CN110208846A - A kind of compressed sensing based Soft X-ray spectrum restoring method - Google Patents
A kind of compressed sensing based Soft X-ray spectrum restoring method Download PDFInfo
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Abstract
The present invention relates to a kind of compressed sensing based Soft X-ray spectrum restoring method, the method uses the rarefaction representation characteristic of orthogonal basis, carry out the rarefaction representation of soft X-ray spectral signal, and construct the observing matrix of soft X-ray spectrum, it is observed using the original soft X-ray spectral signal that observing matrix obtains detection, signal after being changed, the sparse coefficient of soft X-ray spectrum is solved further according to the signal after transformation, then by the rarefaction representation of the sparse coefficient and soft X-ray spectral signal that solve, it is back-calculated to obtain soft X-ray reduction power spectrum.Method of the invention can restore the Soft X-ray spectrum under limited detection channels, and guarantee spectrum unscrambling precision.
Description
Technical field
The present invention relates to spectrum reduction technique fields, restore more particularly to a kind of compressed sensing based Soft X-ray spectrum
Method.
Background technique
[experiment of ICF laser target shooting]
Inertial confinement fusion experiment (Inertial Confinement Fusion, ICF) has become the mankind and explores new energy
One of the important laboratory facilities in source.On earth realize controlled thermonuclear fusion reaction, it would be possible to for the mankind provide it is abundant, economical,
The energy of safety.Inertial confinement fusion (ICF) is one of the approach realizing controlled thermonuclear fusion and getting a good chance of, it is to pass through implosion
Fusionable material is compressed, high-temperature high-density is reached, realizes thermonuclear ignition under inertial confinement in implosion motion process
And burning, thus the method for obtaining fusion energy.No matter the development of ICF area research work is to national economy, Military Application, still
Important and special meaning is suffered from for basic research exploration.
Laser-produced fusion is to use laser as driving source.In ICF experiment, powerful pulse laser or charged particle beam are black
It is intracavitary to form clean, uniform X-radiation field, recycle X-ray radiation ablation to be placed in the pellet at target chamber center, pellet surface
Plasma spraying kickback pressure makes it be compressed to high temperature, high density to implosion, so that controlled nuclear reaction fusion occur, release is a large amount of
Energy.
To the purpose of laser fusion diagnosis be by plasma radiate and fusion reaction product feature measurement come
The state and behavior for disclosing target plasma, gain more insight into laser energy mechanism of absorption and regular characteristic, be laser with
The Best Coupling design of target provides foundation.Laser plasma emits stronger X-ray radiation, and power spectrum focuses primarily upon soft X-ray
Energy area (0.1~1.5KeV), its gross energy, characteristics of energy spectrum, launch time process and spatial distribution are all theoretical and experiment institute
The master data being extremely concerned about, wherein containing the bulk information that plasma participates in implosion process, especially Soft X-ray spectrum is straight
It connects and is relevant to X-ray conversion ratio and radiation temperature the two basic concepts.By the spectrum analysis to grenz ray, can also obtain
To parameters such as the transfer efficiency of X-ray, albedo, radiation temperature and the total flux of X-ray.Therefore the measurement of soft X-ray is
Vital content in ICF diagnosis.
[soft-X-ray laser]
Soft-X-ray laser is that the diagnosis of measurement soft x-ray laser probe bea, equivalent point temperature and radiant flux time course is set
It is standby, it because the energy range of its response covering is wider, and overlaps each other, while being multichannel spectrometer again, spectrum reduction exists certain
Difficulty.And with the increase of target practice laser beam, need the response of more detection channels to restore soft X-ray, but compose
The installation site of instrument is limited, towards interfering with each other, causes soft X-ray reduction inaccurate.If effective spectrum unscrambling can be proposed
Method carries out precise restoration to soft X-ray, by analyzing spectral information, it can be helped to reduce experimental cost, improve experiment effect
Rate.So solving the problems, such as that soft X-ray reduction is to be worth further investigation under limited detection channels.
The spectral pattern reduction of soft X-ray is the problem of always existing in X-ray spectrum research.In order to restore Soft X-ray spectrum, need
Using the Direction response and measurement voltage value of detection channels, calculated by Converse solved method.Currently, there is many methods can be with
For solving this inverse problem, such as following several:
Maximum entropy alternative manner needs artificially to apply a series of physical constraint to solve indirect problem；
It is composed, is suitble to specific using the random devices derived for solving such as Monte Carlo method, genetic algorithm, neural network
Spectral pattern in carry out spectral pattern reduction；
Processing is weighted to each spectrometer response section using Fehl method, to restore radiation flux, however, after weighting
Response be not it is smooth, spectral pattern reduction in can introduce error；
Basic function solution spectrometry chooses basic function appropriate according to the general configuration of spectral pattern, carrys out linear expression source spectrum, with base letter
Several linear combination indicates reduction spectrum, and linear approximation indicates spectral pattern, and certainly with certain error, this method mainly has two
Kind technology, first is that selecting reasonable basic function to reconstruct spectrum, receptance function, piecewise B-Spline function, Gaussian peak function etc. are spectrums
Common basic function in reduction experiment can select base sub in advance using these basic functions in certain rule；Second is that choosing
Suitable calculation method is selected to determine the coefficient of basic function, currently used calculation method has: iteration, pattra leaves based on maximum entropy
This theorem, singular value decomposition (SVD), least square (LS) etc..
Existing power spectrum restoring method is chiefly used in the energy spectrum reconstruction of redundant measurement data, visits used in soft-X-ray laser
It is more to survey channel, so that it may more measured values are obtained, power spectrum reduction may be more accurate, when its measurement data is less,
Energy spectrum reconstruction just will appear distortion phenomenon.However, being continuously increased with laser beam, the photon energy range of soft X-ray becomes larger, benefit
Obtaining more detection channels data with soft-X-ray laser becomes particularly difficult.This is because each detection channels are occupied
Volume is big, and towards interfering with each other, these practical factors cause to utilize increase detection channels power spectrum for installation site and target center opening
The measured value of response is unpractical to realize high-precision Soft X-ray spectrum reduction.
In addition, also radiant flux reduction can be carried out using non-Spectra Unfolding Methods, radiant flux is product of the radiant-energy spectrum to the time
Point, reflect radiation temperature, specific method is to establish equivalent flat response equation, then be weighted place to the channel response value of spectrometer
Reason, smooth spectral pattern.Radiation temperature is also effective information to a certain extent, but most important or radiant-energy spectrum distribution,
So spectrum unscrambling is even more important.
Generally speaking, in the prior art, in the case where understanding substantially spectral pattern, settable detection of energy spectrometer appropriate is logical
There are corresponding different requirement, the detection channels that some methods use in road also according to the difference of method in the quantity of detection channels
Number is more, and spectral pattern reduction is more complete, on the contrary, reducing the port number of spectrometer, results in reduction precision dramatic decrease, causes to compose
Type reduction distortion.For the soft-X-ray laser for laser fusion diagnosis, with the increase of spectrometer detection energy, need
More detection channels restore spectral pattern, but structure is complicated for spectrometer, and the installation site for diagnosing hole is limited, and the direction in each hole
Can have interference, cause spectral pattern reduction to be affected, be embodied in that spectrum unscrambling precision is not high enough, simultaneously because spectral pattern not really
It is fixed, it has higher requirements to the structure setting of soft-X-ray laser, difficulty of test is big, and testing cost is high, such as needs that replacement is taken to visit
It surveys channel, without purpose increase the measures such as response channel number.
Therefore, it is necessary to find the new Spectra Unfolding Methods of one kind to restore the Soft X-ray spectrum under limited detection channels, and guarantee
Spectrum unscrambling precision.
Summary of the invention
Based on this, the object of the present invention is to provide a kind of compressed sensing based Soft X-ray spectrum restoring method, no
Increase detection channels number, while guaranteeing the precision of spectrum unscrambling as far as possible, from the angle for optimizing spectrometer response, reduces the not true of spectrum reduction
It is qualitative, provide the evaluation criterion and design optimization method of Spectrometer performance, it might even be possible to the case where not sacrificing spectrum unscrambling precision, reduce
Detection channels number reduces the interference of each interchannel, saves the installation space of spectrometer, and for the installations of other detectors, provide can
Can, optimize the structure design of spectrometer, reduces the experimental cost that soft-X-ray laser restores spectral pattern.
The technical solution adopted by the present invention is as follows:
A kind of compressed sensing based Soft X-ray spectrum restoring method, the method use the rarefaction representation characteristic of orthogonal basis,
The rarefaction representation of soft X-ray spectral signal is carried out, and constructs the observing matrix of soft X-ray spectrum, detection is obtained using observing matrix
Original soft X-ray spectral signal be observed, the signal after being changed solves soft X-ray spectrum further according to the signal after transformation
Sparse coefficient be back-calculated to obtain soft X-ray reduction then by the rarefaction representation of sparse coefficient and soft X-ray spectral signal solved
Power spectrum.
The concept of compressed sensing: basic thought is if a signal has compressibility or under some orthogonal transformation
It is sparse, then with sparse transformation incoherent observing matrix then signal can be projected to low-dimensional from higher-dimension by one
Restore the signal by a restructing algorithm.Thus the sample rate of signal depends no longer on the bandwidth of signal, and depends on letter
Number structure.It according to compressive sensing theory, the sampling of signal and compression while carrying out, and can greatly reduce sensor number
Mesh.In theory, any signal is all compressible or sparse in the case where some converts basic function, as long as therefore finding phase
The basic function answered, so that it may which compression sampling is carried out to the signal.The core of compressive sensing theory mainly include sparse signal representation,
Three aspects of design and restructing algorithm of calculation matrix.
The method of compressed sensing carrys out Accurate Reconstruction signal, may be used also when necessary in short, least sampling number can be used
Accurately to predict.Such as: to the image of nuclear magnetic resonance, normal sample needs to indicate signal with 6000 discontinuity coefficients,
But using the method for compressed sensing, perhaps only need 1800 discontinuous coefficients, so that it may very close true picture, knot
Fruit is that this method can obtain a very close result with three times or even four times of pendulous frequency is less than.
It is based on compressive sensing theory, Soft X-ray spectrum restoring method of the invention, relative to existing method, spectrum unscrambling as a result,
Speed is fast, and the cost needed is lower, optimizes to spectrometer, keeps spectrometer structure more simple, the essence of spectral pattern reduction
Du Genggao solves the problems, such as the spectrum unscrambling in soft-X-ray laser under the arrangement of the limited position XRD, and it is logical that less sampling can be used
Road can be realized as high-precision spectrum unscrambling, can according to the variation of sampling channel it is adaptive select base in wider base dictionary
Atom carries out spectral pattern reconstruct, solves in previous methods, sub according to the artificial experiential determining base of sampling channel, and base
Atom range of choice is small, in the insufficient situation of ampling channel number, is easy to appear and owes the problem of approaching.
Specifically, the compressed sensing based Soft X-ray spectrum restoring method includes: step S1: obtaining measurement voltage value
D, sensing matrix Ψ, step S5 building observing matrix M, step S4: step S2: building sparse basis dictionary Φ, step S3: are calculated:
It calculates sparse coefficient θ and step S6: calculating soft X-ray reduction power spectrum.
Further, the step S1 is as follows:
The expression formula of the voltage signal in the i-th channel of the oscillograph recording of soft-X-ray laser is write:
Di=∫ S (E) Rt(E) dE, t=1 ..., m (1)
Wherein, E is the photon energy gradually increased, and m is the quantity of detection channels, Rt(E) it is rung for the energy spectral term in the channel t
Function is answered, S (E) is spectral distribution；
Formula (1) is unfolded to solve as the following formula:
Wherein, c is photon energy E increased step-length every time, EqRepresent q photon energies；
By above formula (2), the oscillograph value in all channels is write out:
Wherein, c is constant coefficient, and D is the voltage value that all oscillographs are read, and
If S is about S (Eq) matrix andIt lets R be about Rt(Eq) matrix andThen formula (3) changes
It is written as:
D=cSR (4).
Further, the step S2 is as follows:
With the rarefaction representation characteristic of orthogonal basis, the rarefaction representation of soft X-ray spectral signal, the expression formula conversion of S (E) are carried out
Are as follows:
Wherein, E=[E1,E2,...,ENe]TFor photon energy discrete value, Ne is the discrete number of photon energy,For orthogonal basis function,For sparse coefficient, Nb represents the sub- number of base；
Enable θ=[θ1,θ2,...,θNb]TFor coefficient vector,For orthogonal basis dictionary, then formula (5) changes
It is written as:
Further, in the step S2, Legendre orthogonal basis rarefaction representation spectral signal is selected, just by Legendre
It hands over base to substitute into formula (5), then obtains:
According to sampled value, sparse basis dictionary Φ is indicated are as follows:
Alternatively, it is also possible to other orthogonal basis functions, such as Chebyshev's basic function etc..
Further, the step S3 is as follows:
The observing matrix of soft X-ray spectrum is constructed using random matrixObserving matrix M is by detecting
The response in channel is constituted, and response is determined by the structural parameters of detection channels, and observing matrix M is indicated are as follows:
Further, the step S4 is as follows:
It is observed using the original soft X-ray spectral signal that observing matrix M obtains detection, the voltage letter after being changed
Number, which is indicated with equation are as follows:
Wherein,For sensing matrix, by observing matrixWith sparse basis dictionaryIt is multiplied
It obtains.
Further, the step S5 is as follows:
Formula (10) are converted are as follows:
Sparse coefficient θ in solution formula (11)；
The step S6 are as follows: sparse coefficient θ is substituted into formula (5), soft X-ray reduction spectral distribution S (E) is calculated.
Further, in step S5, sparse system is solved using greedy algorithm, Bayesian Classification Arithmetic or convex relaxing techniques
Number θ.
Further, in step S5, sparse coefficient θ is solved using the Lasso algorithm in convex relaxing techniques.
Compared with the existing technology, compressed sensing based Soft X-ray spectrum restoring method of the invention has below beneficial to effect
Fruit:
1) the spectrum unscrambling process of soft-X-ray laser is become into the mathematical problem based on compressive sensing theory, leads to too small amount of spy
Measured value can precise restoration spectral pattern；
2) it by the thought of rarefaction representation characteristic and norm with orthogonal basis, basis can be adopted from biggish base dictionary
Adaptive base of selecting of sample value is reconstructed, and with the change of spectrometer port number, adaptive solves radiant-energy spectrum；
3) and by this method a small amount of sampling channel can be used, restores the spectral pattern for meeting precision, reduces spectrometer
On design difficulty；
4) the method provides theory support for the survey meter SRD arrangement of the following confined space.
In order to better understand and implement, the invention will now be described in detail with reference to the accompanying drawings.
Detailed description of the invention
Fig. 1 is the flow diagram of compressed sensing based Soft X-ray spectrum restoring method of the invention.
Specific embodiment
It referring to Figure 1, is the flow diagram of compressed sensing based Soft X-ray spectrum restoring method of the invention.
The compressed sensing based Soft X-ray spectrum restoring method carries out soft X with the rarefaction representation characteristic of orthogonal basis
The rarefaction representation of light spectral signal, and the observing matrix of soft X-ray spectrum is constructed, detection is obtained using observing matrix original soft
X-ray spectral signal is observed, the signal after being changed, and the sparse system of soft X-ray spectrum is solved further according to the signal after transformation
Number is back-calculated to obtain soft X-ray reduction power spectrum then by the rarefaction representation of the sparse coefficient and soft X-ray spectral signal that solve.
Specifically, S1~S6 is carried out according to the following steps:
Step S1: measurement voltage value D is obtained
The expression formula of the voltage signal in the kth channel of the oscillograph recording of soft-X-ray laser is write:
Di=∫ S (E) Rt(E) dE, t=1 ..., m (1)
Wherein, N is the quantity of detection channels, and E is the photon energy gradually increased, and m is the quantity of detection channels, Rt(E)
For the energy spectral term receptance function in the channel t, wherein including the geometrical factors such as detector position and solid angle, S (E) is power spectrum point
Cloth, this formula belong to first kind Fredholm Integral Problem；
This Integral Problem can be unfolded to solve:
Wherein, c is photon energy E increased step-length every time, and EqQ photon energies are represented, in certain energy spectrum,
As q=1, E1For initial photon energy, as q=p, EpFor the photon energy of last position, such as work as E1=50eV, Ep=
6000eV, c=11.98352, then p=500.
By above formula (2), the oscillograph value in all channels can be write out
And formula (3) can also write the form of matrix by transformation:
D=cSR (4)
Wherein, c is constant coefficient, and S is about S (Eq), size beMatrix, R be about Rt(Eq), size
ForMatrix, then D is the voltage value that all oscillographs are read, and size is
This process is the process of soft-X-ray laser Forward simulation, and in order to obtain the reduction spectral pattern of soft X-ray we to do
Be reverse spectrum unscrambling, the voltage value provided by instrument solves relatively unknown S (E), i.e., reduction spectral distribution, by with
The comparison of power spectrum is actually entered, to provide the standard of spectrometer design, to carry out more optimized design to soft X-ray instrument.In the past,
Generally acknowledged method is the method using basic function.The method of basic function thinks, under the premise of understanding source spectrum feature, Ke Yishi
When choosing basic function, source spectrum is indicated into thus bring error, mathematics with ε with the linear combination of Nb basic function come approximate
Expression formula are as follows:
And S2~S6 solves S (E) value to the present invention as follows, and Spectra Unfolding Methods are become to the sub-sampling of compressed sensing, it is real
It is existing it is more efficient, accurately restore spectral distribution.
Step S2: building sparse basis dictionary Φ
With the rarefaction representation characteristic of orthogonal basis, the expression formula of S (E) can be converted are as follows:
Its matrix expression are as follows:
Wherein, E=[E1,E2,...,ENe]TFor photon energy discrete value, Ne is the discrete number of photon energy.For sparse coefficient, θ=[θ1,θ2,...,θNb]TFor coefficient vector,For orthogonal basis function,Orthogonal basis dictionary, Nb represent the sub- number of base, and value can control the size of base dictionary, rule of thumb
And pertinent literature, work as Nb=6m, i.e. the sub- number of base should be 6 times of number of samples.It means that when spectral distribution S meet it is dilute
When dredging characteristic, base is picked out by sparse coefficient, can provide complete expression.
As further preferred, using Legendre orthogonal basis rarefaction representation spectral signal, because of its expression formula curve light
The sliding spectral characteristic for meeting soft X-ray, and its expansion order is higher, is conducive to improve soft X-ray spectrum reduction precision, and
Legendre multinomial on its interval of definition [- 1,1] aboutNorm is orthogonal, and the polynomial construction of Ledendre is more
Simply and it is easy to calculate.
Legendre polynomial function expression formula is obtained by circular in definition: setting L0(x)=1, L1(x)=x then (n+1) Ln+1
(x)=(2n+1) Ln(x)-nLn-1(x), n=1,2 ... Nb (6'),
So Legendre orthogonal basis is substituted into formula (5), can be obtained:
According to sampled value, sparse basis dictionaryIt can indicate are as follows:
Step S3: building observing matrix M
Construct the observing matrix of soft X-ray spectrum, observing matrixBy the response structure of detection channels
At, response is determined by detection channels structural parameters, optional structural parameters be the material of filter disc, filter disc thickness, whether make
With plane mirror, solid angle etc..These parameters are limited to manufacture and experiment condition, have determining specification, such as the material of filter disc has
Totally 9 kinds of Al, B, C, Ti, Cr, Fe, Ni, Cu and Zn.Other parameters are also identical, can obtain limited structural parameters according to specification
All combinations are numbered in combination, a shared Z kind combination, however the installation site of soft-X-ray laser is limited, can only be from Z kind
Combination kind is chosen m detection channels and is installed.There are many kinds of the methods of selection, can in order to reduce the cross correlation of sampled point
To construct calculation matrix using random matrix, label can be used to find out the combination of corresponding structural parameters, each group of response by
Ne groups of samples is at the observing matrix for constructing completion can indicate are as follows:
Step S4: sensing matrix Ψ is calculated
The voltage signal after available transformation is observed to original spectrum signal by observing matrix, this process can
To be indicated with equation are as follows:
Wherein,It is sensing matrix, by observing matrixWith base dictionaryMultiplication obtains.
Step S5: sparse coefficient θ is calculated
By solve sparse coefficient θ, can reverse go out restore spectrum-type.Solution formula (10) is a underdetermined equation, is had not
It determines solution, can also write:
Formula (11) is a np hard problem (Non-Deterministic Polynomial), there is the uncertain solution of multiple groups, can
To pass through greedy algorithm (Greedy Algorithm), Bayes's classification (Bayesian Category) and convex relaxing techniques
(Convex Relaxation Technique) is solved.Greedy algorithm is effective, but in the presence of noise, calculates inaccuracy,
Such as match tracing (Matching Pursuit, MP), orthogonal matching pursuit (Orthogonal Matching Pursuit,
OMP) etc..Bayes's classification, can be related with EQUILIBRIUM CALCULATION FOR PROCESS time and reduction error, such as Bayes when handling extensive problem
Vector machine (BCS-RVM).Convex relaxing techniques, such as base tracking (Basis Pursuit, BP) and Lasso return (Lasso
Regression), coefficient convergence and base son select in have compared with outstanding performance, even if in the case where noise is added,
Preferable reduction precision can be obtained.
By Experimental comparison and theory analysis, more preferably, the Lasso algorithm in convex relaxation method is selected to solve sparse coefficient
θ, this algorithm carries in tool box in MATlab to be provided.
Step S6: soft X-ray reduction power spectrum is calculated
Sparse coefficient θ is substituted into formula (5), soft X-ray reduction spectral distribution S (E) is calculated.
The reduction error amount for showing Soft X-ray spectrum restoring method proposed by the present invention by experiment is 0.31%, compared to existing
Methodical reduction error is 3.5%, and reduction precision has a big promotion.Also, for needing 14 groups of detections in the past
The spectral pattern that channel could restore only needs 8 groups of detection channels with the method for the present invention, and identical reduction precision can be obtained, and is soft X
The installation arrangement of luminous energy spectrometer saves 42.86% space.
The benefit of the method for the invention spectrum unscrambling is, it is possible to reduce the port number of spectrometer is arranged, i.e. reduction sampling number, uses
Minimum cost goes to help to design soft-X-ray laser, while meeting the accuracy standard of spectrometer again.
The embodiments described above only express several embodiments of the present invention, and the description thereof is more specific and detailed, but simultaneously
It cannot therefore be construed as limiting the scope of the patent.It should be pointed out that coming for those of ordinary skill in the art
It says, without departing from the inventive concept of the premise, various modifications and improvements can be made, these belong to protection of the invention
Range.
Claims (10)
1. a kind of compressed sensing based Soft X-ray spectrum restoring method, it is characterised in that: special with the rarefaction representation of orthogonal basis
Property, carries out the rarefaction representation of soft X-ray spectral signal, and construct the observing matrix of soft X-ray spectrum, using observing matrix to detecting
To original soft X-ray spectral signal be observed, the signal after being changed solves soft X-ray light further according to the signal after transformation
The sparse coefficient of spectrum is back-calculated to obtain soft X-ray also then by the rarefaction representation of the sparse coefficient and soft X-ray spectral signal that solve
Proper energy spectrum.
2. compressed sensing based Soft X-ray spectrum restoring method according to claim 1, characterized by comprising:
Step S1: measurement voltage value D, step S2: building sparse basis dictionary Φ, step S3: building observing matrix M, step are obtained
S4: sensing matrix Ψ, step S5 are calculated: calculates sparse coefficient θ and step S6: calculating soft X-ray reduction power spectrum.
3. compressed sensing based Soft X-ray spectrum restoring method according to claim 2, it is characterised in that: the step
S1 is as follows:
The expression formula of the voltage signal in the i-th channel of the oscillograph recording of soft-X-ray laser is write:
Di=∫ S (E) Rt(E) dE, t=1 ..., m (1)
Wherein, E is the photon energy gradually increased, and m is the quantity of detection channels, Rt(E) letter is responded for the energy spectral term in the channel t
Number, S (E) are spectral distribution；
Formula (1) is unfolded to solve as the following formula:
Wherein, c is photon energy E increased step-length every time, EqRepresent q photon energies；
By above formula (2), the oscillograph value in all channels is write out:
Wherein, c is constant coefficient, and D is the voltage value that all oscillographs are read, and
If S is about S (Eq) matrix andIt lets R be about Rt(Eq) matrix andThen formula (3) is rewritten
Are as follows:
D=cSR (4).
4. compressed sensing based Soft X-ray spectrum restoring method according to claim 3, it is characterised in that: the step
S2 is as follows:
With the rarefaction representation characteristic of orthogonal basis, the rarefaction representation of soft X-ray spectral signal, the expression formula conversion of S (E) are carried out are as follows:
Wherein, E=[E1,E2,...,ENe]TFor photon energy discrete value, Ne is the discrete number of photon energy,For orthogonal basis function, { θi}I=1,2 ..., NbFor sparse coefficient, Nb represents the sub- number of base；
Enable θ=[θ1,θ2,...,θNb]TFor coefficient vector,For orthogonal basis dictionary, then formula (5) is rewritten are as follows:
5. compressed sensing based Soft X-ray spectrum restoring method according to claim 4, it is characterised in that: the step
In S2, Legendre orthogonal basis rarefaction representation spectral signal is selected, Legendre orthogonal basis is substituted into formula (5), then is obtained:
According to sampled value, sparse basis dictionary Φ is indicated are as follows:
6. compressed sensing based Soft X-ray spectrum restoring method according to claim 5, it is characterised in that: the step
S3 is as follows:
The observing matrix of soft X-ray spectrum is constructed using random matrixObserving matrix M is by detection channels
Response constitute, and response is determined by the structural parameters of detection channels, observing matrix M expression are as follows:
7. compressed sensing based Soft X-ray spectrum restoring method according to claim 6, it is characterised in that: the step
S4 is as follows:
It is observed using the original soft X-ray spectral signal that observing matrix M obtains detection, the voltage signal after being changed,
The process is indicated with equation are as follows:
Wherein,For sensing matrix, by observing matrixWith sparse basis dictionaryMultiplication obtains.
8. compressed sensing based Soft X-ray spectrum restoring method according to claim 7, it is characterised in that: the step
S5 is as follows:
Formula (10) are converted are as follows:
Sparse coefficient θ in solution formula (11)；
The step S6 are as follows: sparse coefficient θ is substituted into formula (5), soft X-ray reduction spectral distribution S (E) is calculated.
9. compressed sensing based Soft X-ray spectrum restoring method according to claim 8, it is characterised in that: in step S5,
Sparse coefficient θ is solved using greedy algorithm, Bayesian Classification Arithmetic or convex relaxing techniques.
10. compressed sensing based Soft X-ray spectrum restoring method according to claim 9, it is characterised in that: step S5
In, sparse coefficient θ is solved using the Lasso algorithm in convex relaxing techniques.
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Application publication date: 20190906 |