CN103886639A - Construction method for mixed pixel decomposition model based on noise immunity - Google Patents

Abstract

The invention discloses a construction method for a mixed pixel decomposition model based on noise immunity. The construction method includes the steps that a noise immunity model is given, an unmixing result of the provided noise immunity model is deduced by a common Euclidean distance and an alternative least squares algorithm, the mixed pixel decomposition performance of the noise immunity model is estimated quantitatively through a mean square error criterion, and the noise immunity model is optimized by adopting an IS distance. The influence, on hyperspectral image mixed pixel decomposition, of additive noise, multiplicative noise and mixed noise are eliminated by constructing a mixed pixel decomposition model based on noise immunity, according to statistics characteristics of the IS distance, the influence of the multiplicative noise is effectively eliminated, the mixed noise is avoided, and accurate signal reconstruction is achieved, accuracy of results of mixed pixel decomposition is improved, the noise immunity model is deduced theoretically, and feasibility and superiority of mixed pixel decomposition based on noise immunity are proved.

Description

A kind of construction method of the Pixel Unmixing Models based on anti-noise

[technical field]

The present invention relates to the technical field of Pixel Unmixing Models, particularly the technical field of the construction method of the Pixel Unmixing Models based on anti-noise.

[background technology]

The production process of high spectrum image is a complicated physical action process, and physical action process occurs between light source, material surface and atmosphere interference etc.In complicated image production process, produced a large amount of noises thus, these noises may comprise additive noise and multiplicative noise, and owing to comprising more than a kind of noise, so also may produce mixed noise.Therefore the generation of high-spectral data is subject to various factors. and noise type is comparatively complicated, thereby in high-spectral data analytic process, noise behavior analysis is seemed to very important.Research shows to depend on the interaction between multiplicative noise and additive noise explaining in the process of some phenomenons, as in the time being explained as follows phenomenon: accidental resonance, at phase transformation and transport superconduct Nodes etc.There is most of high spectrum image analytical algorithm and finally obtain comparatively desirable processing result image because of the good estimation to noise, as: Hyperspectral image compression algorithm, high spectrum image analytical algorithm etc.In actual applications, we usually the variation of effects on surface reflectivity estimate, such as the additivity effect that causes of the property the taken advantage of effect that causes of illumination variation and back scattering, and all can see noise as for these two kinds of effects.For good assessment noise, must build suitable noise model, and the difference of the high light spectrum image-forming sensor that the noise model of high-spectral data uses because of high light data acquisition is different.High light spectrum image-forming sensor is conventional strokes the formula of sweeping and push-broom sensor, and the otherness of these two kinds of sensors has determined the otherness of noise behavior, thereby need to build different noise models for different sensors and carry out noise evaluation.In Decomposition of Mixed Pixels research, conventional real data is obtained by the dirty empty visible ray/Infrared Imaging Spectrometer in jet propulsion laboratory of US National Aeronautics and Space Administration, and AVIRIS employing is push-broom type (whiskbroom) sensor, the principle of push-broom sensor is, utilize the mirror of rotation to arrive the scene of opposite side along scanning direction one side perpendicular to sensor platform, to sweep formula imager heavier, more greatly and more complicated with respect to stroking for push-broom type imager, and it is also larger that its moving range is stroked the formula imager of sweeping.By push-broom type imager because the noise that the factors such as the correlativity of pre-service, image space and the spectral space of optoelectronic scanning mechanism, nonlinear transducer, raw data produce may not be Gaussian noise.For all optical imagerys, its signal to noise ratio (S/N ratio) accounts for leading by photon effect or snapshot, wherein because the effect between random photon and detecting device is multiplicative noise in essence, and it should be noted that especially multiplicative noise depends on sensor temperature, thereby be therefore difficult to the positive multiplicative noise of multiplicative noise modeling deemphasis.Conventionally, in Decomposition of Mixed Pixels process, need to carry out pre-service to the high spectrum image data of input, common pre-service is spectrum normalized, and the normalized object of spectrum is exactly to correct the spectrum being polluted by multiplicative noise the variation of correcting reflectance spectrum light scattering.But unfortunately, cannot thoroughly remove multiplicative noise by these and Processing Algorithm.And present mixed pixel of hyper-spectral image decomposition algorithm is all supposing, in the non-existent situation of multiplicative noise, only to consider the impact of additive white noise, this Decomposition of Mixed Pixels algorithm of ignoring multiplicative noise impact is inappropriate obviously.

[summary of the invention]

Object of the present invention solves the problems of the prior art exactly, propose a kind of construction method of the Pixel Unmixing Models based on anti-noise, can overcome the impact that additive noise, multiplicative noise and mixed noise decompose mixed pixel of hyper-spectral image by the Pixel Unmixing Models based on anti-noise.

For achieving the above object, the present invention proposes a kind of construction method of the Pixel Unmixing Models based on anti-noise, comprise the following steps successively:

A) in image processing process, consider the influence factor of multiplicative noise, described multiplicative noise meets non-Gaussian distribution aspect independence, and multiplicative noise changes along with the variation of image space, so provide anti-noise model:

wherein

refer to the mixed pixel matrix that has comprised multiple noise, represent the end member matrix extracting from the mixed pixel matrix X that contains multiple noise,

represent corresponding end member abundance matrix,

represent random meausrement error matrix,

represent multiplicative noise;

B) adopt conventional Euclidean distance and the derive mixed result of solution of the anti-noise model that we propose of least-squares algorithm alternately, and by mean square deviation criterion MSE qualitative assessment anti-noise model Decomposition of Mixed Pixels performance:

B1) by formula can obtain X ≈ WH _ρ, from formula X ≈ WH _ρin the H that can derive:

the pseudo inverse matrix that represents multiplicative noise matrix ρ, makes U _w=(W ^tw) ^-1w ^tfor the pseudo inverse matrix of end member matrix W, so

calculate anti-noise model

the mean square deviation error of abundance matrix be:

B2) if fixing abundance matrix H solves end member matrix W, the accuracy of the extraction end member of the anti-noise model of can deriving, first from formula X ≈ WH ρ) derivation W, make V _h=(H ^th) ^-lh ^tfor the pseudo inverse matrix of matrix H,

so calculate anti-noise model

the mean square deviation error of end member matrix be:

C) based on IS distance by anti-noise model:

be optimized processing, and be converted into new Optimized model: $\min :D_{\mathrm{IS}}\left(X\right|\left|\mathrm{WH}\right)=\underset{m=1}{\overset{M}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}d\left({\left[X\right]}_{\mathrm{mn}}\right|\left|{\left[\mathrm{WH}\right]}_{\mathrm{mn}}\right),$

$s.t.w_{\mathrm{ij}}\≥0,h_{\mathrm{jt}}\≥0,\underset{j}{\mathrm{\Σ}}{h}_{\mathrm{jt}}=1,$

1≤i≤M,1≤j≤K,1≤t≤N;

Wherein D _iS(X||WH) represent IS distance, d (w||v) represents yardstick cost function, $d_{\mathrm{IS}}\left(w\right|\left|v\right)=\frac{w}{v}-log\frac{w}{v}-1,$ $\hat{L},\hat{F}$ Represent respectively the abundance matrix of actual measurement and the end member matrix of actual measurement, s.t. represents constraint condition, w _ij, h _jtrepresent respectively the element in end member matrix and abundance matrix, difference between abundance matrix and the abundance matrix of actual measurement that represents to calculate,

difference between end member matrix and the end member matrix of actual measurement that represents to calculate.

As preferably, the end member abundance matrix H of described step in a) should meet every row and be a condition, and W matrix and H matrix are nonnegative matrix; Random meausrement error matrix

generation source comprise that additive noise and mixed noise, described mixed noise are the noise being combined into multiplicative noise by additive noise; Described multiplicative noise changes along with the illumination variation of individual element on space, and multiplicative noise is followed gamma and distributed, 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, the distance of IS distance between can two spectrum of fine measurement, and IS is apart from the composition using in maximum likelihood method reconstruction signal, and IS distance has good dynamic intellectual in the time of reconstruction signal; In the time of gamma noise to obey average be 1 independent same distribution, IS is apart from the unique distance with yardstick unchangeability in Shi Xu family degree of separation, insensitive to multiplicative noise.

Beneficial effect of the present invention: the present invention overcomes by the Pixel Unmixing Models building based on anti-noise the impact that additive noise, multiplicative noise and mixed noise decompose mixed pixel of hyper-spectral image, this model is according to the statistical property of IS distance, effectively overcome the impact of multiplicative noise, thereby avoid producing mixed noise, obtain comparatively accurate signal reconstruction, improve the precision of Decomposition of Mixed Pixels result, and anti-noise model is carried out to theory and derive, prove feasibility and the superiority of the Decomposition of Mixed Pixels based on anti-noise model.

[embodiment]

The construction method of a kind of Pixel Unmixing Models based on anti-noise of the present invention, comprises the following steps successively:

A) in image processing process, consider the influence factor of multiplicative noise, described multiplicative noise meets non-Gaussian distribution aspect independence, and multiplicative noise changes along with the variation of image space, so provide anti-noise model:

wherein

refer to the mixed pixel matrix that has comprised multiple noise,

represent the mixed pixel matrix from containing multiple noise, the end member matrix extracting in Y,

represent corresponding end member abundance matrix,

represent random meausrement error matrix,

represent multiplicative noise;

B) adopt conventional Euclidean distance and the derive mixed result of solution of the anti-noise model that we propose of least-squares algorithm alternately, and by mean square deviation criterion MSE qualitative assessment anti-noise model Decomposition of Mixed Pixels performance:

B1) by formula

can obtain X ≈ WH _ρfrom formula X ≈ WH _ρin the H that can derive

the pseudo inverse matrix that represents multiplicative noise matrix ρ, makes UW=(W ^tw) ^-1w ^tfor the pseudo inverse matrix of end member matrix W, so calculate anti-noise model

the mean square deviation error of abundance matrix be:

B2) if fixing abundance matrix H solves end member matrix W,, the accuracy of the extraction end member of the anti-noise model of can deriving, first from formula X ≈ WH _ρderivation W,, make V _h=(H ^th) ^-1h ^tfor the pseudo inverse matrix of matrix H,

so

calculate anti-noise model

the mean square deviation error of end member matrix be:

C) based on IS distance by anti-noise model:

be optimized processing, and be converted into new Optimized model: $\min :D_{\mathrm{IS}}\left(X\right|\left|\mathrm{WH}\right)=\underset{m=1}{\overset{M}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}d\left({\left[X\right]}_{\mathrm{mn}}\right|\left|{\left[\mathrm{WH}\right]}_{\mathrm{mn}}\right),$

$s.t.w_{\mathrm{ij}}\≥0,h_{\mathrm{jt}}\≥0,\underset{j}{\mathrm{\Σ}}{h}_{\mathrm{jt}}=1,$

1≤i≤M,1≤j≤K,1≤t≤N;

Wherein D _iS(X||WH) represent IS distance, d (w||v) represents yardstick cost function, $d_{\mathrm{IS}}\left(w\right|\left|v\right)=\frac{w}{v}-log\frac{w}{v}-1,$ $\hat{L},\hat{F}$ Represent respectively the abundance matrix of actual measurement and the end member matrix of actual measurement, s.t. represents constraint condition, w _ij, h _jtrepresent respectively the element in end member matrix and abundance matrix,

difference between abundance matrix and the abundance matrix of actual measurement that represents to calculate, difference between end member matrix and the end member matrix of actual measurement that represents to calculate.

End member abundance matrix H in described step a) should meet every row and be a condition, and W matrix and H matrix are nonnegative matrix; Random meausrement error matrix

generation source comprise that additive noise and mixed noise, described mixed noise are the noise being combined into multiplicative noise by additive noise; Described multiplicative noise changes along with the illumination variation of individual element on space, and multiplicative noise is followed gamma and distributed, and meets independent same distribution, multiplicative noise

also be a nonnegative matrix, described IS distance belongs to the one of Bu Geleiman distance, the IS distance distance between can two spectrum of fine measurement, IS is apart from the composition using in maximum likelihood method reconstruction signal, and IS distance has good dynamic intellectual in the time of reconstruction signal; In the time of gamma noise to obey average be 1 independent same distribution, IS is apart from the unique distance with yardstick unchangeability in Shi Xu family degree of separation, insensitive to multiplicative noise.

The present invention overcomes by the Pixel Unmixing Models building based on anti-noise the impact that additive noise, multiplicative noise and mixed noise decompose mixed pixel of hyper-spectral image, this model is according to the statistical property of IS distance, effectively overcome the impact of multiplicative noise, thereby avoid producing mixed noise, obtain comparatively accurate signal reconstruction, improve the precision of Decomposition of Mixed Pixels result, and anti-noise model is carried out to theory and derive, prove feasibility and the superiority of the Decomposition of Mixed Pixels based on anti-noise model.

Above-described embodiment is to explanation of the present invention, is not limitation of the invention, any scheme after simple transformation of the present invention is all belonged to protection scope of the present invention.

Claims (3)

1. a construction method for the Pixel Unmixing Models based on anti-noise, comprises the following steps successively:

A) in image processing process, consider the influence factor of multiplicative noise, described multiplicative noise meets non-Gaussian distribution aspect independence, and multiplicative noise changes along with the variation of image space, so provide anti-noise model:

wherein refer to the mixed pixel matrix that has comprised multiple noise,

represent the end member matrix extracting from the mixed pixel matrix X that contains multiple noise,

represent corresponding end member abundance matrix,

represent random meausrement error matrix,

represent multiplicative noise;

B) adopt conventional Euclidean distance and the derive mixed result of solution of the anti-noise model that we propose of least-squares algorithm alternately, and by mean square deviation criterion MSE qualitative assessment anti-noise model Decomposition of Mixed Pixels performance:

B1) by formula

can obtain X ≈ WH _ρ, from formula X ≈ WH _ρin the H that can derive:

the pseudo inverse matrix that represents multiplicative noise matrix ρ, makes U _w=(W ^tw) ^-1w ^tfor the pseudo inverse matrix of end member matrix W, so

calculate anti-noise model

the mean square deviation error of abundance matrix be:

B2) if fixing abundance matrix H solves end member matrix W, the accuracy of the extraction end member of the anti-noise model of can deriving, first from formula X ≈ WH _ρderivation W, makes V _h=(H ^th) ^-1h ^tfor the pseudo inverse matrix of matrix H,

so

calculate anti-noise model

the mean square deviation error of end member matrix be:

C) based on IS distance by anti-noise model:

be optimized processing, and be converted into new

Optimized model: $\min :D_{\mathrm{IS}}\left(X\right|\left|\mathrm{WH}\right)=\underset{m=1}{\overset{M}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}d\left({\left[X\right]}_{\mathrm{mn}}\right|\left|{\left[\mathrm{WH}\right]}_{\mathrm{mn}}\right),$

$s.t.w_{\mathrm{ij}}\≥0,h_{\mathrm{jt}}\≥0,\underset{j}{\mathrm{\Σ}}{h}_{\mathrm{jt}}=1,$

1≤i≤M,1≤j≤K,1≤t≤N;

Wherein D _iS(X||WH) represent IS distance, d (w||v) represents yardstick cost function, $d_{\mathrm{IS}}\left(w\right|\left|v\right)=\frac{w}{v}-log\frac{w}{v}-1,$ $\hat{L},\hat{F}$ Represent respectively the abundance matrix of actual measurement and the end member matrix of actual measurement, s.t. represents constraint condition, w _ij, h _jtrepresent respectively the element in end member matrix and abundance matrix, ζ _hdifference between abundance matrix and the abundance matrix of actual measurement that represents to calculate, ζ _wdifference between end member matrix and the end member matrix of actual measurement that represents to calculate.

2. the construction method of a kind of Pixel Unmixing Models based on anti-noise as claimed in claim 1, is characterized in that: the end member abundance matrix H in described step a) should meet every row and be a condition, and W matrix and H matrix are nonnegative matrix; Random meausrement error matrix

generation source comprise that additive noise and mixed noise, described mixed noise are the noise being combined into multiplicative noise by additive noise; Described multiplicative noise changes along with the illumination variation of individual element on space, and multiplicative noise is followed gamma and distributed, and meets independent same distribution, and multiplicative noise ρ is also a nonnegative matrix.

3. the construction method of a kind of Pixel Unmixing Models based on anti-noise as claimed in claim 1, it is characterized in that: described IS distance belongs to the one of Bu Geleiman distance, the IS distance distance between can two spectrum of fine measurement, IS is apart from the composition using in maximum likelihood method reconstruction signal, and IS distance has good dynamic intellectual in the time of reconstruction signal; In the time of gamma noise to obey average be 1 independent same distribution, IS is apart from the unique distance with yardstick unchangeability in Shi Xu family degree of separation, insensitive to multiplicative noise.