CN104165844A - Spectral measurement and blind source separation combined mixed pigment component analytical method - Google Patents

Abstract

The invention relates to a spectral measurement and blind source separation combined mixed pigment component analytical method. The method comprises the following steps: (1) enough amount of spectral reflectivity R is obtained from mixed pigments; (2) R is converted to corresponding absorbing and scattering ratio K/S, and whitening process is carried out; (3) blind source separation is carried out on a signal which has undergone whitening process so as to obtain final isolated component; (4) K/S for indicating the isolated component matches K/S of a known basic pigment in a database so as to obtain a corresponding basic pigment type; and (5) according to K/S of the basic pigment and K/S of the mixed pigments and by the theorem of Kubelka-Munk, an equation set is established for solving so as to obtain proportion of the basic pigment. By the above method, mixed pigment component analysis is carried out to obtain type information of the basic pigment and obtain proportion information of the basic pigment in the mixed pigments. Meanwhile, the whole process is automated, and the method provided by the invention has high execution efficiency.

Description

The spectral measurement hybrid pigment component analyzing method that combine separated with blind source

Technical field

The present invention relates to component analyzing method, particularly a kind of spectral measurement hybrid pigment component analyzing method of combining separated with blind source.

Background technology

In hybrid pigment constituent analysis field, common method comprises following two classes:

First kind method there are differences characteristics such as the diffraction of different rays, transmission, scatterings according to pigment, and utilization variance is distinguished pigment.These class methods mainly comprise: X-ray diffraction analysis (X-Ray Diffraction, be called for short XRD), x-ray fluorescence analysis (X-Ray Fluorescence, be called for short XRF), particle excitated X-fluorescence technology (Particle Induced X-Ray Emission, be called for short PIXE), laser Raman spectroscopy (Laser Raman Spectroscopy, be called for short LRS), scanning electron microscope-electron probe microanalysis (SEM-EPMA), scanning electron microscope-X-ray energy spectrum (SEM-EDX), Laser-induced Breakdown Spectroscopy (Laser-Induced Breakdown Spectroscopy, be called for short LIBS), polarizing microscope (Polarized Light Microscopy, be called for short PLM), stereomicroscope (Stereo Light Microscopy, be called for short SLM) etc.The process of these methods is as follows: first, adopt high precision apparatus to measure hybrid pigment, obtain representing the spectral informations such as diffraction, transmission, scattering of pigment characteristics; Then, the spectral information of measurement is mated with the spectral information of known pigment in database, thereby determine compound, the element kind comprising; For some measurement result, by semidefinite quantization method, can obtain the content of compound or element.

Equations of The Second Kind method there are differences natural light reflection characteristic according to pigment, and utilization variance is distinguished pigment.These class methods mainly comprise: reflection spectrometry (Reflectance Spectroscopy is called for short RS), derivative spectrophotometry (Derivative Spectrophotometry is called for short DS) etc.These methods can access the ratio of basic pigment.At present, the application of RS method is more, and its process is as follows: first, adopt spectrometer or multi-optical spectrum imaging system to measure hybrid pigment, obtain the spectral reflectance of hybrid pigment; Then, by calculating the kind that judges basic pigment that hybrid pigment comprises with the similarity of known pigment spectral reflectance; Finally, pigment spectral reflectance is converted to ABSORPTION AND SCATTERING ratio, by setting up and solve Kubelka-Munk colour mixture system of equations, calculates the ratio of basic pigment.DS method is similar with the basic step of RS method, and difference is: RS method is compared to processing object with spectral reflectance, and DS method is usingd the derivative of spectral reflectance as processing object; RS method is calculated basic pigment ratio by Kubelka-Munk theorem, and DS method is by the basic pigment solution of the multiple variable concentrations of configuration, carries out recovery experiment to obtain working curve, by this curve, determines basic pigment ratio.

There is following defect in above-mentioned two class methods:

(1) robotization is difficult: when first kind method is carried out diffraction, transmission, scattering spectrum coupling, be mainly to mate according to its peak value position, in most cases also need artificial participation.While calculating the content of compound or element, generally adopt semidefinite quantization method, the feature of this method is in qualitative simulation, to use the emulation of quantitative information, because information can not all quantize, so be difficult to robotization, completes.When the DS method of Equations of The Second Kind method is carried out recovery experiment, its flow process is first to adopt derivative spectrophotometry to obtain the position A at basic pigment characteristics peak; Then configure the basic pigment solution of variable concentrations, measure its derivative spectrum, take concentration as horizontal ordinate, the derivative peak height at A place, position is ordinate, drawing curve; Finally on working curve, find position corresponding to basic pigment characteristics to be measured peak, determine the content of basic pigment.Find out thus, this method needs the artificial configuration solution that participates in, and finds the position of characteristic peak etc., and very difficult robotization completes.

(2) poor accuracy: first kind method need to be come match peak position by observation, the outwardness collimation error, objectively also there is error in the qualitative part of semidefinite quantization method, and these errors can reduce the accuracy of the method.While calculating curve of spectrum similarity, the RS method of Equations of The Second Kind method is subject to multiple basic pigment impact in hybrid pigment, can introduce the error of calculation; DS method needs artificial participation in the recovery experimental phase, also has error; These two kinds of errors all can reduce the accuracy of the method.

(3) be difficult to obtain complete composition information: this defect is mainly present in first kind method.X-ray fluorescence analysis, scanning electron microscope-electron probe microanalysis only can detect element, cannot determine basic color chemistry formula; Adopt XRF semi-quantitative analysis, proton excitation X-fluorescence technology, the basic comprising obtaining is oxide and content thereof, but some basic pigment is not oxide; X-ray diffraction analysis, laser Raman spectroscopy, scanning electron microscope-X-ray energy spectrum, Laser-induced Breakdown Spectroscopy, polarizing microscope etc. can only draw basic pigment type, cannot determine blending ratio; Stereomicroscope is a kind of assistant analysis means, can go deep into, observe meticulously surface of pigments, but cannot detect basic pigment type and blending ratio.

Hybrid pigment constituent analysis is by scientific instrument and analysis means, determines the basic pigment type and the ratio that form hybrid pigment, in fields such as criminal investigation discriminating, verification retrieval, dyestuff are synthetic, has extremely important effect.There is robotization difficulty, poor accuracy, be difficult to obtain the complete defects such as composition information in above-mentioned conventional method, has seriously limited the application of conventional method in hybrid pigment constituent analysis.For the defect existing in prior art, the present invention proposes the spectral measurement hybrid pigment component analyzing method that combine separated with blind source, by spectrometer or multi-optical spectrum imaging system, in conjunction with basic pigment ABSORPTION AND SCATTERING, than K/S database, working procedure is realized hybrid pigment constituent analysis on computers.

Summary of the invention

The object of this invention is to provide a kind of spectral measurement hybrid pigment component analyzing method of combining separated with blind source.

Technical scheme of the present invention: a kind of spectral measurement hybrid pigment component analyzing method of combining separated with blind source, comprises the following steps:

(1) from m hybrid pigment of sufficient amount, obtain corresponding m spectral reflectance R;

(2) m spectral reflectance R is converted to a corresponding m ABSORPTION AND SCATTERING than K/S, and is considered as mixed signal, carry out albefaction processing, obtain orthonormal signal;

(3) signal after albefaction processing is carried out to the separation of blind source, obtain a final n isolated component;

(4) K/S n isolated component being represented mates with the K/S of known basic pigment in database, according to the maximum principle of similarity, determines n the basic pigment type that isolated component is corresponding;

(5) according to the K/S of step (4) gained n basic pigment, and the m of a hybrid pigment ABSORPTION AND SCATTERING is than K/S, according to Kubelka-Munk theorem, sets up system of equations and solves, and draws the ratio of n basic pigment.

Tradition RS method is calculated the similarity of hybrid pigment spectral reflectance and known basic pigment spectral reflectance, is easily subject to multiple basic pigment impact in hybrid pigment, thereby produces the error of calculation.And the present invention is considered as mixed signal by hybrid pigment K/S, calculate isolated component represents after the separation of blind source K/S and the similarity of known basic pigment K/S, avoided the impact of this potential error, there is higher accuracy.In addition, due to the problem of measurement means self, most of classic methods can only obtain basic pigment type information, cannot obtain the percent information of basic pigment in hybrid pigment, and the present invention can obtain basic pigment type and ratio two parts information, there is good integrality.

Now for the flow process of five steps of the present invention, introduce one by one, the flow process of each step of the present invention all can be written as computer program module, is comprehensively then a complete program, thus automated execution.

Technical scheme of the present invention, step (1) is obtained corresponding m spectral reflectance R from m hybrid pigment of sufficient amount.

Concrete, the described m of step (1) hybrid pigment forms by identical several basic pigment, but in each hybrid pigment, the ratio of basic pigment is different.Described in step (1), from m hybrid pigment of sufficient amount, obtain corresponding m spectral reflectance R, its effect is to guarantee that the number m of hybrid pigment spectral reflectance R is not less than the number of basic pigment.

Concrete, step (1) can adopt following operation steps: if obtain m when initial ₁individual spectral reflectance R, the blind source of step (3) lock out operation has solution, now m=m ₁; If obtain m when initial ₂individual spectral reflectance R, the blind source of step (3) lock out operation, without solution, needs to increase the number of the spectral reflectance R obtaining, until the blind source of step (3) lock out operation has solution.

Blind source separation algorithm can, the in the situation that of information source and the equal the unknown of transmission channel parameter, draw each baseband signal of information source from mixed signal.According to the relation of mixed signal number and baseband signal number, blind source separation algorithm can be divided into overdetermination, positive definite and owe fixed three kinds, they represent that respectively mixed signal number is greater than, equals and be less than baseband signal number; In general, overdetermination and positive definite problem have maturation, unified and stable solution, and the problem of owing to determine does not have fixing solution.The present invention is considered as baseband signal by basic pigment K/S, and hybrid pigment K/S is considered as mixed signal; In order to improve the accuracy of hybrid pigment constituent analysis, we require the number m of hybrid pigment K/S to be not less than the number of basic pigment K/S.Because ABSORPTION AND SCATTERING is derived by spectral reflectance R than K/S, there is one-to-one relationship in K/S, R, pigment each other, so this restrictive condition equivalence is expressed as " the number m of hybrid pigment spectral reflectance R is not less than the number of basic pigment ".If the number that obtains hybrid pigment spectral reflectance R is less than the number of basic pigment, so blind source lock out operation, without solution, needs to continue to increase the number of hybrid pigment spectral reflectance R, until blind source lock out operation has solution.

More specifically, the spectral reflectance R in step (1), can obtain by multi-optical spectrum imaging system or spectrometer.If adopt spectrometer directly to obtain; If employing multi-optical spectrum imaging system, by transition matrix H and the digital response g of multi-optical spectrum imaging system, according to formula R=H ⁺g obtains, H ⁺the generalized inverse matrix that represents H.

Multi-optical spectrum imaging system transition matrix H can adopt disclosed either method in prior art, is preferably as follows scheme: adopt light source, one group of optical filter and sensor (as digital camera) to form multi-optical spectrum imaging system.First in multi-optical spectrum imaging system, place some standard color card samples that spectral reflectance R ' is known, obtain a series of camera digital response g '; Then utilize formula H=g ' R ' ⁺obtain the transition matrix H of this multi-optical spectrum imaging system.

Technical scheme of the present invention, step (2) is converted to ABSORPTION AND SCATTERING than K/S by spectral reflectance R, and is considered as mixed signal, carries out albefaction processing, obtains orthonormal signal.

Concrete, step (2) spectral reflectance R is converted to ABSORPTION AND SCATTERING and than the conversion regime of K/S is: K/S=(1-R) ²/ (2R).Because spectral reflectance R is a continuous curve in form, so ABSORPTION AND SCATTERING is also a continuous curve than K/S in form, can be considered as signal and processes; In addition, the discussion according to Kubelka-Munk theorem about hybrid pigment K/S and basic pigment K/S relation, can be considered as hybrid pigment K/S the linear combination of basic pigment K/S.Albefaction is processed can be converted to hybrid pigment K/S quadrature normalizing component, meets the requirement of blind source separation.

Concrete, the described albefaction of step (2) is processed and is comprised the following steps: generate standardization K/S curve, calculating covariance matrix, computation of characteristic values and proper vector, structure albefaction matrix, generate albefaction K/S curve.

More specifically, step (2) albefaction is processed and is comprised the steps:

1. generate standardization K/S curve: m ABSORPTION AND SCATTERING is considered as to m bar vector X than K/S _i(t), i=1 ..., m, to every vectorial executable operations: wherein std[X _i(t)] be respectively X _i(t) average, standard deviation;

2. calculate covariance matrix: by Y (t)=[Y ₁(t), Y ₂(t) ..., Y _m(t)] ^tin every group of signal be considered as a stochastic variable, calculate covariance each other, obtain m * m matrix V;

3. covariance matrix is carried out to svd: first, the eigenvalue λ of calculating covariance matrix V '=[λ ' ₁, λ ' ₂..., λ ' _m] and proper vector E '=[e ' ₁, e ' ₂..., e ' _m], λ ' _iand e ' _icorresponding one by one.Then, to λ ' ascending sort, obtain orderly eigenvalue λ=[λ ₁, λ ₂..., λ _m], meet 0≤λ ₁≤ λ ₂≤ ... ≤ λ _m; According to corresponding relation, adjust the position of each component of proper vector E ' simultaneously, obtain character pair vector E=[e ₁, e ₂..., e _m], λ _iand e _icorresponding one by one.Finally, V is carried out to svd: V=Q Σ T ^*, wherein Q and T are orthonormal square formations, are called the left and right singular matrix of V, Q=E, T ^*be the conjugate transpose of T, Σ is diagonal matrix, Σ=Diag[λ ₁, λ ₂..., λ _m], meet λ _i=σ _i ², σ _ithe singular value of V, non-zero singular value σ wherein _inumber n be the number of basic pigment.

4. construct albefaction matrix: build albefaction matrix wherein ${\mathrm{\Δ}}_n^{-1}=\mathrm{Diag}[\frac{1}{{\mathrm{\σ}}_{m-n+1}},\frac{1}{{\mathrm{\σ}}_{m-n+2}},...,\frac{1}{{\mathrm{\σ}}_m}],$ Q ' non-zero column vector in Q forms.

5. generate albefaction K/S curve: vectorial Y (t) is carried out to albefaction, i.e. Z (t)=UY (t), Z (t) meets orthonomality matter, can carry out follow-up blind source separated.

Technical scheme of the present invention, it is separated that the signal after step (3) is processed albefaction carries out blind source, obtains a final n isolated component, specifically comprises the following steps: structure separation matrix W, calculating isolating construction, superposed average component.

The separation of blind source can, in the situation that the parameters such as information source and transmission channel are all unknown, according to the statistical property of input source signal, only recover each independent component in information source by observation signal.In the present invention, the ABSORPTION AND SCATTERING of using the separation of blind source to obtain basic pigment than K/S by the ABSORPTION AND SCATTERING of hybrid pigment compares K/S.Blind source separation algorithm is divided three classes: the blind source separated, based on the sparse property of source signal, blind source separated, based on second-order statistic, blind source based on independent component analysis is separated, wherein, use the most generally blind source separation based on independent component analysis, note by abridging as ICA.ICA algorithm comprises multiple, as the ICA algorithm based on maximum-likelihood criterion, ICA algorithm based on Minimum mutual information, ICA algorithm based on information maximization, fast ICA Algorithm algorithm (FastICA) etc.Wherein, fast ICA Algorithm algorithm has the features such as iteration stability, fast convergence and separation matrix orthogonality, and application is wider.

The present invention can adopt disclosed arbitrary blind source separate technology scheme in prior art, as fast ICA Algorithm algorithm.Fast ICA Algorithm algorithm comprises separation matrix initialization and two steps of refine separation matrix, main flow process is as follows: (1) separation matrix initialization: a non-Quadratic Function Optimization G (y) is arbitrarily set, obtains respectively its first order derivative g (y), second derivative g ' (y); Then, the row vector w that is m to each length _i, i=1...n carries out randomization, and normalization by column, by the w obtaining _ibe set to w _i(0); (2) refine separation matrix: establish i=1, k=0, according to w _i(k) iterative computation w _i(k+1): wherein, E[] represent to average, Z (t) is whitened signal, be 1 * p matrix, represent w _i(k) transposition, * represent dot product, two matrix element correspondences of identical scale multiply each other, or matrix all elements is with being multiplied by certain element, representing matrix multiplication; Simultaneously to the w obtaining _i(k+1) carry out Schimidt orthogonalization: $w_i(k+1)-\underset{j=1}{\overset{i-1}{\mathrm{\Σ}}}\mathrm{dot}(w_i(k+1),w_j)\text{\·\×}{w}_j\→w_i(k+1),$ Wherein, dot () represents inner product of vectors, * represent dot product, implication is the same, after Schimidt orthogonalization to w _i(k+1) be normalized: w _i(k+1)/|| w _i(k+1) || ₂→ w _i(k+1); By calculating w _iand w (k) _i(k+1) inner product judges w _i(k+1) whether restrain; If w _i(k+1) do not restrain, k=k+1, continues iterative computation; If w _i(k+1) convergence, by w _i(k+1) as w _i, i=i+1, when i≤n, carries out the operations such as initialization, iteration according to step continuation above; When i>n, calculate w=[w ₁, w ₂..., w _n] ^teach component absolute value sum, obtains vectorial sw=[sw ₁, sw ₂..., sw _n] ^t, wherein, sw _ii component w _iabsolute value sum; Vectorial sw ascending order is arranged, obtain new vectorial sw ', adjust the respective column in separation matrix w simultaneously, obtain new separation matrix w '=[w _i1, w _i2..., w _in] ^t, from w ', select front n row, form needed separation matrix W=[w ' _i1, w ' _i2..., w ' _iq] ^t.

After above-mentioned steps obtains separation matrix W, according to R (t)=WZ (t), just can isolate n isolated component R (t).But, because process through zero-mean in the albefaction stage, so also need separating resulting R (t) according to formula compensate.If superposed average component not in the present invention isolated component R (t) average obtaining is so 0; When the average of original mixed signal X (t) is non-vanishing, will produce inconsistency, so need to compensate by superposed average component.In addition,, because the result of blind source separation exists amplitude uncertain, separating resulting may be the product of original signal and certain coefficient, if this coefficient is negative value, separating resulting and original signal are anti-phase so, and the similarity of the two is also negative value, are unfavorable for the pigment coupling of step (4); Because ABSORPTION AND SCATTERING is more permanent than K/S is positive number, so the separating resulting obtaining after anti-phase must be negative.Therefore, if separating resulting is negative value, need to carry out anti-phase processing (in separating resulting, each element is multiplied by-1), making it permanent is positive number, thereby obtains a final n isolated component.

Because there is certain difference in the K/S that final n isolated component represents and actual basic pigment K/S, so also need to be in basic pigment K/S database, find the K/S that represents with n isolated component recently like n the K/S of pigment substantially, basic pigment used when these basic pigment are regarded as mixing.

Technical scheme of the present invention, the K/S that step (4) represents n isolated component mates with the K/S of known basic pigment in database, according to the maximum principle of similarity, determines n the basic pigment type that isolated component is corresponding.

Concrete, the K/S of known basic pigment is considered as to vectorial C, calculate isolated component F _i(t) with its included angle cosine, i=1 ..., n, as shown in Equation 1:

$\mathrm{CosA}=\frac{\⟨F_i\left(t\right),C\⟩}{\left|F_i\left(t\right)\right|\·\left|C\right|}---\left(1\right)$

In formula 1, included angle cosine is regarded as isolated component F _i(t) with the similarity of basic pigment, therefore can be using the basic pigment of similarity maximum as isolated component F _i(t) corresponding basic pigment.If the basic pigment K/S of the n kind obtaining is B _i, i=1 ..., n.

Technical scheme of the present invention, step (5) is according to the K/S of step (4) gained n basic pigment, and the m of a hybrid pigment ABSORPTION AND SCATTERING is than K/S, sets up Kubelka-Munk system of equations and solves, and draws the ratio of n basic pigment.

Specific as follows: according to Kubelka-Munk theorem, can to set up hybrid pigment K/S matrix X (t)=[X ₁(t), X ₂(t) ..., X _m(t)] ^twith basic pigment K/S matrix B=[B ₁, B ₂..., B _n] ^tbetween relation: X (t)=AB, wherein A means m * n matrix of pigment mixed relationship, the vectorial A that i row element forms in A _ithe ratio of required basic pigment while represent forming i kind hybrid pigment, i.e. capable, the j column element A of i _i,jthe ratio of the basic pigment of required j kind while representing to form i kind hybrid pigment.Therefore, solving equation group X (t)=AB just can obtain the ratio of basic pigment from matrix A.

Utilize the spectral measurement hybrid pigment component analyzing method that combine separated with blind source in the present invention, carry out hybrid pigment constituent analysis, there is good completeness, can not only obtain the kind of information of basic pigment, can also obtain the percent information of basic pigment in hybrid pigment, full process automatization simultaneously, has higher execution efficiency.

Accompanying drawing explanation

Fig. 1 is the spectral measurement hybrid pigment component analyzing method process flow diagram that combines separated with blind source;

Fig. 2-1, Fig. 2-2, Fig. 2-3 are respectively the spectral reflectance R curve of 3 kinds of basic pigment in Meng Saier full gloss colour system;

Fig. 3-1 is that the ABSORPTION AND SCATTERING of the basic pigment in Fig. 2-1 is than K/S curve;

Fig. 3-2 are that the ABSORPTION AND SCATTERING of the basic pigment in Fig. 2-2 is than K/S curve;

Fig. 3-3 are that the ABSORPTION AND SCATTERING of the basic pigment in Fig. 2-3 is than K/S curve;

Fig. 4-1, Fig. 4-2, Fig. 4-3, Fig. 4-4, Fig. 4-5, Fig. 4-6 are respectively the ABSORPTION AND SCATTERING of 6 kinds of hybrid pigments than K/S curve;

Fig. 5-1 is that the standardization ABSORPTION AND SCATTERING of Fig. 4-1 hybrid pigment is than K/S curve;

Fig. 5-2 are that the standardization ABSORPTION AND SCATTERING of Fig. 4-2 hybrid pigment is than K/S curve;

Fig. 5-3 are that the standardization ABSORPTION AND SCATTERING of Fig. 4-3 hybrid pigment is than K/S curve;

Fig. 5-4 are that the standardization ABSORPTION AND SCATTERING of Fig. 4-4 hybrid pigment is than K/S curve;

Fig. 5-5 are that the standardization ABSORPTION AND SCATTERING of Fig. 4-5 hybrid pigment is than K/S curve;

Fig. 5-6 are that the standardization ABSORPTION AND SCATTERING of Fig. 4-6 hybrid pigment is than K/S curve;

Fig. 6-1, Fig. 6-2, Fig. 6-3 are respectively the quadrature normalizing signal after albefaction is processed;

Fig. 7-1, Fig. 7-2, Fig. 7-3 are respectively the basic pigment ABSORPTION AND SCATTERING calculated after separating resulting than K/S curve;

Fig. 8-1 is that basic pigment ABSORPTION AND SCATTERING after the superposed average component of Fig. 7-1 is than K/S curve;

Fig. 8-2 are that basic pigment ABSORPTION AND SCATTERING after the superposed average component of Fig. 7-2 is than K/S curve;

Fig. 8-3 are that basic pigment ABSORPTION AND SCATTERING after the superposed average component of Fig. 7-3 is than K/S curve;

Fig. 8-4 are that basic pigment ABSORPTION AND SCATTERING after the anti-phase processing in Fig. 8-3 is than K/S curve;

Fig. 9-1 is that the ABSORPTION AND SCATTERING of the actual corresponding basic pigment in Fig. 8-1 is than K/S curve;

Fig. 9-2 are that the ABSORPTION AND SCATTERING of the actual corresponding basic pigment in Fig. 8-2 is than K/S curve;

Fig. 9-3 are that the ABSORPTION AND SCATTERING of the actual corresponding basic pigment in Fig. 8-4 is than K/S curve.

The horizontal ordinate of Fig. 2-1 of the present invention, Fig. 2-2, Fig. 2-3 represents wavelength, and unit is nanometer, and ordinate represents spectral reflectance R, and unit is 1; In institute's drawings attached except Fig. 1, Fig. 2-1, Fig. 2-2, Fig. 2-3, horizontal ordinate all represents wavelength, and unit is nanometer, and ordinate represents that ABSORPTION AND SCATTERING is than K/S, and unit is 1.

Embodiment

Following examples are used for illustrating the present invention, but are not used for limiting the scope of the invention.

Embodiment 1

The present embodiment is selected 3 kinds of colors that basic pigment is corresponding from Meng Saier full gloss colour system, according to different ratios, is mixed into 6 kinds, and according to Kubelka-Munk colour mixture formula, the ABSORPTION AND SCATTERING that obtains hybrid pigment compares K/S.It is separated with blind source that this tests comprehensive spectral representation, from the ABSORPTION AND SCATTERING of 6 kinds of hybrid pigments than the ABSORPTION AND SCATTERING that obtains 3 kinds of basic pigment K/S than K/S, then judge accordingly kind and the blending ratio of basic pigment.

1, structure hybrid pigment spectroscopic data

1.1 is K/S curve by basic pigment spectral reflectance R Curve transform

From Meng Saier colour system, extract 3 kinds of colour atla information, its wavelength coverage is 400-780nm, and the shape of 3 kinds of basic pigment spectral reflectance R curves is as shown in Fig. 2-1, Fig. 2-2, Fig. 2-3.

Because the spectral reflectance R of every kind of basic pigment is the sequence that some numerical value forms, thus to each element in this sequence according to formula K/S=(1-R) ²/ (2R) change, thereby obtain corresponding ABSORPTION AND SCATTERING, compare K/S.

The K/S curve of the basic pigment in Fig. 2-1 is as shown in Fig. 3-1; The K/S curve of the basic pigment in Fig. 2-2 is as shown in Fig. 3-2; The K/S curve of the basic pigment in Fig. 2-3 is as shown in Fig. 3-3.

The K/S curve of 1.2 structure hybrid pigments

According to ratio described in table 1,3 kinds of basic pigment are mixed into 6 kinds, wherein the blending ratio of 3 kinds of basic pigment of 3 of every row data representations.

Table 1 is constructed the ratio of 6 kinds of hybrid pigments by 3 kinds of basic pigment

From Kubelka-Munk colour mixture formula, the K/S curve of hybrid pigment is the linear combination of basic pigment K/S curve.Can obtain thus the K/S curve of 6 kinds of hybrid pigments, in table 1, the K/S curve of the 1st kind of hybrid pigment is as shown in Fig. 4-1; In table 1, the K/S curve of the 2nd kind of hybrid pigment is as shown in Fig. 4-2; In table 1, the K/S curve of the 3rd kind of hybrid pigment is as shown in Fig. 4-3; In table 1, the K/S curve of the 4th kind of hybrid pigment is as shown in Fig. 4-4; In table 1, the K/S curve of the 5th kind of hybrid pigment is as shown in Fig. 4-5; In table 1, the K/S curve of the 6th kind of hybrid pigment as Figure 4-Figure 6.

2, the ABSORPTION AND SCATTERING of 6 kinds of hybrid pigments is considered as to mixed signal than K/S, carries out albefaction processing, obtain orthonormal signal.

2.1 generate standardization K/S curve

The step that generates standardization K/S curve is: 6 ABSORPTION AND SCATTERING are considered as to 6 vectorial X than K/S _i(t), i=1 ..., 6, to every vectorial executable operations: wherein std[X _i(t)] be respectively X _i(t) average, standard deviation;

According to aforesaid operations step, respectively Fig. 4-1, Fig. 4-2, Fig. 4-3, Fig. 4-4, Fig. 4-5, every of Fig. 4-6 hybrid pigment K/S curve are carried out to normalizing operation, correspond respectively to Fig. 5-1, Fig. 5-2, Fig. 5-3, Fig. 5-4, Fig. 5-5, Fig. 5-6.

2.2 calculate covariance matrix

Covariance matrix in calculating chart 5 between different hybrid pigment K/S curves, specific as follows: by Y (t)=[Y ₁(t), Y ₂(t) ..., X ₆(t)] ^tin every group of signal be considered as a stochastic variable, calculate covariance each other, 6 * 6 matrix V that obtain, are called the covariance matrix of Y (t).

Result is as shown in table 2.

Covariance matrix V between the different hybrid pigment K/S of table 2 curve

?	1	2	3	4	5	6
							1	0.1226	0.0273	0.1431	0.0747	0.0110	0.0441
2	0.0273	0.0202	0.0686	0.0601	0.0113	0.0456
							3	0.1431	0.0686	0.2708	0.2077	0.0342	0.1497
4	0.0747	0.0601	0.2077	0.1860	0.0324	0.1416
							5	0.0110	0.0113	0.0342	0.0342	0.0068	0.0254
6	0.0441	0.0456	0.1497	0.1416	0.0254	0.1097

2.3 pairs of covariance matrixes carry out svd

First, the eigenwert of covariance matrix V shown in reckoner 2, and arrange according to ascending order, the eigenvalue λ obtaining is: λ ₁=λ ₂=λ ₃=0, λ ₄=0.0022, λ ₅=0.096, λ ₆=0.618; E is as shown in table 3 for eigenvalue λ characteristic of correspondence vector.

The eigenvalue λ of covariance matrix shown in table 3 table 2 characteristic of correspondence vector E

?	1	2	3	4	5	6
							1	0	0	0	0.2565	-0.7965	0.3156
2	0	0	0	0.5376	0.0914	0.1742
							3	0	0	0	-0.3601	-0.1978	0.6570
4	0	0	0	-0.1104	0.3713	0.5287
							5	0	0	0	0.6935	0.0906	0.0897
6	0	0	0	0.1497	0.4147	0.3883

Then, shown in his-and-hers watches 2, covariance matrix V carries out svd: V=Q Σ T ^*, wherein Q is the left singular matrix of V, proper vector E as shown in Table 2 forms; Σ consists of the eigenvalue λ of V, Σ=Diag[λ ₁..., λ ₆]=Diag[0,0,0,0.0022,0.096,0.618]; By singular value σ _iwith eigenvalue λ _ibe related to λ _i=σ _i ², the singular value of known V is σ ₁=σ ₂=σ ₃=0, σ ₄=0.0469, σ ₅=0.3098, σ ₆=0.7861.Because non-zero singular value σ _inumber n=3, so the number of basic pigment is 3.

2.4 structure albefaction matrixes

According to the result structure albefaction matrix of svd, specific as follows: to build albefaction matrix wherein n is the number of basic pigment, ${\mathrm{\Δ}}_n^{-1}=\mathrm{Diag}[\frac{1}{{\mathrm{\σ}}_4},\frac{1}{{\mathrm{\σ}}_5},\frac{1}{{\mathrm{\σ}}_6}]=\left[\mathrm{21.3220,3.2279,1.2721}\right],$ Q ' rear 3 row of non-zero in Q form.

Result is as shown in table 4.

Table 4 albefaction matrix

?	1	2	3	4	5	6
							1	5.4570	11.4358	-7.6599	-2.3496	14.7537	3.1856
2	-2.5713	0.2952	-0.6386	1.1985	0.2925	1.3388

3

0.4015

0.2216

0.8357

0.6725

0.1141

0.4939

2.5 generate albefaction K/S curve

Through albefaction operation, generating orthogonal normalization K/S curve (albefaction K/S curve), specific as follows: i.e. Z (t)=UY (t), Z (t) meets orthonomality matter, and result is as shown in Fig. 6-1, Fig. 6-2, Fig. 6-3.

3, hybrid pigment K/S curve is separated

3.1 separation matrix initialization

Structure separation matrix W=[w ₁, w ₂, w ₃] ^t, wherein, w _ithat length is 6 row vector.Main flow process is as follows: first, a non-Quadratic Function Optimization is set obtain respectively its first order derivative $g\left(y\right)=(1-y^2)\·e^{\frac{{-y}^2}{2}},$ Second derivative $g^{\′}\left(y\right)=(y^3-3y)\·e^{\frac{{-y}^2}{2}};$ Then, to w _i, i=1...3 carries out randomization, and normalization by column, and result is as shown in table 5.

The method that adopts randomization separating vector, obtains initially-separate matrix, as shown in table 5.

Table 5 initially-separate matrix

?	1	2	3	4	5	6
							1	0.4410	0.5558	0.1562	0.4609	0.4268	0.0959
2	0.4903	0.3848	0.3067	0.0753	0.2164	0.2851
							3	0.0687	0.0593	0.5370	0.4638	0.3568	0.6190

3.2 refine separation matrixes

If i=1, k=0, according to w _i(k) iterative computation w _i(k+1), simultaneously to the w obtaining _i(k+1) carry out Schimidt orthogonalization and normalization; If w _i(k+1) do not restrain, k=k+1, continues iterative computation; If w _i(k+1) convergence, by w _i(k+1) as w _i, i=i+1; When i≤3, according to step continuation above, carry out the operations such as initialization, iteration.When i>3, adjust matrix w=[w ₁, w ₂, w ₃] ^t, and therefrom select front 3 row formation refine separation matrix W, as shown in table 6.

Table 6 refine separation matrix

?	1	2	3
				1	-1.5552	-0.6693	1.0270

2	4.8168	11.2519	-7.6521
				3	-3.3061	-1.9645	0.4132

3.3 calculate separating resulting

After above-mentioned steps obtains separation matrix W, according to R (t)=WZ (t), just can obtain each isolated component R (t).

According to separation matrix, obtain isolated basic pigment K/S curve, as shown in Fig. 7-1, Fig. 7-2, Fig. 7-3.

3.4 superposed average components

Because process through zero-mean in the albefaction stage, so also need separating resulting R (t) to compensate, obtain final isolated component

Therefore, we,, by superposed average component, compensate separating resulting shown in Fig. 7-1, Fig. 7-2, Fig. 7-3 respectively, and after over-compensation, the K/S curve that isolated component represents corresponds respectively to Fig. 8-1, Fig. 8-2, Fig. 8-3.

Because isolated component is negative value in Fig. 8-3, so need to carry out anti-phase processing, the K/S curve after correction is as shown in Fig. 8-4.

4, basic pigment type coupling

Because there is certain difference in the K/S that isolated component represents and actual basic pigment K/S, so the hybrid matrix obtaining and actual hybrid matrix also there are differences.Therefore also need in basic pigment K/S database, find the K/S that represents with isolated component recently like basic pigment, basic pigment used when these basic pigment are considered as mixing.

According to the maximum principle of similarity, determine the basic pigment that each isolated component is corresponding.

The K/S of known basic pigment is considered as to vectorial C, calculates isolated component F _i(t) with its included angle cosine, i=1 ..., 3, as shown in Equation 1:

$\mathrm{CosA}=\frac{\⟨F_i\left(t\right),C\⟩}{\left|F_i\left(t\right)\right|\·\left|C\right|}---\left(1\right)$

In formula 1, included angle cosine is regarded as isolated component F _i(t) with the similarity of basic pigment, therefore can be using the basic pigment of similarity maximum as isolated component F _i(t) corresponding basic pigment.If 3 kinds of basic pigment K/S that obtain are B _i, i=1 ..., 3.

With the best basic pigment K/S curve of Fig. 8-1 matching degree as shown in Fig. 9-1, with the best basic pigment K/S curve of Fig. 8-2 matching degree as shown in Fig. 9-2, as shown in Fig. 9-3, corresponding similarity matrix is as shown in table 7 with the best basic pigment K/S curve of Fig. 8-4 matching degree.

The similarity matrix of table 7 isolated component and basic pigment K/S

?	1	2	3
				1	0.9969	-0.0443	-0.0641
2	0.0560	0.9819	0.1808
				3	0.0553	-0.1841	0.9814

5, basic pigment contribution calcutation

According to the K/S curve shown in Fig. 4-1～Fig. 4-6 and Fig. 9-1～Fig. 9-3, and Kubelka-Munk colour mixture formula, in the time of can obtaining mixing, the blending ratio of basic pigment, as shown in table 8.

Table 8 calculates the blending ratio of basic pigment while mixing

The calculating blending ratio matrix of the original mixed ratio matrix of comparison sheet 1 and table 8, can find out, the 1st, 2 row of the two are put upside down mutually.The reason that produces this phenomenon is that blind source separation algorithm has order uncertainty, and separation signal is not necessarily identical with original signal order.In the result of calculation of the present embodiment, when shown in Fig. 9-1, the ratio of basic pigment is mixed with step 1.2, the ratio of the basic pigment in Fig. 3-2 is corresponding, when shown in Fig. 9-2, the ratio of basic pigment is mixed with step 1.2, the ratio of the basic pigment in Fig. 3-1 is corresponding, the phenomenon that exists calculating blending ratio matrix and original mixed ratio matrix to put upside down mutually at the 1st, 2 row.

Although above the present invention is described in detail with a general description of the specific embodiments, on basis of the present invention, can make some modifications or improvements it, this will be apparent to those skilled in the art.Therefore, these modifications or improvements, all belong to the scope of protection of present invention without departing from theon the basis of the spirit of the present invention.

Claims (10)

1. the spectral measurement hybrid pigment component analyzing method that combine separated with blind source, is characterized in that, comprises the following steps:

(1) from m hybrid pigment of sufficient amount, obtain corresponding m spectral reflectance R;

(2) m spectral reflectance R is converted to a corresponding m ABSORPTION AND SCATTERING than K/S, and is considered as mixed signal, carry out albefaction processing, obtain orthonormal signal;

(3) signal after albefaction processing is carried out to the separation of blind source, obtain a final n isolated component;

(4) K/S n isolated component being represented mates with the K/S of known basic pigment in database, according to the maximum principle of similarity, determines n the basic pigment type that isolated component is corresponding;

(5) according to the K/S of step (4) gained n basic pigment, and the m of a hybrid pigment ABSORPTION AND SCATTERING is than K/S, according to Kubelka-Munk theorem, sets up system of equations and solves, and draws the ratio of n basic pigment.

2. hybrid pigment component analyzing method according to claim 1, is characterized in that: the described m of step (1) hybrid pigment forms by identical several basic pigment, but the ratio of basic pigment is different in each hybrid pigment; The step of obtaining corresponding m spectral reflectance R from m hybrid pigment of sufficient amount is as follows: if obtain m when initial ₁individual spectral reflectance R, the blind source of step (3) lock out operation has solution, now m=m ₁; If obtain m when initial ₂individual spectral reflectance R, the blind source of step (3) lock out operation, without solution, needs to increase the number of the spectral reflectance R obtaining, until the blind source of step (3) lock out operation has solution.

3. hybrid pigment component analyzing method according to claim 1, is characterized in that: the spectral reflectance R in step (1) is by transition matrix H and the digital response g of multi-optical spectrum imaging system, according to formula R=H ⁺g obtains, H ⁺the generalized inverse matrix that represents H.

4. hybrid pigment component analyzing method according to claim 1, is characterized in that: step (2) spectral reflectance R is converted to ABSORPTION AND SCATTERING and than the conversion regime of K/S is: K/S=(1-R) ²/ (2R).

5. hybrid pigment component analyzing method according to claim 1, is characterized in that: the described albefaction processing of step (2) comprises generation standardization K/S curve, calculates covariance matrix, covariance matrix is carried out svd, structure albefaction matrix, generates albefaction K/S curve.

6. hybrid pigment component analyzing method according to claim 5, is characterized in that: step (2) albefaction is processed and comprised the following steps:

(1) generate standardization K/S curve: the K/S of m hybrid pigment is considered as to m bar vector X _i(t), i=1 ..., m, to every vectorial executable operations: wherein std[X _i(t)] be respectively X _i(t) average, standard deviation, obtain Y _i(t);

(2) calculate covariance matrix: by Y (t)=[Y ₁(t), Y ₂(t) ..., Y _m(t)] ^tin every group of signal be considered as a stochastic variable, calculate covariance each other, the m * m matrix V obtaining;

(3) covariance matrix is carried out to svd: the eigenvalue λ of calculating covariance matrix V '=[λ ' ₁, λ ' ₂..., λ ' _m] and proper vector E '=[e ' ₁, e ' ₂..., e ' _m], λ ' _iand e ' _icorresponding one by one; Then, to λ ' ascending sort, obtain orderly eigenvalue λ=[λ ₁, λ ₂..., λ _m], meet 0≤λ ₁≤ λ ₂≤ ... ≤ λ _m; According to corresponding relation, adjust the position of each component of proper vector E ' simultaneously, obtain character pair vector E=[e ₁, e ₂..., e _m], λ _iand e _icorresponding one by one; Finally, V is carried out to svd: V=Q Σ T ^*, wherein Q and T are orthonormal square formations, are called the left and right singular matrix of V, Q=E, T ^*be the conjugate transpose of T, Σ is diagonal matrix, Σ=Diag[λ ₁, λ ₂..., λ _m], meet λ _i=σ _i ², σ _ithe singular value of V, non-zero singular value σ wherein _inumber n be the number of basic pigment; By svd, obtain Q and σ _i;

(4) structure albefaction matrix: build albefaction matrix wherein ${\mathrm{\Δ}}_n^{-1}=\mathrm{Diag}[\frac{1}{{\mathrm{\σ}}_{m-n+1}},\frac{1}{{\mathrm{\σ}}_{m-n+2}},...,\frac{1}{{\mathrm{\σ}}_m}],$ Q ' non-zero column vector in Q forms;

(5) generate albefaction K/S curve: vectorial Y (t) is carried out to albefaction, Z (t)=UY (t), Z (t) meets orthonomality matter, can carry out follow-up blind source separation.

7. hybrid pigment component analyzing method according to claim 6, is characterized in that: the signal after step (3) is processed albefaction carries out the separation of blind source and comprises structure separation matrix W, calculates separating resulting, superposed average component.

8. hybrid pigment component analyzing method according to claim 7, is characterized in that: step (3) comprises the following steps:

(1) structure separation matrix W;

(2) calculate separating resulting: according to R (t)=WZ (t), obtain each isolated component R (t);

(3) superposed average component: to separating resulting R (t) according to formula compensate, and the isolated component that is negative value by signal value carries out anti-phase correction, thereby obtain final isolated component F (t).

9. hybrid pigment component analyzing method according to claim 8, is characterized in that: the process of step (4) is as follows: the K/S of known basic pigment is considered as to vectorial C, adopts formula i=1 ..., n calculates final isolated component F _i(t), with the similarity of vectorial C, according to the maximum principle of similarity, determine final isolated component F _i(t) corresponding n basic pigment type.

10. hybrid pigment component analyzing method according to claim 9, it is characterized in that: the detailed process of step (5) is as follows: according to the K/S of step (4) gained n basic pigment, and the m of a hybrid pigment ABSORPTION AND SCATTERING compares K/S, according to Kubelka-Munk theorem, set up m hybrid pigment K/S matrix X (t)=[X ₁(t), X ₂(t) ..., X _m(t)] ^twith n basic pigment K/S matrix B=[B ₁, B ₂..., B _n] ^tbetween relation: X (t)=AB, by solving this system of equations, obtains representing m * n matrix A of basic pigment proportionate relationship when pigment mixes.