CN103886639B - A kind of construction method of Pixel Unmixing Models based on anti-noise - Google Patents
A kind of construction method of Pixel Unmixing Models based on anti-noise Download PDFInfo
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Abstract
The invention discloses the construction method of a kind of Pixel Unmixing Models based on anti-noise, including providing anti-noise model:
Description
[technical field]
The present invention relates to the technical field of Pixel Unmixing Models, be based particularly on the Pixel Unmixing Models of anti-noise
The technical field of construction method.
[background technology]
The generation process of high spectrum image is a complicated physical action process, physical action process occur light source,
Between material surface and air interference etc..In thus complicated image creation process, creating substantial amounts of noise, these noises can
Additive noise and multiplicative noise can be included, and owing to including more than one noise, so being also possible to produce mixed noise.The highest
The generation of spectroscopic data is influenced by factors. and noise type is complex, thus during high-spectral data is analyzed,
It is analyzed noise behavior seeming particularly significant.Research show explain depend on during some phenomenons multiplicative noise and
Interaction between additive noise, as when being explained as follows phenomenon: accidental resonance, superconduct at node etc. in phase transformation and transport
Deng.There is most of high spectrum image parser because good estimation of noise is finally obtained ideal image procossing
As a result, such as: Hyperspectral image compression algorithm, high spectrum image parser etc..In actual applications, we are usually anti-to surface
The change penetrating rate is estimated, the property taken advantage of effect that such as illumination variation causes and the additivity effect that back scattering causes, and for
Both effects are all considered as noise.In order to well assess noise, it is necessary to build suitable noise model, and EO-1 hyperion
The difference of the high light spectrum image-forming sensor that the noise model of data is used because of high light data acquisition and different.EO-1 hyperion becomes
Stroking the formula of sweeping and push-broom sensor as sensor is conventional, the diversity of both sensors determines the diversity of noise behavior,
So that build different noise models for different sensors to carry out noise evaluation.In Decomposition of Mixed Pixels is studied,
Conventional real data is obtained by the dirty empty visible ray/Infrared Imaging Spectrometer in the jet propulsion laboratory of US National Aeronautics and Space Administration
Taking, and AVIRIS uses push-broom type (whiskbroom) sensor, the principle of push-broom sensor is, utilizes the mirror rotated
Son edge is perpendicular to the scanning direction side scene to opposite side of sensor platform, and push-broom type imager sweeps formula imaging relative to stroking
Instrument is heavier, more greatly and more complicated, it is the biggest that its moving range relatively strokes the formula imager of sweeping.By push-broom type imager because photoelectricity is swept
Produced by the factors such as the dependency retouching mechanism, nonlinear transducer, the pretreatment of initial data, image space and spectral space
Noise is not likely to be Gaussian noise.From the point of view of all of optical imagery, its signal to noise ratio is accounted for master by photon effect or snapshot
Lead, wherein because effect between random photon and detector is substantially multiplicative noise, and particularly noteworthy be to take advantage of
Property noise independent in sensor temperature, therefore be difficult to multiplicative noise modeling thus go correct multiplicative noise.Generally, at mixing picture
In unit's catabolic process, need the hyperspectral image data of input is carried out pretreatment, at common pretreatment i.e. spectral normalization
Reason, the purpose of spectral normalization is exactly to correct the spectrum polluted by multiplicative noise the change correcting reflectance spectrum light scattering.But
It is unfortunately, cannot thoroughly remove multiplicative noise by these and Processing Algorithm.And present mixed pixel of hyper-spectral image
Decomposition algorithm the most all, in the case of assuming that multiplicative noise is non-existent, only considers that the impact of additive white noise, this ignoring are taken advantage of
The Decomposition of Mixed Pixels algorithm of property influence of noise is inappropriate obviously.
[summary of the invention]
The purpose of the present invention solves the problems of the prior art exactly, proposes a kind of Decomposition of Mixed Pixels mould based on anti-noise
The construction method of type, it is possible to overcome additive noise, multiplicative noise and mixing by Pixel Unmixing Models based on anti-noise
The impact that mixed pixel of hyper-spectral image is decomposed by noise.
For achieving the above object, the present invention proposes the construction method of a kind of Pixel Unmixing Models based on anti-noise,
Comprise the following steps successively:
A) considering the influence factor of multiplicative noise in image processing process, described multiplicative noise is in terms of independence
Meet non-gaussian distribution, and multiplicative noise change along with the change of image space, then provide anti-noise model:WhereinRefer to the mixed pixel matrix of multiple noise,Table
Show the end member matrix extracted from the mixed pixel matrix X containing multiple noise,Represent corresponding end member abundance
Matrix,Represent random meausrement error matrix,Representing multiplicative noise, in formula, M represents spectrum ripple
Hop count, N represents that number of pixels, K represent end member number；
B) use conventional Euclidean distance and alternately least-squares algorithm derive it is proposed that anti-noise solution to model
Mixed result, and by mean square deviation criterion MSE qualitative assessment anti-noise model Decomposition of Mixed Pixels performance:
B1) by formulaCan obtain X ≈ WH ρ, can derive from formula X ≈ WH ρ H: Represent the pseudo inverse matrix of multiplicative noise matrix ρ, make UW=(WTW)-1WTFor end member
The pseudo inverse matrix of matrix W, thenCalculate anti-noise modelAbundance matrix
Mean square deviation error is:
B2) if fixing abundance matrix H, end member matrix W is solved, the accuracy extracting end member of anti-noise model of can deriving, i.e.
First from formula X ≈ WH ρ derivation W, V is madeH=(HTH)-1HTFor the pseudo inverse matrix of matrix H,SoThen calculate anti-noise modelThe mean square deviation error of end member matrix be:
C) based on IS distance by anti-noise model:It is optimized process, and is converted into new excellent
Change model:
Wherein DIS(X | | WH) expression IS distance, d (ω | | υ) represent yardstick cost function, Representing the abundance matrix of actual measurement and the end member matrix of actual measurement respectively, s.t. represents constraints, wij、hjtRepresent end respectively
Element in variable matrix and abundance matrix, ζHRepresent the difference between abundance matrix and the abundance matrix of actual measurement calculated, ζWRepresent
Difference between the end member matrix and the end member matrix of actual measurement that calculate.
As preferably, end member abundance matrix H in described step a) should meet each column and be a condition, and W matrix and H square
Battle array is nonnegative matrix；Random meausrement error matrixGeneration source include that additive noise and mixed noise, described mixing are made an uproar
Sound is the noise being combined into multiplicative noise by additive noise；Described multiplicative noise is along with the illumination variation of spatially individual element
And change, multiplicative noise follows gamma distribution, and meets independent same distribution, and multiplicative noise ρ is also a nonnegative matrix.
As preferably, described IS distance belongs to the one of Bu Geleiman distance, and IS distance can measure two spectrum very well
Between distance, IS distance uses the composition in maximum likelihood method reconstruction signal, and IS distance has when reconstruction signal well
Dynamic intellectual；When gamma noise obeys the independent same distribution that average is 1, the only one in IS distance Shi Xu race separating degree has
There is the distance of scale invariability, insensitive to multiplicative noise.
Beneficial effects of the present invention: the present invention overcomes additivity to make an uproar by building Pixel Unmixing Models based on anti-noise
The impact that mixed pixel of hyper-spectral image is decomposed by sound, multiplicative noise and mixed noise, this model is special according to the statistics of IS distance
Property, efficiently against the impact of multiplicative noise, thus avoid producing mixed noise, it is thus achieved that more accurate signal reconstruction, improve
The precision of Decomposition of Mixed Pixels result, and anti-noise model is carried out theoretical derivation, it was demonstrated that mixed pixel based on anti-noise model
The feasibility decomposed and superiority.
[detailed description of the invention]
The construction method of a kind of Pixel Unmixing Models based on anti-noise of the present invention, comprises the following steps successively:
A) considering the influence factor of multiplicative noise in image processing process, described multiplicative noise is in terms of independence
Meet non-gaussian distribution, and multiplicative noise change along with the change of image space, then provide anti-noise model:WhereinRefer to the mixed pixel matrix of multiple noise,Table
Show the end member matrix extracted from the mixed pixel matrix X containing multiple noise,Represent corresponding end member rich
Degree matrix,Represent random meausrement error matrix,Representing multiplicative noise, in formula, M represents spectrum ripple
Hop count, N represents that number of pixels, K represent end member number；
B) use conventional Euclidean distance and alternately least-squares algorithm derive it is proposed that anti-noise solution to model
Mixed result, and by mean square deviation criterion MSE qualitative assessment anti-noise model Decomposition of Mixed Pixels performance:
B1) by formulaCan obtain X ≈ WH ρ, can derive from formula X ≈ WH ρ H: Represent the pseudo inverse matrix of multiplicative noise matrix ρ, make UW=(WTW)-1WTFor end
The pseudo inverse matrix of variable matrix W, thenCalculate anti-noise modelAbundance matrix
Mean square deviation error be:
B2) if fixing abundance matrix H, end member matrix W is solved, the accuracy extracting end member of anti-noise model of can deriving, i.e.
First from formula X ≈ WH ρ derivation W, V is madeH=(HTH)-1HTFor the pseudo inverse matrix of matrix H,SoThen calculate anti-noise modelThe mean square deviation error of end member matrix be:
C) based on IS distance by anti-noise model:It is optimized process, and is converted into new optimization
Model:
Wherein DIS(X | | WH) expression IS distance, d (ω | | υ represents yardstick cost function, Representing the abundance matrix of actual measurement and the end member matrix of actual measurement respectively, s.t. represents constraints, wij、hjtRepresent respectively
Element in end member matrix and abundance matrix, ζHRepresent the difference between abundance matrix and the abundance matrix of actual measurement calculated, ζWTable
Show the difference between the end member matrix of calculating and the end member matrix of actual measurement.
End member abundance matrix H in described step a) should meet each column and be a condition, and W matrix and H-matrix are non-
Negative matrix；Random meausrement error matrixGeneration source include additive noise and mixed noise, described mixed noise is for by adding
The noise that property noise is combined into multiplicative noise；Described multiplicative noise changes along with the illumination variation of spatially individual element,
Multiplicative noise follows gamma distribution, and meets independent same distribution, and multiplicative noise ρ is also a nonnegative matrix, described IS distance
Belonging to the one of Bu Geleiman distance, IS distance can measure the distance between two spectrum very well, and IS distance uses maximum seemingly
So composition in method reconstruction signal, IS distance has good dynamic intellectual when reconstruction signal；Average is obeyed at gamma noise
When being the independent same distribution of 1, the only one in IS distance Shi Xu race separating degree has the distance of scale invariability, makes an uproar the property taken advantage of
Sound is insensitive.
The present invention overcomes additive noise, multiplicative noise and mixing by building Pixel Unmixing Models based on anti-noise
The impact that mixed pixel of hyper-spectral image is decomposed by noise, this model is according to the statistical property of IS distance, efficiently against the property taken advantage of
Effect of noise, thus avoid producing mixed noise, it is thus achieved that more accurate signal reconstruction, improves Decomposition of Mixed Pixels result
Precision, and anti-noise model is carried out theoretical derivation, it was demonstrated that the feasibility of Decomposition of Mixed Pixels based on anti-noise model and superior
Property.
Above-described embodiment is the description of the invention, is not limitation of the invention, any to simple transformation of the present invention after
Scheme belong to protection scope of the present invention.
Claims (3)
1. a construction method for Pixel Unmixing Models based on anti-noise, comprises the following steps successively:
A) considering the influence factor of multiplicative noise in image processing process, described multiplicative noise meets in terms of independence
Non-gaussian distribution, and multiplicative noise changes along with the change of image space, then provides anti-noise model:
WhereinRefer to the mixed pixel matrix of multiple noise,Represent and make an uproar from containing multiple
The end member matrix extracted in the mixed pixel matrix X of sound,Represent corresponding end member abundance matrix,Represent random meausrement error matrix,Representing multiplicative noise, in formula, M represents spectral band number, N
Representing number of pixels, K represents end member number；
B) use conventional Euclidean distance and alternately least-squares algorithm derive it is proposed that the mixed knot of anti-noise solution to model
Really, and by mean square deviation criterion MSE qualitative assessment anti-noise model Decomposition of Mixed Pixels performance:
B1) by formulaX ≈ WH can be obtainedρ, from formula X ≈ WHρIn can derive H: Represent the pseudo inverse matrix of multiplicative noise matrix ρ, make UW=(WTW)-1WTFor end member
The pseudo inverse matrix of matrix W, thenCalculate anti-noise modelAbundance matrix
Mean square deviation error be:
B2) if fixing abundance matrix H, end member matrix W is solved, the accuracy extracting end member of anti-noise model of can deriving, first
From formula X ≈ WHρDerivation W, makes VH=(HTH)-1HTFor the pseudo inverse matrix of matrix H,SoThen calculate anti-noise modelThe mean square deviation error of end member matrix be:
C) based on IS distance by anti-noise model:It is optimized process, and is converted into new optimization mould
Type:
Wherein DIS(X | | WH) expression IS distance, d (ω | | υ) represent yardstick cost function, Representing the abundance matrix of actual measurement and the end member matrix of actual measurement respectively, s.t. represents constraints, wij、hjtRepresent end respectively
Element in variable matrix and abundance matrix, ζHRepresent the difference between abundance matrix and the abundance matrix of actual measurement calculated, ζWRepresent
Difference between the end member matrix and the end member matrix of actual measurement that calculate.
A kind of construction method of Pixel Unmixing Models based on anti-noise, it is characterised in that: institute
State end member abundance matrix H in step a) each column should be met and be a condition, and W matrix and H-matrix are nonnegative matrix；At random
Measurement error matrixGeneration source include additive noise and mixed noise, described mixed noise for by additive noise with the property taken advantage of
The noise of noise group synthesis；Described multiplicative noise changes along with the illumination variation of spatially individual element, and multiplicative noise is followed
Gamma is distributed, and meets independent same distribution, and multiplicative noise ρ is also a nonnegative matrix.
A kind of construction method of Pixel Unmixing Models based on anti-noise, it is characterised in that: institute
Stating IS distance and belong to the one of Bu Geleiman distance, IS distance can measure the distance between two spectrum very well, and IS distance makes
With the composition in maximum likelihood method reconstruction signal, IS distance has good dynamic intellectual when reconstruction signal；At gamma noise
When obeying the independent same distribution that average is 1, the only one in IS distance Shi Xu race separating degree has the distance of scale invariability,
Insensitive to multiplicative noise.
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| CN110738659A (en) * | 2019-12-23 | 2020-01-31 | 中电健康云科技有限公司 | analysis method of micro-fluorescence hyperspectral image based on deconvolution and unmixing |
| CN116188333B (en) * | 2023-05-04 | 2023-07-11 | 北京师范大学 | Multiplicative additive mixed noise removal method based on structured integral least square |
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| CN101221243A (en) * | 2007-11-01 | 2008-07-16 | 复旦大学 | Remote sensing image mixed pixels decomposition method based on nonnegative matrix factorization |
| CN102193090A (en) * | 2010-03-19 | 2011-09-21 | 复旦大学 | Mixed pixel decomposition method for remote sensing images |
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| CN101221243A (en) * | 2007-11-01 | 2008-07-16 | 复旦大学 | Remote sensing image mixed pixels decomposition method based on nonnegative matrix factorization |
| CN102193090A (en) * | 2010-03-19 | 2011-09-21 | 复旦大学 | Mixed pixel decomposition method for remote sensing images |
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