is met, if the cutoff condition is not met, entering step S5, and if the cutoff condition is met, entering step S6;
step S5, calculating and updating the weight matrix WtIn step S3, the process proceeds to the weight matrix WtThe expression of (a) is:
Figure BDA0003214093660000031
Figure BDA0003214093660000032
Figure BDA0003214093660000033
wherein, WtIs the weight matrix for the t-th iteration,
Figure BDA0003214093660000034
is WtMain diagonal line w oftThe ith element of (1);
Figure BDA0003214093660000035
fitting spectral baseline z for the t-1 st timet-1The (i) th element of (a),
Figure BDA0003214093660000036
correcting the spectrum d for the t-1 th fitt-1The ith element of (1), yiFor the i-th element of the original spectrum y,
Figure BDA0003214093660000037
is a criterion for spectral peak and background region,
Figure BDA0003214093660000038
and
Figure BDA0003214093660000039
respectively as a weighting function of a spectral peak region and a background region;
and step S6, outputting the spectrum baseline, and obtaining final spectrum correction data according to the spectrum baseline correction.
In one embodiment, in the step S2, the weight matrix is initialized
Figure BDA00032140936600000310
a1Is a constant.
In one embodiment, in the step S2, the weight matrix is initialized
Figure BDA00032140936600000311
In one embodiment, in the step S3, the spectrum baseline ztThe expression of (a) is:
zt＝(Wt+λDn'Dn)-1Wty；
wherein, WtThe coefficient is a weight matrix of the t iteration, the smooth parameter lambda is a weight coefficient for controlling the fitting degree and the smooth degree, D is a difference matrix, n is the order number of the difference matrix, and y is an original spectrum.
In one embodiment, in step S3, the order of the difference matrix
Figure BDA00032140936600000312
In one embodiment, the cutoff condition of step S4 is determined by comparing h (w)t,y,zt) And h (w)t-1,y,zt-1) Wherein h (w)t-1,y,zt-1) As a characteristic function of the result of the t-1 th iteration, h (w)t,y,zt) Is a characteristic function of the result of the t-th iteration.
In one embodiment, the cutoff condition of step S4 is:
||h(wt,y,zt)-h(wt-1,y,zt-1)||≤a2；
wherein, a2To calculate the accuracy parameter.
In one embodiment, the calculation accuracy parameter a2The following expression is satisfied:
Figure BDA00032140936600000313
where y is the original spectrum.
In one embodiment, the cutoff condition of step S4 is:
||h(wt,y,zt)||≤b2||h(wt-1,y,zt-1)||；
wherein, b2To calculate the accuracy parameter.
In one embodiment, the calculation accuracy parameter b2The following expression is satisfied:
Figure BDA0003214093660000041
in one embodiment, the characteristic function h (w) of the result of the t-th iteration of step S4t,y,zt) Is defined as h (w)t,y,zt)＝a3wt+b3y+c3zt+d3Wherein a is3、b3、c3And d3Is a constant value, wtThe main diagonal elements of the weight matrix for the t-th iteration, y the original spectrum, ztFitting spectral baseline for the t-th time.
In one embodiment, in step S4, a3＝1，b3＝d3＝c 30 or a3＝b3＝d3＝0，c 31 or a3＝d3＝0，b3＝1，c3＝-1。
In one embodiment, the cutoff condition of step S4 is furtherOne step includes limiting the maximum number of iterations tmax：
When the iteration number is larger than the maximum iteration number tmaxWhen it is, the cutoff condition is considered to be satisfied.
In one embodiment, the maximum number of iterations t of step S4max＝10。
In an embodiment, the calculating of step S5 updates the weight matrix, which can be further detailed as:
step S51, defining a spectrum peak and a background area;
step S52, definition of weighting function of spectral peak region and background region.
In an embodiment, the determination condition of the spectral peak and the background region in step S51
Figure BDA0003214093660000042
Is defined as
Figure BDA0003214093660000043
Wherein j (d)t) Correcting the spectrum d according to the t-th fittDefining the statistical indexes;
fitting correction spectrum d for the t timetThe statistical index of (1) includes dtAverage value of (2)
Figure BDA0003214093660000044
Standard deviation of
Figure BDA0003214093660000045
Median number
Figure BDA0003214093660000046
And quantile
Figure BDA0003214093660000047
In one embodiment of the present invention, the substrate is,
Figure BDA0003214093660000048
wherein a is4，b4，c4，d4And e4Is a constant.
In one embodiment, in step S51, a4＝c4＝d4＝e4＝0，b 41 or a4＝b4＝c4＝e4＝0，d 41 or a4＝b4＝c4＝d4＝0，e 41 or a4＝d4＝e4＝0，b4＝1,
Figure BDA0003214093660000049
In one embodiment, in the step S52, the weight matrix WtOf (2) element(s)
Figure BDA0003214093660000051
The following conditions are satisfied:
Figure BDA0003214093660000052
wherein, a5And b5Is a constant.
In one embodiment, in step S52, a50 and b5＝1。
In one embodiment, in the step S52, the weighting function of the spectral peak region and the background region
Figure BDA0003214093660000053
And
Figure BDA0003214093660000054
the following expression is satisfied:
Figure BDA0003214093660000055
and is
Figure BDA0003214093660000056
And
Figure BDA0003214093660000057
is about
Figure BDA0003214093660000058
Is a monotonic function of (a).
In one embodiment, in the step S52, the weight matrix WtOf (2) element(s)
Figure BDA0003214093660000059
The following conditions are satisfied:
Figure BDA00032140936600000510
wherein, a6Is a constant number of times, and is,
Figure BDA00032140936600000511
is a characteristic function.
In one embodiment, in step S52, a6＝1。
In one embodiment, in step S52,
Figure BDA00032140936600000512
with t and
Figure BDA00032140936600000513
increasing and decreasing.
In one embodiment, in the step S52, the characteristic function
Figure BDA00032140936600000514
Is defined as:
Figure BDA00032140936600000515
or
Figure BDA00032140936600000516
Or
Figure BDA00032140936600000517
Wherein, a7、b7And c7Is a constant.
In one embodiment, the constant a7And c7The following expression is satisfied: a is7>0 and c7>1。
In one embodiment, the constant a7、b7And c7The following expression is satisfied: a is7＝1，b7＝0，c7＝2。
In order to achieve the above object, the present invention provides an automatic convergence spectrum correction apparatus for spectrum analysis, comprising:
a memory for storing instructions executable by the processor;
a processor for executing the instructions to implement the method of any one of the above.
To achieve the above object, the present invention provides a computer storage medium having computer instructions stored thereon, wherein the computer instructions, when executed by a processor, perform the method as described in any one of the above.
According to the automatic convergence spectrum correction method and device for spectrum analysis, the problem of the existing spectrum baseline fitting technology based on the Whittaker algorithm is solved through a brand-new defined weight matrix and a cut-off condition, the effectiveness and stability of fitting a spectrum baseline are improved, and the reliability of analysis and interpretation of spectrum data is improved.
Drawings
The above and other features, properties and advantages of the present invention will become more apparent from the following description of the embodiments with reference to the accompanying drawings in which like reference numerals denote like features throughout the several views, wherein:
FIG. 1 discloses a flow chart of a method for automatically converging spectrum correction for spectral analysis according to an embodiment of the invention;
FIG. 2 is a diagram illustrating a spectral peak and background region determination rule according to an embodiment of the present invention;
FIG. 3 discloses a diagram of a baseline of a raw spectrum and a fitted spectrum according to an embodiment of the invention;
FIG. 4 is a diagram illustrating an original spectrum and a corrected spectrum according to an embodiment of the invention;
FIG. 5a discloses a diagram of a prior art raw spectrum and a fitted spectral baseline;
FIG. 5b discloses a schematic diagram of a prior art corrected spectrum;
FIG. 6a discloses a diagram of an original spectrum and a fitted spectral baseline according to a first embodiment of the present invention;
FIG. 6b discloses a schematic diagram of a corrected spectrum according to the first embodiment of the present invention;
FIG. 7a discloses a diagram of an original spectrum and a fitted spectral baseline according to a second embodiment of the present invention;
FIG. 7b discloses a diagram of a corrected spectrum according to a second embodiment of the present invention;
FIG. 8a discloses a diagram of an original spectrum and a fitted spectral baseline according to a third embodiment of the present invention;
FIG. 8b discloses a diagram of a corrected spectrum according to a third embodiment of the present invention;
FIG. 9 discloses a block diagram of an apparatus for automatically converging spectrum correction for spectral analysis according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Fig. 1 is a flowchart of an automatic convergence spectrum calibration method for spectrum analysis according to an embodiment of the present invention, and as shown in fig. 1, the automatic convergence spectrum calibration method for spectrum analysis according to the present invention includes the following steps:
step S1, acquiring an original spectrum y and setting a smooth parameter lambda;
step S2, weighting matrix WtInitializing to obtain the initialChange weight matrix
Figure BDA0003214093660000071
Step S3, calculating a fitting spectrum baseline z according to the Whittaker algorithmt；
Step S4, judging whether a cutoff condition is met, if the cutoff condition is not met, entering step S5, and if the cutoff condition is met, entering step S6;
step S5, calculating and updating the weight matrix WtIn step S3, the process proceeds to the weight matrix WtThe expression of (a) is:
Figure BDA0003214093660000072
Figure BDA0003214093660000073
Figure BDA0003214093660000074
wherein, WtIs the weight matrix for the t-th iteration,
Figure BDA0003214093660000075
is WtMain diagonal line w oftThe ith element of (1);
Figure BDA0003214093660000076
fitting spectral baseline z for the t-1 st timet-1The (i) th element of (a),
Figure BDA0003214093660000077
correcting the spectrum d for the t-1 th fitt-1The ith element of (1), yiFor the i-th element of the original spectrum y,
Figure BDA0003214093660000078
is a determination condition of a spectral peak and a background region，
Figure BDA0003214093660000079
And
Figure BDA00032140936600000710
respectively as a weighting function of a spectral peak region and a background region;
and step S6, outputting the spectrum baseline, and obtaining final spectrum correction data according to the spectrum baseline correction.
Each step of the present invention is described in detail below.
And step S1, acquiring the original spectrum y and setting a smoothing parameter lambda.
The smoothness parameter lambda is used for controlling the weight of the fitting degree and the smoothness degree, and if the lambda is large, the smoothness degree of the fitting spectrum baseline is high, and the fitting degree is poor; and if the lambda is small, the smoothness degree of the fitted spectrum baseline is low, and the fitting degree is high.
Step S2, weighting matrix WtInitializing to obtain an initialized weight matrix
Figure BDA00032140936600000711
Initializing a weight matrix
Figure BDA00032140936600000712
a1Is a constant.
Further, the weight matrix is initialized
Figure BDA00032140936600000713
Step S3, calculating a fitting spectrum baseline z according to the Whittaker algorithmt。
Calculating according to Whittaker algorithm to obtain spectrum baseline ztThe expression of (a) is:
zt＝(Wt+λDn'Dn)-1Wty；
wherein, WtThe weight matrix of the t-th iteration, and the smoothness parameter lambda is the weight for controlling the degree of fitting and the degree of smoothnessAnd the coefficient, D is a difference matrix, n is the order of the difference matrix, and y is the original spectrum.
Difference matrix DnIs defined as:
Figure BDA0003214093660000081
where E is an m × m identity matrix, and E ═ E1；…ei；…em),E∈R(m,m)，ei＝(ei1,...eij,...eim)；
When i ═ j, e ij1 is ═ 1; when i ≠ j, eij＝0。
When n is equal to 1, the compound is,
Figure BDA0003214093660000082
preferably, the order of the difference matrix
Figure BDA0003214093660000083
Step S4, judging whether a cutoff condition is met, if the cutoff condition is not met, entering step S5, and if the cutoff condition is met, entering step S6;
the cut-off condition is controlled by the characteristic function difference and the maximum iteration times of adjacent iteration results, and the cut-off condition difference caused by the original spectrum difference can be overcome, so that the effectiveness and consistency of the cut-off condition of the fitting baseline are controlled, and the quality of the fitting spectrum baseline is further ensured.
In the present embodiment, the cutoff condition is determined by comparing h (w)t,y,zt) And h (w)t-1,y,zt-1) Wherein h (w)t-1,y,zt-1) A characteristic function, h (w), representing the result of the t-1 th iterationt,y,zt) Is a characteristic function of the result of the t-th iteration.
Further, the cutoff condition may be | | | h (w)t,y,zt)-h(wt-1,y,zt-1)||≤a2Wherein a is2To calculate the accuracy parameter.
Calculating the precision parameter a2According to the requirement of calculation accuracy.
Preferably, a2The following expression is satisfied:
Figure BDA0003214093660000084
where y is the original spectrum.
Further, the cutoff condition may be | | | h (w)t,y,zt)||≤b2||h(wt-1,y,zt-1) I, where b2To calculate the accuracy parameter.
Calculating a precision parameter b2According to the requirement of calculation accuracy.
Preferably, b2The following expression is satisfied:
Figure BDA0003214093660000091
in this embodiment, the function h (w) of the characteristics of the result of the t-th iterationt,y,zt) Is defined as h (w)t,y,zt)＝a3wt+b3y+c3zt+d3Wherein a is3、b3、c3And d3Is a constant value, wtThe main diagonal elements of the weight matrix for the t-th iteration, y the original spectrum, ztFitting spectral baseline for the t-th time.
Preferably, a3＝1，b3＝d3＝c 30 or a3＝b3＝d3＝0，c 31 or a3＝d3＝0，b3＝1，c3＝-1。
Further, the cutoff condition further includes limiting the maximum number of iterations tmaxWhen the number of iterations is greater than the maximum number of iterations tmaxWhen it is, the cutoff condition is considered to be satisfied.
Preferably, the maximum number of iterations tmax＝10。
Step S5, calculating and updating the weight matrix WtThe process proceeds to step S3.
The baseline fitting of the spectrum is similar to the smoothness of the spectrum, and the fitting degree and the smoothness degree between the fitted spectrum and the original spectrum need to be controlled, and the difference is that the baseline fitting only needs to control the fitting degree of the background area, and the peak area only needs to control the smoothness degree of the curve and does not need to control the fitting degree. The weight of a spectrum peak area is smaller than that of a background area by defining a weight matrix W of the Whittaker algorithm, so that the fitting degree is dominated by the background area, and the purpose of selectively fitting the background area to obtain a fitting spectrum baseline is achieved.
Thus, the key to the baseline fitting is the definition of the weight matrix, which can be iteratively applied to WtOptimized, the weight matrix WtThe expression of (a) is:
Figure BDA0003214093660000092
Figure BDA0003214093660000093
Figure BDA0003214093660000094
wherein, WtIs the weight matrix for the t-th iteration,
Figure BDA0003214093660000095
is WtMain diagonal line w oftThe ith element of (1);
Figure BDA0003214093660000101
fitting spectral baseline z for the t-1 st timet-1The (i) th element of (a),
Figure BDA0003214093660000102
correcting the spectrum d for the t-1 th fitt-1The ith element of (1), yiFor the i-th element of the original spectrum y,
Figure BDA0003214093660000103
is a criterion for spectral peak and background region,
Figure BDA0003214093660000104
and
Figure BDA0003214093660000105
respectively, the spectral peak region and the background region.
In an embodiment, the step S5 of calculating the updated weight matrix may be further detailed as: step S51, definition of spectral peak and background regions, and step S52, definition of weighting functions of spectral peak regions and background regions.
And step S51, definition of a spectrum peak and a background area.
Fig. 2 is a schematic diagram illustrating a determination rule of spectral peaks and background regions according to an embodiment of the present invention, as shown in fig. 2,
Figure BDA0003214093660000106
the determination conditions for the spectral peak and background region are:
when in use
Figure BDA0003214093660000107
The time is a spectrum peak region, namely a square frame filling region in the figure 2;
when in use
Figure BDA0003214093660000108
The time is the background area, i.e. the area outside the filled area of the square in fig. 2.
Furthermore, the determination conditions of the spectral peak and the background region
Figure BDA0003214093660000109
Is defined as
Figure BDA00032140936600001010
Wherein j (d)t) Correcting spectra from the t-th fitdtDefining the statistical indexes;
fitting correction spectrum d for the t timetThe statistical index of (1) includes dtAverage value of (2)
Figure BDA00032140936600001011
Standard deviation of
Figure BDA00032140936600001012
Median number
Figure BDA00032140936600001013
And quantile
Figure BDA00032140936600001014
In a further step, the method comprises the following steps of,
Figure BDA00032140936600001015
wherein a is4，b4，c4，d4And e4Is a constant.
Preferably, a4＝c4＝d4＝e4＝0，b 41 or a4＝b4＝c4＝e4＝0，d 41 or a4＝b4＝c4＝d4＝0，e 41 or a4＝d4＝e4＝0，b4＝1,
Figure BDA00032140936600001016
In this example, by dtThe statistical indexes define the spectrum peak and the background area range, effectively avoid the problems that the existing algorithm overestimates the spectrum peak area intensity and generates the spectrum peak which does not exist in the original spectrum, can improve the effectiveness of fitting the spectrum base line and improve the reliability of analyzing and reading the spectrum data; in addition, the iterative process of fitting the spectral baseline is converted from the divergence state to the convergence state of the existing method, so that the stability of fitting the spectral baseline is improved.
Step S52, definition of weighting function of spectral peak region and background region.
Weight matrix passing of spectral peak and background region
Figure BDA00032140936600001017
Is determined when
Figure BDA00032140936600001018
When the spectrum is detected, the spectrum peak region is obtained,
Figure BDA0003214093660000111
when in use
Figure BDA0003214093660000112
When the image is in the background area, the image is the background area,
Figure BDA0003214093660000113
further, the weight matrix WtOf (2) element(s)
Figure BDA0003214093660000114
The following conditions are satisfied:
Figure BDA0003214093660000115
wherein, a5And b5Is a constant.
Preferably, a50 and b5＝1。
In this embodiment, the weight matrix W is usedtThe optimization limits the weight range, and avoids the problem of unstable matrix calculation caused by overlarge weight in the optimization process of the existing method, thereby improving the stability of the algorithm.
Further, a weighting function of the spectral peak region and the background region
Figure BDA0003214093660000116
And
Figure BDA0003214093660000117
the following expression is satisfied:
Figure BDA0003214093660000118
and is
Figure BDA0003214093660000119
And
Figure BDA00032140936600001110
is about
Figure BDA00032140936600001111
Is a monotonic function of (a).
Further, the weight matrix WtOf (2) element(s)
Figure BDA00032140936600001112
The following conditions are satisfied:
Figure BDA00032140936600001113
wherein, a6Is a constant number of times, and is,
Figure BDA00032140936600001114
is a characteristic function.
Preferably, a6＝1。
Preferably, the first and second liquid crystal display panels are,
Figure BDA00032140936600001115
with t and
Figure BDA00032140936600001116
increasing and decreasing.
Preferably, the characteristic function
Figure BDA00032140936600001117
Is defined as:
Figure BDA00032140936600001118
or
Figure BDA00032140936600001119
Or
Figure BDA00032140936600001120
Wherein, a7、b7And c7Is a constant.
Preferably, constant a7And c7The following expression is satisfied: a is7>0 and c7>1。
Preferably, constant a7、b7And c7The following expression is satisfied: a is7＝1，b7＝0，c7＝2。
And step S6, outputting the spectrum baseline, and obtaining final spectrum correction data according to the spectrum baseline correction.
FIG. 3 illustrates a diagram of an original spectrum and a fitted spectral baseline that tends to converge as the number of iterations increases, as shown in FIG. 3, in accordance with an embodiment of the present invention.
FIG. 4 is a diagram illustrating an original spectrum and a corrected spectrum according to an embodiment of the present invention, wherein the corrected spectrum tends to converge as the number of iterations increases, as shown in FIG. 4.
The technical effect of the present invention will be described below by comparing three embodiments according to the present invention with the prior art. In order to compare the technical effects of the invention and the prior art, the iteration cut-off condition only sets the maximum iteration time limit, wherein the maximum iteration time tmax＝10。
Fig. 5a shows a diagram of a baseline of a prior art raw spectrum and a fitted spectrum, fig. 5b shows a diagram of a prior art corrected spectrum, and in the prior art shown in fig. 5a and 5b, the airPLS spectrum baseline fitting algorithm most closely resembling the present invention is used.
Fig. 5a shows a fitted spectrum baseline of an original spectrum and different iterations, fig. 5b shows a corrected spectrum for different iterations, and as the number of iterations increases, the fitted baseline of the prior art in fig. 5a diverges, and the corresponding corrected spectrum in fig. 5b also diverges.
The fitted baselines in FIG. 5a are at 700 and 2800cm-1The region deviates from the original spectrum, so that the corrected spectrum in FIG. 5b, at 700cm-1The spectral peak intensity of the region was overestimated at 2800cm-1The regions show spectral peaks that were not present in the original spectrum. The limitation of the prior art causes the iterative spectrum baseline fitting result to be dispersed, so that the spectral peak is overestimated and a new spectral peak source appears, and the spectrum baseline fitting is invalid. According to the prior art, the divergence state becomes more serious as the number of iterations increases. In practical application, divergence superposition of the original spectrum in the prior art makes the baseline fitting result more uncontrollable and more prone to failure.
Fig. 6a discloses a diagram of an original spectrum and a fitted spectrum baseline according to a first embodiment of the present invention, and fig. 6b discloses a diagram of a corrected spectrum according to a first embodiment of the present invention, and in the first embodiment shown in fig. 6a and fig. 6b, only the optimized spectrum peak and background region definitions proposed by the present invention are used, and the weight matrix adopts the prior art shown in fig. 5a and fig. 5 b.
In the first embodiment, the determination condition of the spectral peak and the background region is a4＝c4＝d4＝e4＝0，b 41 is ═ 1, i.e
Figure BDA0003214093660000121
Fig. 6a is a fitted spectral baseline of the original spectrum with different iterations, and fig. 6b is a corrected spectrum with different iterations. As the number of iterations increases, the fitted baseline in fig. 6a overlaps the original spectrum in the background region, and the intensity of the corrected spectrum in fig. 6b approaches 0 in the background region.
The first embodiment circumvents the problem of overestimating the spectral peak regions and generating spectral peaks that are not present in the original spectrum of the prior art method shown in fig. 5a and 5b, while allowing the fitted spectral baseline in the iterative process to change from the divergent state to the convergent state of the prior art method.
The partial optimization results from the definition of the spectral peak region, from which it can be speculated that when a4＝b4＝c4＝e4＝0，d 41 or a4＝b4＝c4＝d4＝0，e 41 or a4＝d4＝e4＝0，b4＝1,
Figure BDA0003214093660000131
All can reach a4＝c4＝d4＝e4＝0，b 41 the same or similar effect.
Fig. 7a discloses a diagram of the original spectrum and the fitted spectrum baseline according to the second embodiment of the present invention, and fig. 7b discloses a diagram of the corrected spectrum according to the second embodiment of the present invention, and in the second embodiment shown in fig. 7a and fig. 7b, only the weight matrix definition proposed by the present invention is used, and the spectrum peak and background region definition uses the prior art as shown in fig. 5a and fig. 5 b.
In a second embodiment, the weight matrix is passed
Figure BDA0003214093660000132
And
Figure BDA0003214093660000133
definition, which defines the range of weights
Figure BDA0003214093660000134
FIG. 7a is a spectrum baseline of the original spectrum and the corrected spectrum of different iterations, FIG. 7b is a spectrum baseline of the corrected spectrum of different iterations, and the second embodiment defines the range of the weight matrix while obtaining the similar spectrum baseline fitting effect as the prior art method shown in FIG. 5a and FIG. 5b
Figure BDA0003214093660000135
Thereby avoiding the weightThe matrix calculation is unstable due to overlarge, and the stability of the algorithm is improved.
Fig. 8a discloses a diagram of an original spectrum and a fitted spectrum baseline according to a third embodiment of the present invention, and fig. 8b discloses a diagram of a corrected spectrum according to the third embodiment of the present invention, and the optimized spectrum peak and background region definitions and weight matrix definitions proposed by the present invention are adopted in the third embodiment shown in fig. 8a and fig. 8 b.
In the third embodiment, the determination condition of the spectral peak and the background region is a4＝c4＝d4＝e4＝0，b 41 is ═ 1, i.e
Figure BDA0003214093660000136
Weight matrix passing
Figure BDA0003214093660000137
And
Figure BDA0003214093660000138
definition, which defines the range of weights
Figure BDA0003214093660000139
Fig. 8a is a fitted spectral baseline of the original spectrum with different iterations, and fig. 8b is a corrected spectrum with different iterations. As the number of iterations increases, the fitted baseline in fig. 8a overlaps the original spectrum in the background region, and the intensity of the corrected spectrum in fig. 8b approaches 0 in the background region.
The third embodiment avoids the problems of overestimating the spectral peak region and generating spectral peaks which do not exist in the original spectrum in the existing method shown in fig. 5a and 5b, and simultaneously can change the fitted spectral baseline in the iterative process from the divergence state of the existing method to the convergence state; further, the third embodiment defines the range of the weight matrix
Figure BDA0003214093660000141
The problem of unstable matrix calculation caused by overlarge weight is avoided, and the stability of the algorithm is improved.
FIG. 9 discloses a block diagram of an apparatus for automatically converging spectrum correction for spectral analysis according to an embodiment of the present invention. The automatically converging spectrum correction apparatus for spectrum analysis may include an internal communication bus 701, a processor (processor)702, a Read Only Memory (ROM)703, a Random Access Memory (RAM)704, a communication port 705, and a hard disk 707. The internal communication bus 701 may enable data communication between components of the auto-convergent spectrum correction device for spectral analysis. The processor 702 may make the determination and issue the prompt. In some embodiments, the processor 702 may be comprised of one or more processors.
The communication port 705 may enable data transmission and communication between the automatically converging spectral correction apparatus for spectral analysis and an external input/output device. In some embodiments, an automatically converging spectrum correction device for spectral analysis may send and receive information and data from a network through communication port 705. In some embodiments, the automatically converging spectral correction apparatus for spectral analysis may be in wired form for data transfer and communication with an external input/output device via input/output 706.
The self-converging spectrum correction device for spectral analysis may also include various forms of program storage units and data storage units, such as a hard disk 707, Read Only Memory (ROM)703 and Random Access Memory (RAM)704, capable of storing various data files for computer processing and/or communication, and possibly program instructions for execution by the processor 702. The processor 702 executes these instructions to implement the main parts of the method. The results of the processing by the processor 702 are communicated to an external output device via the communication port 705 for display on a user interface of the output device.
For example, the implementation process file of the above-mentioned automatic convergence spectrum correction method for spectrum analysis may be a computer program, stored in the hard disk 707, and recorded in the processor 702 for execution, so as to implement the method of the present application.
When the implementation process file of the automatic convergence spectrum correction method for spectrum analysis is a computer program, the implementation process file can also be stored in a computer readable storage medium as an article of manufacture. For example, computer-readable storage media can include but are not limited to magnetic storage devices (e.g., hard disk, floppy disk, magnetic strips), optical disks (e.g., Compact Disk (CD), Digital Versatile Disk (DVD)), smart cards, and flash memory devices (e.g., electrically Erasable Programmable Read Only Memory (EPROM), card, stick, key drive). In addition, various storage media described herein can represent one or more devices and/or other machine-readable media for storing information. The term "machine-readable medium" can include, without being limited to, wireless channels and various other media (and/or storage media) capable of storing, containing, and/or carrying code and/or instructions and/or data.
The invention provides an automatic convergence spectrum correction method and device for spectrum analysis, which have the following beneficial effects:
1) correcting the spectrum d by fittingtThe statistical indexes define the spectral peak and the background area, so that the problems that the intensity of the spectral peak area is overestimated and the spectral peak which does not exist in the original spectrum is generated in the conventional method are effectively avoided, the effectiveness of spectral baseline fitting is improved, and the reliability of spectral data analysis and interpretation is improved;
2) correcting the spectrum d by fittingtThe statistical indexes define a spectrum peak and a background area, so that the iterative process of spectrum baseline fitting is changed from a divergence state to a convergence state of the existing method, and the stability of fitting the spectrum baseline can be improved;
3) optimizes the definition of the spectrum peak and the background weight matrix, obtains the similar spectrum baseline fitting effect with the prior method, and limits the range of the weight matrix
Figure BDA0003214093660000151
The problem of unstable matrix calculation caused by overlarge weight is avoided, and the stability of the algorithm is improved;
4) based on the convergence characteristic of the algorithm, the cut-off condition is defined through the characteristic function of adjacent iteration results, the dependence of the cut-off condition on the original spectrum is avoided, the cut-off condition standard is defined by the fitting result, the effectiveness and consistency of the cut-off condition of the fitting baseline are controlled, and the quality of the fitting spectral baseline is further ensured.
While, for purposes of simplicity of explanation, the methodologies are shown and described as a series of acts, it is to be understood and appreciated that the methodologies are not limited by the order of acts, as some acts may, in accordance with one or more embodiments, occur in different orders and/or concurrently with other acts from that shown and described herein or not shown and described herein, as would be understood by one skilled in the art.
As used in this application and the appended claims, the terms "a," "an," "the," and/or "the" are not intended to be inclusive in the singular, but rather are intended to be inclusive in the plural unless the context clearly dictates otherwise. In general, the terms "comprises" and "comprising" merely indicate that steps and elements are included which are explicitly identified, that the steps and elements do not form an exclusive list, and that a method or apparatus may include other steps or elements.
The embodiments described above are provided to enable persons skilled in the art to make or use the invention and that modifications or variations can be made to the embodiments described above by persons skilled in the art without departing from the inventive concept of the present invention, so that the scope of protection of the present invention is not limited by the embodiments described above but should be accorded the widest scope consistent with the innovative features set forth in the claims.

Claims (20)

1. A method for automatically converging spectra for spectral analysis, comprising the steps of:
step S1, acquiring an original spectrum y and setting a smooth parameter lambda;
step S2, weighting matrix WtInitializing to obtain an initialized weight matrix
Figure FDA0003214093650000011
Step S3, calculating a fitting spectrum baseline z according to a Whitchman algorithmt；
Step S4, judging whether a cutoff condition is met, if the cutoff condition is not met, entering step S5, and if the cutoff condition is met, entering step S6;
step S5, calculating and updating the weight matrix WtIn step S3, the process proceeds to the weight matrix WtThe expression of (a) is:
Figure FDA0003214093650000012
Figure FDA0003214093650000013
Figure FDA0003214093650000014
wherein, WtIs the weight matrix for the t-th iteration,
Figure FDA0003214093650000015
is WtMain diagonal line w oftThe ith element of (1);
Figure FDA0003214093650000016
fitting spectral baseline z for the t-1 st timet-1The (i) th element of (a),
Figure FDA0003214093650000017
correcting the spectrum d for the t-1 th fitt-1The ith element of (1), yiFor the i-th element of the original spectrum y,
Figure FDA0003214093650000018
is a criterion for spectral peak and background region,
Figure FDA0003214093650000019
and
Figure FDA00032140936500000110
respectively as a weighting function of a spectral peak region and a background region;
and step S6, outputting the spectrum baseline, and obtaining final spectrum correction data according to the spectrum baseline correction.
2. The method for automatically converging spectrum of claim 1, wherein in step S3, the spectrum baseline ztThe expression of (a) is:
zt＝(Wt+λDn'Dn)-1Wty；
wherein, WtThe coefficient is a weight matrix of the t iteration, the smooth parameter lambda is a weight coefficient for controlling the fitting degree and the smooth degree, D is a difference matrix, n is the order number of the difference matrix, and y is an original spectrum.
3. The method for automatically converging spectrum of claim 1, wherein the cut-off condition of step S4 is determined by comparing h (w)t,y,zt) And h (w)t-1,y,zt-1) Wherein h (w)t-1,y,zt-1) As a characteristic function of the result of the t-1 th iteration, h (w)t,y,zt) Is a characteristic function of the result of the t-th iteration.
4. The method for automatically converging spectrum correction for spectral analysis of claim 3, wherein the cutoff conditions of step S4 are:
||h(wt,y,zt)-h(wt-1,y,zt-1)||≤a2；
wherein, a2To calculate the accuracy parameter.
5. The method of claim 4, wherein the calculation accuracy parameter a is a2The following expression is satisfied:
Figure FDA0003214093650000021
0.1×||y||]；
where y is the original spectrum.
6. The method for automatically converging spectrum correction for spectral analysis of claim 3, wherein the cutoff conditions of step S4 are:
||h(wt,y,zt)||≤b2||h(wt-1,y,zt-1)||；
wherein, b2To calculate the accuracy parameter.
7. The method of claim 6, wherein the calculation accuracy parameter b is a function of the spectral analysis2The following expression is satisfied:
Figure FDA0003214093650000022
8. the method for automatically converging spectrum correction for spectral analysis of claim 3, wherein the characteristic function h (w) of the result of the t-th iteration of step S4t,y,zt) Is defined as h (w)t,y,zt)＝a3wt+b3y+c3zt+d3Wherein a is3、b3、c3And d3Is a constant value, wtThe main diagonal elements of the weight matrix for the t-th iteration, y the original spectrum, ztFitting spectral baseline for the t-th time.
9. The method for automatically converging spectrum correction for spectral analysis of claim 8, wherein in said step S4:
a3＝1，b3＝d3＝c30 or
a3＝b3＝d3＝0，c31 or
a3＝d3＝0，b3＝1，c3＝-1。
10. The method for automatically converging spectrum correction for spectral analysis according to claim 1, wherein the determination condition of the spectral peak and background region of step S5
Figure FDA0003214093650000031
Is defined as
Figure FDA0003214093650000032
Wherein j (d)t) Correcting the spectrum d according to the t-th fittDefining the statistical indexes;
fitting correction spectrum d for the t timetThe statistical index of (1) includes dtAverage value of (2)
Figure FDA0003214093650000033
Standard deviation of
Figure FDA0003214093650000034
Median number
Figure FDA0003214093650000035
And quantile
Figure FDA0003214093650000036
Figure FDA0003214093650000037
Wherein, a4，b4，c4，d4And e4Is a constant.
11. The method for automatically converging spectrum correction for spectral analysis of claim 10, wherein in step S5:
a4＝c4＝d4＝e4＝0，b41 or
a4＝b4＝c4＝e4＝0，d41 or
a4＝b4＝c4＝d4＝0，e41 or
a4＝d4＝e4＝0，b4＝1,
Figure FDA0003214093650000038
12. The method for automatically converging spectrum of claim 1, wherein in step S5, the weight matrix WtOf (2) element(s)
Figure FDA0003214093650000039
The following conditions are satisfied:
Figure FDA00032140936500000310
wherein, a5And b5Is a constant.
13. The method for automatically converging spectrum correction for spectral analysis of claim 12, wherein in step S5, a50 and b5＝1。
14. The method for automatically converging spectrum correction for spectral analysis of claim 1, wherein in step S5, the weighting function of the spectral peak region and the background region
Figure FDA0003214093650000041
And
Figure FDA0003214093650000042
is enough to satisfyThe following expressions:
Figure FDA0003214093650000043
and is
Figure FDA0003214093650000044
And
Figure FDA0003214093650000045
is about
Figure FDA0003214093650000046
Is a monotonic function of (a).
15. The method for automatically converging spectrum of claim 1, wherein in step S5, the weight matrix WtOf (2) element(s)
Figure FDA0003214093650000047
The following conditions are satisfied:
Figure FDA0003214093650000048
wherein, a6Is a constant;
Figure FDA0003214093650000049
in order to be a function of the characteristics,
Figure FDA00032140936500000410
with t and
Figure FDA00032140936500000411
increasing and decreasing in value.
16. The method for automatically converging spectrum correction for spectral analysis of claim 15, wherein in step S5,characteristic function
Figure FDA00032140936500000412
Is defined as:
Figure FDA00032140936500000413
or
Figure FDA00032140936500000414
Or
Figure FDA00032140936500000415
Wherein, a7、b7And c7Is a constant.
17. The method of automatically converging spectrum correction for spectral analysis of claim 16, wherein the constant a is7And c7The following expression is satisfied: a is7>0 and c7>1。
18. The method of automatically converging spectrum correction for spectral analysis of claim 16, wherein the constant a is7、b7And c7The following expression is satisfied: a is7＝1，b7＝0，c7＝2。
19. An automatically converging spectrum correction apparatus for spectral analysis, comprising:
a memory for storing instructions executable by the processor;
a processor for executing the instructions to implement the method of any one of claims 1-18.
20. A computer storage medium having computer instructions stored thereon, wherein the computer instructions, when executed by a processor, perform the method of any of claims 1-18.
CN202110939238.0A 2021-08-16 2021-08-16 Automatic convergence spectrum correction method and device for spectrum analysis Pending CN113673409A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110939238.0A CN113673409A (en) 2021-08-16 2021-08-16 Automatic convergence spectrum correction method and device for spectrum analysis

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110939238.0A CN113673409A (en) 2021-08-16 2021-08-16 Automatic convergence spectrum correction method and device for spectrum analysis

Publications (1)

Publication Number Publication Date
CN113673409A true CN113673409A (en) 2021-11-19

Family

ID=78543101

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110939238.0A Pending CN113673409A (en) 2021-08-16 2021-08-16 Automatic convergence spectrum correction method and device for spectrum analysis

Country Status (1)

Country Link
CN (1) CN113673409A (en)

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101408912A (en) * 2008-11-21 2009-04-15 天津师范大学 Method for automatically extracting characteristic function of traditional Chinese medicine pulse manifestation
US20160259792A1 (en) * 2015-03-05 2016-09-08 Bio-Rad Laboratories, Inc. Optimized spectral matching and display
CN108844939A (en) * 2018-03-14 2018-11-20 西安电子科技大学 Raman spectrum based on asymmetric weighted least-squares detects baseline correction method
CN111125625A (en) * 2019-11-29 2020-05-08 北京遥测技术研究所 Spectrum baseline calculation method based on embedded system
CN111307751A (en) * 2020-03-18 2020-06-19 安徽大学 Spectrogram baseline correction method, system and detection method in tea near infrared spectrum analysis
CN112102898A (en) * 2020-09-22 2020-12-18 安徽大学 Method and system for identifying mode of spectrogram in solid fermentation process of vinegar grains

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101408912A (en) * 2008-11-21 2009-04-15 天津师范大学 Method for automatically extracting characteristic function of traditional Chinese medicine pulse manifestation
US20160259792A1 (en) * 2015-03-05 2016-09-08 Bio-Rad Laboratories, Inc. Optimized spectral matching and display
CN108844939A (en) * 2018-03-14 2018-11-20 西安电子科技大学 Raman spectrum based on asymmetric weighted least-squares detects baseline correction method
CN111125625A (en) * 2019-11-29 2020-05-08 北京遥测技术研究所 Spectrum baseline calculation method based on embedded system
CN111307751A (en) * 2020-03-18 2020-06-19 安徽大学 Spectrogram baseline correction method, system and detection method in tea near infrared spectrum analysis
CN112102898A (en) * 2020-09-22 2020-12-18 安徽大学 Method and system for identifying mode of spectrogram in solid fermentation process of vinegar grains

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
杨桂燕;李路;陈和;陈思颖;张寅超;郭磐;: "基于广义Whittaker平滑器的拉曼光谱基线校正方法", 中国激光, no. 09, 10 September 2015 (2015-09-10) *
马真;马恩;熊飞兵;许国澎;李冲;: "动态移动最小二乘多项式平滑的拉曼全自动基线校正算法", 应用激光, no. 04, 15 August 2017 (2017-08-15) *

Similar Documents

Publication Publication Date Title
Pitt et al. On some properties of Markov chain Monte Carlo simulation methods based on the particle filter
Battaglia et al. Practical considerations in raking survey data
Gordy Saddlepoint approximation of CreditRisk+
US9609180B2 (en) Radiometric calibration from noise distributions
Fengler et al. Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints
Xing et al. Robust minimum variance portfolio with L-infinity constraints
Hausman et al. Errors in the dependent variable of quantile regression models
Tsaig et al. Analyzing the impact of credit migration in a portfolio setting
Engelmann et al. Calibration of the Heston stochastic local volatility model: A finite volume scheme
Zhan et al. Kernel approaches for differential expression analysis of mass spectrometry-based metabolomics data
Chockalingam et al. An approximate moving boundary method for American option pricing
Meyer et al. Adaptive rejection Metropolis sampling using Lagrange interpolation polynomials of degree 2
Düring et al. High-order compact finite difference scheme for option pricing in stochastic volatility jump models
Charmpi et al. Optimizing network propagation for multi-omics data integration
Huang et al. Estimating precipitation extremes using the log‐histospline
Chernyavskiy et al. Correlated Poisson models for age‐period‐cohort analysis
CN113673409A (en) Automatic convergence spectrum correction method and device for spectrum analysis
Forneron A Sieve‐SMM Estimator for Dynamic Models
Wei et al. Two-stage iteratively reweighted smoothing splines for baseline correction
Giribone et al. Option pricing via radial basis functions: Performance comparison with traditional numerical integration scheme and parameters choice for a reliable pricing
Tocino et al. Asymptotic mean-square stability of two-step Maruyama schemes for stochastic differential equations
Ďuriš et al. Comparison of the analytical approximation formula and newton's method for solving a class of nonlinear Black–Scholes parabolic equations
CN115546157A (en) Method, device and storage medium for evaluating radiation quality of satellite image
Tong et al. Computing equilibrium prices for a capital asset pricing model with heterogeneous beliefs and margin-requirement constraints
CN115631497A (en) Industrial and commercial management system and method thereof

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination