CN103745487B - The mixed compression sensing method of Bayes's EO-1 hyperion solution based on structural sparse priori - Google Patents

Abstract

The invention discloses the mixed compression sensing method of a kind of Bayes's EO-1 hyperion solution based on structural sparse priori, for solving the technical problem of the mixed Compression of hyperspectral images cognitive method low precision of existing combined spectral solution.Technical scheme is that compression process mixes the low-rank character excavating high-spectral data inherence by linear solution, uses wavelet transformation that Abundances converts to structural sparse signal, uses compressed sensing to obtain compression data afterwards.Process of reconstruction, suitable end member matrix is selected from library of spectra, introduce the structural sparse priori of Abundances wavelet coefficient, then use the Bayesian inference method accurate reconstruction Abundances matrix based on gibbs sampler, finally use linear mixed model to rebuild initial data.About 10% is promoted relative to background technology compressed sensing class arithmetic accuracy.

Description

The mixed compression sensing method of Bayes's EO-1 hyperion solution based on structural sparse priori

Technical field

The present invention relates to the mixed compression sensing method of a kind of EO-1 hyperion solution, particularly relate to the mixed compression sensing method of a kind of Bayes's EO-1 hyperion solution based on structural sparse priori.

Background technology

Owing to hyperspectral image data amount is huge, the compression algorithm of high compression ratio, for the collection of high spectrum image, transmission and process, there is very profound significance.nullCurrent existing Hyperspectral image compression algorithm is broadly divided into two classes，One class is traditional compression method based on information coding，This kind of method is to expand from the compression method of normal image，Lay particular emphasis on the redundancy removed in high spectrum image between each wave band inside and wave band to be compressed，Impulsive Difference coding (Cluster-baseddifferentialpulse-codemodulation including cluster,CDPCM)，3 D wavelet transformation (3dimensiondiscretewavelettransformation,3D-DWT)，Three-dimensional DCT (3dimensiondiscretecosinetransformation,3D-DCT) etc.，But this kind of compression algorithm can only be compressed after image acquisition，Need nonetheless remain for substantial amounts of hardware gather and temporarily store data，And generally compression ratio is low；Another kind of method is then based on the compression method of compressed sensing (CompressiveSensing), such method can be passed through to gather the sparse signal that a small amount of sample point accurate reconstruction is original, providing theoretical foundation for reducing the hardware consumption gathering data needs, the method is more focused on process of reconstruction.

Document " Acompressivesensingandunmixingschemeforhyperspectraldata processing; IEEETransactionsonImageProcessing; 2012,21 (3): 1,200 1210 " discloses the Compression of hyperspectral images cognitive method that a kind of combined spectral solution is mixed.The method is mixed by linear solution and high-spectral data is decomposed into Abundances matrix and end member matrix；Abundances matrix gradient on Spatial Dimension has openness, it is possible to adopt the mode of compressed sensing to be compressed rebuilding.Specific practice is, obtains compression data first by compressed sensing matrix；In conjunction with library of spectra, select suitable end member；The method using compressed sensing afterwards rebuilds the Abundances matrix comprising sparse gradient；Finally, linear mixed model is used to rebuild the high-spectral data needing to gather.But, gradient is openness, and can not to excavate the deeper structure of Abundances matrix openness, and the method that this article uses augmentation Lagrange rebuilds Abundances, and the method can not the proportion coefficients of the openness regular terms of adaptively selected gradient.The two factor directly affects the reconstruction precision of this compression algorithm.

Summary of the invention

In order to overcome the deficiency of the mixed Compression of hyperspectral images cognitive method low precision of existing combined spectral solution, the present invention provides a kind of Bayes's EO-1 hyperion solution based on structural sparse priori to mix compression sensing method.The method compression process is mixed by linear solution and is excavated the low-rank character that high-spectral data is inherent, uses wavelet transformation that Abundances converts to structural sparse signal, uses compressed sensing to obtain compression data afterwards.Process of reconstruction, suitable end member matrix is selected from library of spectra, introduce the structural sparse priori of Abundances wavelet coefficient, then use the Bayesian inference method accurate reconstruction Abundances matrix based on gibbs sampler, finally use linear mixed model to rebuild initial data.The data of the present invention are in the urban data that HYDICE satellite shoots, when compression ratio is 1:16, normalized mean square error is less than 0.4, in the Indiana data of AVIRIS shooting, when compression ratio is 1:16, normalized mean squared error is similarly less than 0.4, promotes about 10% relative to background technology compressed sensing class arithmetic accuracy.

The technical solution adopted for the present invention to solve the technical problems is: a kind of Bayes's EO-1 hyperion solution based on structural sparse priori mixes compression sensing method, is characterized in comprising the following steps:

Step one, for a panel height spectroscopic datan_pRepresent total number of pixels that high-spectral data spatially comprises, n_bRepresent the wave band number that high-spectral data comprises, x_i, i=1 ..., n_bRepresent that the image of each wave band launches the column vector formed by row.Each pixel is at n_bDifferent reflected values on individual wave band constitute the spectrum of this pixel.This spectrum adopts linear mixed model to describe.Linear mixed model thinks that any one mixed spectra is the linear combination of all end members, and end member ratio shared by mixed spectra is called Abundances.X represents Abundances matrix and the linear combination of end member matrix:

X=HW(1)

Wherein,For Abundances matrix,Represent the ratio shared by i-th end member, n in the mixed spectra of each pixel_eRepresent the number of end member,For end member matrix, whereinRepresent each end member.

Wavelet transform is used for Abundances:

Θ=Ψ^TH(2)

Y=Ψ^TX=Ψ^THW=Θ W

Wherein,For wavelet basis,Representing the wavelet coefficient of Abundances, Y represents the wavelet coefficient of whole data.Represent h_iWavelet coefficient, there is structure openness.

Step 2, utilize wavelet coefficient rebuild Abundances matrix, finally realize the reconstruction of whole data:

1, the stochastic variable meeting Gauss distribution is used to produce m × n_pThe matrix of size, and every string is normalized and obtains random perception matrixUse Φ that the initial data after wavelet transformation is sampled, obtain compression data

F=Φ Y=Φ Ψ^TX(3)

Wherein, m represents length is n_pSignal Compression after data length, general m < n_p。

2, for the scene of limited dimension, the environmental factors impact on spectrum is ignored, it is assumed that end member is Limited Number.Use ASTER library of spectra, for specific scene selectively from library of spectra extracting part spectral as end member.Finally determine and comprise n_eThe matrix W of individual end member.

3, adopt Bayesian inference mode from compression after data estimation Abundances matrix.

(1) by formula (2) and formula (3), method of least square is utilized to obtain the wavelet coefficient of Abundances matrix by the data after individually compressing

G=FW^T(WW^T)^-1=Φ Θ+N(4) wherein,Represent the noise item utilizing method of least square and introduce.

(2) the vector form g of formula (4) is obtained_i=Φ θ_i+n_i, it is assumed that noise n_iObeying average is 0, and covariance isGauss distributionAnd independent same distribution between each noise vector, then obtain θ_i, i=1,2 ..., n_eLikelihood function:

$p\left(g_i\right|{\mathrm{\&theta;}}_i,{\mathrm{\&beta;}}_i^{-1})={\left(2\mathrm{\&pi;}{\mathrm{\&beta;}}_i^{-1}\right)}^{-\frac{m}{2}}\exp (-\frac{1}{2{\mathrm{\&beta;}}_i^{-1}}{\left|\right|g_i-{\mathrm{\&Phi;\&theta;}}_i\left|\right|}_2^2)---\left(5\right)$

β_iPrecision for noise vector, it is intended that β_iPriori be the distribution of following gamma:

p(β_i|κ₀,υ₀)=Gamma (κ₀,υ₀) (6)

κ₀=10^-6,υ₀=10^-6Form parameter and scale parameter for gamma distribution.

(3) θ is set up_iIn the structural sparse priori of each element.Structural sparse priori is mainly reflected in the tree construction of wavelet coefficient, and when parent node is 0, its child node is also probably 0, and vice versa:

$p\left({\mathrm{\&theta;}}_{s,\mathrm{ji}}\right|{\mathrm{\&beta;}}_{s,i}^{-1})=(1-{\mathrm{\&pi;}}_{s,\mathrm{ji}}){\mathrm{\&delta;}}_0+{\mathrm{\&pi;}}_{s,\mathrm{ji}}N(0,{\mathrm{\&beta;}}_{s,i}^{-1})---\left(7\right)$

Wherein, s represents the yardstick s=1 in wavelet transformation ..., L, L is the total number of yardstick, θ_s,jiRepresent θ_iThe jth element at yardstick s place.δ₀It it is a distribution being totally absorbed in 0 place.π_s,jiIt is a proportionality coefficient, works as π_s,jiWhen tending to 0, θ_s,jiIt is 0, otherwise, π_s,jiWhen tending to 1, θ_s,jiCome from a Gauss distribution.π_s,jiDetermined by the tree construction of wavelet transformation:

${\mathrm{\&pi;}}_{s,\mathrm{ji}}=\left\{\begin{array}{cc}{\mathrm{\&pi;}}_r& \mathrm{ifs}=1\\ {\mathrm{\&pi;}}_s^0& \mathrm{if}2\&le;s\&le;L,{\mathrm{\&theta;}}_{\mathrm{pa}(s,\mathrm{ji})}=0\\ {\mathrm{\&pi;}}_s^1& \mathrm{if}2\&le;s\&le;L,{\mathrm{\&theta;}}_{\mathrm{pa}(s,\mathrm{ji})}\&NotEqual;0\end{array}\right.---\left(8\right)$

θ_pa(s,ji)It is θ_s,jiParent node, work as θ_pa(s,ji)When=0, π_s,jiBeing set to high probability is 0Work as θ_pa(s,ji)When ≠ 0, π_s,jiBeing set to high probability is 1β_s,iIt is θ_s,jiThe precision of Gauss distribution in priori.π_r,And β_s,iPrior distribution as follows:

$\begin{array}{cc}{\mathrm{\&pi;}}_r~\mathrm{Beta}({\mathrm{\&epsiv;}}_0^r,{\mathrm{\&gamma;}}_0^r),& {\mathrm{\&pi;}}_s^0~\mathrm{Beta}({\mathrm{\&epsiv;}}_0^s,{\mathrm{\&gamma;}}_0^s),\\ {\mathrm{\&pi;}}_s^1~\mathrm{Beta}({\mathrm{\&epsiv;}}_1^s,{\mathrm{\&gamma;}}_1^s),& {\mathrm{\&beta;}}_{s,i}~\mathrm{Gamma}({\mathrm{\&kappa;}}_1,{\mathrm{\&upsi;}}_1)\end{array}---\left(9\right)$

Wherein, ${\mathrm{\&kappa;}}_1={10}^{-6},{\mathrm{\&upsi;}}_1={10}^{-6},[{\mathrm{\&epsiv;}}_0^r,{\mathrm{\&gamma;}}_0^r]=\left[\mathrm{0.9,0.1}\right]\&times;N_1,[{\mathrm{\&epsiv;}}_0^s,{\mathrm{\&gamma;}}_0^s,]=[1/n_p,1/n_p]\&times;N_s,$ N_sRepresent wavelet transformation s=1 ..., the number of the wavelet coefficient of L layer.

(4) sampled wavelet coefficient θ_s,ji.Wavelet coefficient θ is obtained by above-mentioned (2), (3) step_s,jiLikelihood function, θ_s,jiStructural sparse priori, and the prior distribution of other unknown parameters.Need the wavelet coefficient Θ estimated, obtained by following Bayesian inference:

P (Θ | G) ∝ ∫ p (G | Θ, β) p (Θ | Ω) p (Ω) p (β) d Ω (10)

Wherein, $\mathrm{\&Omega;}=\{{\left\{{\mathrm{\&beta;}}_{s,i}\right\}}_{i=1:n_e}^{s=2:L},{\mathrm{\&pi;}}_r,{\{{\mathrm{\&pi;}}_0^s,{\mathrm{\&pi;}}_1^s\}}_{s=2:L}\},\mathrm{\&beta;}={[{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_2,...,{{\mathrm{\&beta;}}_n}_e]}^T$ For all of noise precision, it is assumed that the element independent same distribution in β and Ω, then p (β) and p (Ω) is as follows respectively:

$p\left(\mathrm{\&beta;}\right)=\underset{i=1}{\overset{n_e}{\mathrm{\&Pi;}}}\mathrm{Gamma}({\mathrm{\&kappa;}}_0,{\mathrm{\&upsi;}}_0),p\left(\mathrm{\&Omega;}\right)=\underset{i=1}{\overset{n_e}{\mathrm{\&Pi;}}}\left\{\begin{array}{c}\underset{s=1}{\overset{L}{\mathrm{\&Pi;}}}\mathrm{Gamma}({\mathrm{\&kappa;}}_1,{\mathrm{\&upsi;}}_1)\&times;\mathrm{Beta}({\mathrm{\&epsiv;}}_0^r,{\mathrm{\&gamma;}}_0^r)\\ \&times;\underset{s=1}{\overset{L}{\mathrm{\&Pi;}}}\mathrm{Beta}({\mathrm{\&epsiv;}}_0^s,{\mathrm{\&gamma;}}_0^s)\mathrm{Beta}({\mathrm{\&epsiv;}}_1^s,{\mathrm{\&gamma;}}_1^s)\end{array}\right\}---\left(11\right)$

Adopt the Markov monte carlo method based on gibbs sampler, be similar to, by being distributed sample drawn from corresponding condition, the Posterior distrbutionp needing predictor.θ_s,jiGibbs sampler as follows:

$\begin{array}{c}p\left({\mathrm{\&theta;}}_{s,\mathrm{ji}}\right|~)=(1-{\mathrm{\&pi;}}_{s,\mathrm{ji}}){\mathrm{\&delta;}}_0+{\mathrm{\&pi;}}_{s,\mathrm{ji}}N({\mathrm{\&mu;}}_{s,\mathrm{ji}},{\mathrm{\&beta;}}_{s,\mathrm{ji}}^{-1})\\ {\mathrm{\&beta;}}_{s,\mathrm{ji}}={\mathrm{\&beta;}}_{s,i}+{\mathrm{\&beta;}}_i{\mathrm{\&Phi;}}_j^T{\mathrm{\&Phi;}}_j,{\mathrm{\&mu;}}_{\mathrm{sji}}={\mathrm{\&beta;}}_{s,\mathrm{ji}}^{-1}{\mathrm{\&Phi;}}_j^T[g_i-\underset{k\&NotEqual;j}{\overset{n_p}{\mathrm{\&Sigma;}}}{\mathrm{\&Phi;}}_k^T{\mathrm{\&Phi;}}_k]\end{array}---\left(12\right)$

Wherein, other parameters needed in the distribution of～expression condition, Φ_jRepresent Φ_jIn jth row.

(5) sampling noiset precision β_i.Sample distribution meets following gamma distribution:

$p\left({\mathrm{\&beta;}}_i\right|~)=\mathrm{Gamma}({{\mathrm{\&kappa;}}_{\mathrm{\&beta;}}}_i,{{\mathrm{\&upsi;}}_{\mathrm{\&beta;}}}_i),{{\mathrm{\&kappa;}}_{\mathrm{\&beta;}}}_i={\mathrm{\&kappa;}}_0+\frac{m}{2},{{\mathrm{\&upsi;}}_{\mathrm{\&beta;}}}_i={\mathrm{\&upsi;}}_0+\frac{1}{2}{(g_i-{\mathrm{\&Phi;\&theta;}}_i)}^T(g_i-{\mathrm{\&Phi;\&theta;}}_i)---\left(13\right)$

(6) sampling hyper parameterConcrete sample distribution is as follows:

$p\left({\mathrm{\&beta;}}_{s,i}\right|~)=\mathrm{Gamma}({{\mathrm{\&kappa;}}_{\mathrm{\&beta;}}}_{s,i},{{\mathrm{\&upsi;}}_{\mathrm{\&beta;}}}_{s,i}),{{\mathrm{\&kappa;}}_{\mathrm{\&beta;}}}_{s,i}={\mathrm{\&kappa;}}_1+\frac{1}{2}\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}1({\mathrm{\&theta;}}_{s,\mathrm{ji}}\&NotEqual;0),{{\mathrm{\&upsi;}}_{\mathrm{\&beta;}}}_{s,j}={\mathrm{\&upsi;}}_1+\frac{1}{2}\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}{\mathrm{\&theta;}}_{s,\mathrm{ji}}^2---\left(14\right)$

$p\left({\mathrm{\&pi;}}_r\right|~)=\mathrm{Gamma}({{\mathrm{\&epsiv;}}_{\mathrm{\&pi;}}}_r,{{\mathrm{\&gamma;}}_{\mathrm{\&pi;}}}_r),{{\mathrm{\&epsiv;}}_{\mathrm{\&pi;}}}_r={\mathrm{\&epsiv;}}_0^r+\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}1({\mathrm{\&theta;}}_{s,\mathrm{ji}}\&NotEqual;0),{{\mathrm{\&gamma;}}_{\mathrm{\&pi;}}}_r={\mathrm{\&gamma;}}_0^r+\frac{1}{2}\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}1({\mathrm{\&theta;}}_{s,\mathrm{ji}}=0)---\left(15\right)$

$\begin{array}{c}p\left({\mathrm{\&pi;}}_{s,i}^0\right|~)=\mathrm{Gamma}({\mathrm{\&epsiv;}}_{{\mathrm{\&pi;}}_{s,i}^0},{\mathrm{\&gamma;}}_{{\mathrm{\&pi;}}_{s,i}^0})\\ {\mathrm{\&epsiv;}}_{{\mathrm{\&pi;}}_{s,i}^0}={\mathrm{\&epsiv;}}_0^s+\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}1({\mathrm{\&theta;}}_{s,\mathrm{ji}}\&NotEqual;0,{\mathrm{\&theta;}}_{\mathrm{pa}(s,\mathrm{ji})}=0),{\mathrm{\&gamma;}}_{{\mathrm{\&pi;}}_{s,i}^0}={\mathrm{\&gamma;}}_0^s+\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}1({\mathrm{\&theta;}}_{s,\mathrm{ji}}=0,{\mathrm{\&theta;}}_{\mathrm{pa}(s,\mathrm{ji})}=0)\end{array}---\left(16\right)$

$\begin{array}{c}p\left({\mathrm{\&pi;}}_{s,i}^1\right|~)=\mathrm{Gamma}({\mathrm{\&epsiv;}}_{{\mathrm{\&pi;}}_{s,i}^1},{\mathrm{\&gamma;}}_{{\mathrm{\&pi;}}_{s,i}^1})\\ {\mathrm{\&epsiv;}}_{{\mathrm{\&pi;}}_{s,i}^1}={\mathrm{\&epsiv;}}_1^s+\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}1({\mathrm{\&theta;}}_{s,\mathrm{ji}}\&NotEqual;0,{\mathrm{\&theta;}}_{\mathrm{pa}(s,\mathrm{ji})}\&NotEqual;0),{\mathrm{\&gamma;}}_{{\mathrm{\&pi;}}_{s,i}^1}={\mathrm{\&gamma;}}_1^s+\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}1({\mathrm{\&theta;}}_{s,\mathrm{ji}}=0,{\mathrm{\&theta;}}_{\mathrm{pa}(s,\mathrm{ji})}\&NotEqual;0)\end{array}---\left(17\right)$

Wherein, 1 (x) is 1 when x is genuine, is otherwise 0.

(7) circulating execution (4), (5), (6) three steps successively for each wavelet coefficient in Θ to sample, until meeting the condition of convergence or end condition, obtaining the wavelet coefficient of final estimationM_sFor total number of sampling,For the result sampled each time.The end condition used is iterations, wherein, sampler stable process 400 times, sampling process 200 times.

4, the high-spectral data rebuild is obtained according to linear mixed model (1)

The invention has the beneficial effects as follows: the method compression process is mixed by linear solution and excavated the low-rank character that high-spectral data is inherent, use wavelet transformation that Abundances converts to structural sparse signal, use compressed sensing to obtain compression data afterwards.Process of reconstruction, suitable end member matrix is selected from library of spectra, introduce the structural sparse priori of Abundances wavelet coefficient, then use the Bayesian inference method accurate reconstruction Abundances matrix based on gibbs sampler, finally use linear mixed model to rebuild initial data.The data of the present invention are in the urban data that HYDICE satellite shoots, when compression ratio is 1:16, normalized mean square error is less than 0.4, in the Indiana data of AVIRIS shooting, when compression ratio is 1:16, normalized mean squared error is similarly less than 0.4, promotes about 10% relative to background technology compressed sensing class arithmetic accuracy.

Below in conjunction with detailed description of the invention, the present invention is elaborated.

Detailed description of the invention

The present invention specifically comprises the following steps that based on the mixed compression sensing method of Bayes's EO-1 hyperion solution of structural sparse priori

For a panel height spectroscopic datan_pRepresent total number of pixels that high-spectral data spatially comprises, n_bRepresent the wave band number that high-spectral data comprises, x_i, i=1 ..., n_bRepresent that the image of each wave band launches the column vector formed by row.Each pixel is at n_bDifferent reflected values on individual wave band constitute the spectrum of this pixel.Generally, unique spectrum that pure material has is referred to as end member.Due to factor impacts such as low spatial resolution, the spectrum of pixel is often the mixing of multiple pure object spectrum.This spectral mixing phenomenon can use linear mixed model or nonlinear mixed model to describe.Only focus on herein in linear mixed model.This model thinks that any one mixed spectra is the linear combination of all end members, and end member ratio shared by mixed spectra is called Abundances.X can be expressed as Abundances matrix and the linear combination of end member matrix, as follows:

X=HW(1)

Wherein,For Abundances matrix,Represent the ratio shared by i-th end member, n in the mixed spectra of each pixel_eRepresent the number of end member,For end member matrix, whereinRepresent each end member.Owing to each end member is had approximate Abundances by adjacent pixel, therefore, Abundances matrix inherits the similarity of spatially neighbor.In order to excavate from Abundances matrix, there is the signal that structure is sparse, use wavelet transform (DWT) for Abundances:

Θ=Ψ^TH(2)

Y=Ψ^TX=Ψ^THW=Θ W

Wherein,For wavelet basis,Representing the wavelet coefficient of Abundances, Y represents the wavelet coefficient of whole data.Represent h_iWavelet coefficient, there is structure openness.It is required for compression data herein exactly and uses the wavelet coefficient that compressed sensing reconstruction is sparse, utilize wavelet coefficient to rebuild Abundances matrix afterwards, finally realize the reconstruction of whole data, specifically comprise the following steps that

1, the acquisition of data is compressed.

The stochastic variable meeting Gauss distribution is used to produce m × n_pThe matrix of size, and every string is normalized and obtains random perception matrixUse Φ that the initial data after wavelet transformation is sampled, obtain compression dataAs follows:

F=Φ Y=Φ Ψ^TX(3)

Wherein, m represents length is n_pSignal Compression after data length, general m < n_p。

2, end member selects.

For the scene of limited dimension, ignore the environmental factors impact on spectrum, it is assumed that end member is Limited Number.Herein use ASTER library of spectra, for specific scene selectively from library of spectra extracting part spectral as end member.Finally determine and comprise n_eThe matrix W of individual end member.Usual fixed scene only comprises a small amount of end member, therefore by the mixed low-rank characteristic that can excavate high-spectral data itself of linear solution.

3, Bayesian inference rebuilds Abundances matrix.

For the accurate reconstruction of initial data, the mode of Bayesian inference is adopted to come from the data estimation Abundances matrix after compression herein.The process of implementing is divided into following step:

(1) by formula (2) and (3), method of least square (Leastsquares) is utilized to obtain the wavelet coefficient of Abundances matrix by the data after individually compressing

G=FW^T(WW^T)^-1=Φ Θ+N(4)

Wherein,Represent the noise item utilizing method of least square and introduce.

(2) the Gauss likelihood function of wavelet structure coefficient.Obtain the vector form g of formula (4)_i=Φ θ_i+n_i, it is assumed that noise n_iObeying average is 0, and covariance isGauss distributionAnd independent same distribution between each noise vector, then can obtain θ_i, i=1,2 ..., n_eLikelihood function:

$p\left(g_i\right|{\mathrm{\&theta;}}_i,{\mathrm{\&beta;}}_i^{-1})={\left(2\mathrm{\&pi;}{\mathrm{\&beta;}}_i^{-1}\right)}^{-\frac{m}{2}}\exp (-\frac{1}{2{\mathrm{\&beta;}}_i^{-1}}{\left|\right|g_i-{\mathrm{\&Phi;\&theta;}}_i\left|\right|}_2^2)---\left(5\right)$

β_iFor the precision of noise vector, specify β herein_iPriori be the distribution of following gamma:

p(β_i|κ₀,υ₀)=Gamma (κ₀,υ₀) (6)

κ₀=10^-6,υ₀=10^-6Form parameter and scale parameter for gamma distribution.

(3) θ is set up_iIn the structural sparse priori of each element.Structural sparse priori is mainly reflected in the tree construction of wavelet coefficient, and when parent node is 0, its child node is also probably 0, and vice versa:

$p\left({\mathrm{\&theta;}}_{s,\mathrm{ji}}\right|{\mathrm{\&beta;}}_{s,i}^{-1})=(1-{\mathrm{\&pi;}}_{s,\mathrm{ji}}){\mathrm{\&delta;}}_0+{\mathrm{\&pi;}}_{s,\mathrm{ji}}N(0,{\mathrm{\&beta;}}_{s,i}^{-1})---\left(7\right)$

Wherein, s represents the yardstick s=1 in wavelet transformation ..., L, L is the total number of yardstick, θ_s,jiRepresent θ_iThe jth element at yardstick s place.δ₀It it is a distribution being totally absorbed in 0 place.π_s,jiIt is a proportionality coefficient, works as π_s,jiWhen tending to 0, θ_s,jiIt is 0, otherwise, π_s,jiWhen tending to 1, θ_s,jiCome from a Gauss distribution.π_s,jiDetermined by the tree construction of wavelet transformation:

${\mathrm{\&pi;}}_{s,\mathrm{ji}}=\left\{\begin{array}{cc}{\mathrm{\&pi;}}_r& \mathrm{ifs}=1\\ {\mathrm{\&pi;}}_s^0& \mathrm{if}2\&le;s\&le;L,{\mathrm{\&theta;}}_{\mathrm{pa}(s,\mathrm{ji})}=0\\ {\mathrm{\&pi;}}_s^1& \mathrm{if}2\&le;s\&le;L,{\mathrm{\&theta;}}_{\mathrm{pa}(s,\mathrm{ji})}\&NotEqual;0\end{array}\right.---\left(8\right)$

θ_pa(s,ji)It is θ_s,jiParent node, work as θ_pa(s,ji)When=0, π_s,jiBeing set to high probability is 0Work as θ_pa(s,ji)When ≠ 0, π_s,jiBeing set to high probability is 1β_s,iIt is θ_s,jiThe precision of Gauss distribution in priori.π_r,And β_s,iPrior distribution as follows:

$\begin{array}{cc}{\mathrm{\&pi;}}_r~\mathrm{Beta}({\mathrm{\&epsiv;}}_0^r,{\mathrm{\&gamma;}}_0^r),& {\mathrm{\&pi;}}_s^0~\mathrm{Beta}({\mathrm{\&epsiv;}}_0^s,{\mathrm{\&gamma;}}_0^s),\\ {\mathrm{\&pi;}}_s^1~\mathrm{Beta}({\mathrm{\&epsiv;}}_1^s,{\mathrm{\&gamma;}}_1^s),& {\mathrm{\&beta;}}_{s,i}~\mathrm{Gamma}({\mathrm{\&kappa;}}_1,{\mathrm{\&upsi;}}_1)\end{array}---\left(9\right)$

Wherein, ${\mathrm{\&kappa;}}_1={10}^{-6},{\mathrm{\&upsi;}}_1={10}^{-6},[{\mathrm{\&epsiv;}}_0^r,{\mathrm{\&gamma;}}_0^r]=\left[\mathrm{0.9,0.1}\right]\&times;N_1,[{\mathrm{\&epsiv;}}_0^s,{\mathrm{\&gamma;}}_0^s,]=[1/n_p,1/n_p]\&times;N_s,$ N_sRepresent wavelet transformation s=1 ..., the number of the wavelet coefficient of L layer.

(4) sampled wavelet coefficient θ_s,ji.Wavelet coefficient θ is obtained by above-mentioned (2), (3) step_s,jiLikelihood function, θ_s,jiStructural sparse priori, and the prior distribution of other unknown parameters.Need the wavelet coefficient Θ estimated, it is possible to obtained by following Bayesian inference:

P (Θ | G) ∝ ∫ p (G | Θ, β) p (Θ | Ω) p (Ω) p (β) d Ω (10)

Wherein, $\mathrm{\&Omega;}=\{{\left\{{\mathrm{\&beta;}}_{s,i}\right\}}_{i=1:n_e}^{s=2:L},{\mathrm{\&pi;}}_r,{\{{\mathrm{\&pi;}}_0^s,{\mathrm{\&pi;}}_1^s\}}_{s=2:L}\},\mathrm{\&beta;}={[{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_2,...,{{\mathrm{\&beta;}}_n}_e]}^T$ For all of noise precision, it is assumed that the element independent same distribution in β and Ω, then p (β) and p (Ω) is as follows respectively:

$p\left(\mathrm{\&beta;}\right)=\underset{i=1}{\overset{n_e}{\mathrm{\&Pi;}}}\mathrm{Gamma}({\mathrm{\&kappa;}}_0,{\mathrm{\&upsi;}}_0),p\left(\mathrm{\&Omega;}\right)=\underset{i=1}{\overset{n_e}{\mathrm{\&Pi;}}}\left\{\begin{array}{c}\underset{s=1}{\overset{L}{\mathrm{\&Pi;}}}\mathrm{Gamma}({\mathrm{\&kappa;}}_1,{\mathrm{\&upsi;}}_1)\&times;\mathrm{Beta}({\mathrm{\&epsiv;}}_0^r,{\mathrm{\&gamma;}}_0^r)\\ \&times;\underset{s=1}{\overset{L}{\mathrm{\&Pi;}}}\mathrm{Beta}({\mathrm{\&epsiv;}}_0^s,{\mathrm{\&gamma;}}_0^s)\mathrm{Beta}({\mathrm{\&epsiv;}}_1^s,{\mathrm{\&gamma;}}_1^s)\end{array}\right\}---\left(11\right)$

Owing to formula (10) is difficult to solve, so adopting the Markov monte carlo method based on gibbs sampler herein.It is similar to the Posterior distrbutionp needing predictor by being distributed sample drawn from corresponding condition.θ_s,jiGibbs sampler as follows:

$\begin{array}{c}p\left({\mathrm{\&theta;}}_{s,\mathrm{ji}}\right|~)=(1-{\mathrm{\&pi;}}_{s,\mathrm{ji}}){\mathrm{\&delta;}}_0+{\mathrm{\&pi;}}_{s,\mathrm{ji}}N({\mathrm{\&mu;}}_{s,\mathrm{ji}},{\mathrm{\&beta;}}_{s,\mathrm{ji}}^{-1})\\ {\mathrm{\&beta;}}_{s,\mathrm{ji}}={\mathrm{\&beta;}}_{s,i}+{\mathrm{\&beta;}}_i{\mathrm{\&Phi;}}_j^T{\mathrm{\&Phi;}}_j,{\mathrm{\&mu;}}_{\mathrm{sji}}={\mathrm{\&beta;}}_{s,\mathrm{ji}}^{-1}{\mathrm{\&Phi;}}_j^T[g_i-\underset{k\&NotEqual;j}{\overset{n_p}{\mathrm{\&Sigma;}}}{\mathrm{\&Phi;}}_k^T{\mathrm{\&Phi;}}_k]\end{array}---\left(12\right)$

Wherein, other parameters needed in the distribution of～expression condition, Φ_jRepresent Φ_jIn jth row.

(5) sampling noiset precision β_i.Sample distribution meets following gamma distribution:

$p\left({\mathrm{\&beta;}}_i\right|~)=\mathrm{Gamma}({{\mathrm{\&kappa;}}_{\mathrm{\&beta;}}}_i,{{\mathrm{\&upsi;}}_{\mathrm{\&beta;}}}_i),{{\mathrm{\&kappa;}}_{\mathrm{\&beta;}}}_i={\mathrm{\&kappa;}}_0+\frac{m}{2},{{\mathrm{\&upsi;}}_{\mathrm{\&beta;}}}_i={\mathrm{\&upsi;}}_0+\frac{1}{2}{(g_i-{\mathrm{\&Phi;\&theta;}}_i)}^T(g_i-{\mathrm{\&Phi;\&theta;}}_i)---\left(13\right)$

(6) sampling hyper parameterConcrete sample distribution is as follows:

$p\left({\mathrm{\&beta;}}_{s,i}\right|~)=\mathrm{Gamma}({{\mathrm{\&kappa;}}_{\mathrm{\&beta;}}}_{s,i},{{\mathrm{\&upsi;}}_{\mathrm{\&beta;}}}_{s,i}),{{\mathrm{\&kappa;}}_{\mathrm{\&beta;}}}_{s,i}={\mathrm{\&kappa;}}_1+\frac{1}{2}\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}1({\mathrm{\&theta;}}_{s,\mathrm{ji}}\&NotEqual;0),{{\mathrm{\&upsi;}}_{\mathrm{\&beta;}}}_{s,j}={\mathrm{\&upsi;}}_1+\frac{1}{2}\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}{\mathrm{\&theta;}}_{s,\mathrm{ji}}^2---\left(14\right)$

$p\left({\mathrm{\&pi;}}_r\right|~)=\mathrm{Gamma}({{\mathrm{\&epsiv;}}_{\mathrm{\&pi;}}}_r,{{\mathrm{\&gamma;}}_{\mathrm{\&pi;}}}_r),{{\mathrm{\&epsiv;}}_{\mathrm{\&pi;}}}_r={\mathrm{\&epsiv;}}_0^r+\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}1({\mathrm{\&theta;}}_{s,\mathrm{ji}}\&NotEqual;0),{{\mathrm{\&gamma;}}_{\mathrm{\&pi;}}}_r={\mathrm{\&gamma;}}_0^r+\frac{1}{2}\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}1({\mathrm{\&theta;}}_{s,\mathrm{ji}}=0)---\left(15\right)$

$\begin{array}{c}p\left({\mathrm{\&pi;}}_{s,i}^0\right|~)=\mathrm{Gamma}({\mathrm{\&epsiv;}}_{{\mathrm{\&pi;}}_{s,i}^0},{\mathrm{\&gamma;}}_{{\mathrm{\&pi;}}_{s,i}^0})\\ {\mathrm{\&epsiv;}}_{{\mathrm{\&pi;}}_{s,i}^0}={\mathrm{\&epsiv;}}_0^s+\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}1({\mathrm{\&theta;}}_{s,\mathrm{ji}}\&NotEqual;0,{\mathrm{\&theta;}}_{\mathrm{pa}(s,\mathrm{ji})}=0),{\mathrm{\&gamma;}}_{{\mathrm{\&pi;}}_{s,i}^0}={\mathrm{\&gamma;}}_0^s+\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}1({\mathrm{\&theta;}}_{s,\mathrm{ji}}=0,{\mathrm{\&theta;}}_{\mathrm{pa}(s,\mathrm{ji})}=0)\end{array}---\left(16\right)$

$\begin{array}{c}p\left({\mathrm{\&pi;}}_{s,i}^1\right|~)=\mathrm{Gamma}({\mathrm{\&epsiv;}}_{{\mathrm{\&pi;}}_{s,i}^1},{\mathrm{\&gamma;}}_{{\mathrm{\&pi;}}_{s,i}^1})\\ {\mathrm{\&epsiv;}}_{{\mathrm{\&pi;}}_{s,i}^1}={\mathrm{\&epsiv;}}_1^s+\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}1({\mathrm{\&theta;}}_{s,\mathrm{ji}}\&NotEqual;0,{\mathrm{\&theta;}}_{\mathrm{pa}(s,\mathrm{ji})}\&NotEqual;0),{\mathrm{\&gamma;}}_{{\mathrm{\&pi;}}_{s,i}^1}={\mathrm{\&gamma;}}_1^s+\underset{j=1}{\overset{N_s}{\mathrm{\&Sigma;}}}1({\mathrm{\&theta;}}_{s,\mathrm{ji}}=0,{\mathrm{\&theta;}}_{\mathrm{pa}(s,\mathrm{ji})}\&NotEqual;0)\end{array}---\left(17\right)$

Wherein, 1 (x) is 1 when x is genuine, is otherwise 0.

(7) circulating execution (4), (5), (6) three steps successively for each wavelet coefficient in Θ to sample, until meeting the condition of convergence or end condition, obtaining the wavelet coefficient of final estimationM_sFor total number of sampling,For the result sampled each time.End condition used herein is iterations, wherein, sampler stable process 400 times, sampling process 200 times.

4, high-spectral data is rebuild.

The high-spectral data rebuild is obtained according to linear mixed model (1)

Claims (1)

1. the mixed compression sensing method of the Bayes's EO-1 hyperion solution based on structural sparse priori, it is characterised in that comprise the following steps:

Step one, for a panel height spectroscopic datan_pRepresent total number of pixels that high-spectral data spatially comprises, n_bRepresent the wave band number that high-spectral data comprises, x_i, i=1 ..., n_bRepresent that the image of each wave band launches the column vector formed by row；Each pixel is at n_bDifferent reflected values on individual wave band constitute the spectrum of this pixel；This spectrum adopts linear mixed model to describe；Linear mixed model thinks that any one mixed spectra is the linear combination of all end members, and end member ratio shared by mixed spectra is called Abundances；X represents Abundances matrix and the linear combination of end member matrix:

X=HW (1)

Wherein,For Abundances matrix,Represent the ratio shared by i-th end member, n in the mixed spectra of each pixel_eRepresent the number of end member,For end member matrix, whereinRepresent each end member；

Wavelet transform is used for Abundances:

Wherein,For wavelet basis,Representing the wavelet coefficient of Abundances, Y represents the wavelet coefficient of whole data；Represent h_iWavelet coefficient, there is structure openness；

Step 2, utilize wavelet coefficient rebuild Abundances matrix, finally realize the reconstruction of whole data:

Step 1, use meet the stochastic variable of Gauss distribution and produce m × n_pThe matrix of size, and every string is normalized and obtains random perception matrixUse Φ that the initial data after wavelet transformation is sampled, obtain compression data

F=Φ Y=Φ Ψ^TX(3)

Wherein, m represents length is n_pSignal Compression after data length, general m < n_p；

Step 2, for the scene of limited dimension, ignore the environmental factors impact on spectrum, it is assumed that end member is Limited Number；Use ASTER library of spectra, for specific scene selectively from library of spectra extracting part spectral as end member；Finally determine and comprise n_eThe matrix W of individual end member；

Step 3, adopt Bayesian inference mode from compression after data estimation Abundances matrix；

(1) by formula (2) and formula (3), method of least square is utilized to obtain the wavelet coefficient of Abundances matrix by the data after individually compressing

G=FW^T(WW^T)^-1=Φ Θ+N (4)

Wherein,Represent the noise item utilizing method of least square and introduce；

(2) the vector form g of formula (4) is obtained_i=Φ θ_i+n_i, it is assumed that noise n_iObeying average is 0, and covariance isGauss distributionAnd independent same distribution between each noise vector, then obtain θ_i, i=1,2 ..., n_eLikelihood function:

β_iPrecision for noise vector, it is intended that β_iPriori be the distribution of following gamma:

p(β_i|κ₀,υ₀)=Gamma (κ₀,υ₀)(6)

κ₀=10^-6,υ₀=10^-6Form parameter and scale parameter for gamma distribution；

(3) θ is set up_iIn the structural sparse priori of each element；Structural sparse priori is mainly reflected in the tree construction of wavelet coefficient, and when parent node is 0, its child node is also probably 0, and vice versa:

Wherein, s represents the yardstick s=1 in wavelet transformation ..., L, L is the total number of yardstick, θ_s,jiRepresent θ_iThe jth element at yardstick s place；δ₀It it is a distribution being totally absorbed in 0 place；π_s,jiIt is a proportionality coefficient, works as π_s,jiWhen tending to 0, θ_s,jiIt is 0, otherwise, π_s,jiWhen tending to 1, θ_s,jiCome from a Gauss distribution；π_s,jiDetermined by the tree construction of wavelet transformation:

θ_pa(s,ji)It is θ_s,jiParent node, work as θ_pa(s,ji)When=0, π_s,jiBeing set to high probability is 0Work as θ_pa(s,ji)When ≠ 0, π_s,jiBeing set to high probability is 1β_s,iIt is θ_s,jiThe precision of Gauss distribution in priori；π_r, And β_s,iPrior distribution as follows:

Wherein, κ₁=10-⁶,υ₁=10^-6, N_sRepresent wavelet transformation s=1 ..., the number of the wavelet coefficient of L layer；

(4) sampled wavelet coefficient θ_s,ji；Wavelet coefficient θ is obtained by above-mentioned (2), (3) step_s,jiLikelihood function, θ_s,jiStructural sparse priori, and the prior distribution of other unknown parameters；Need the wavelet coefficient Θ estimated, obtained by following Bayesian inference:

p(Θ|G)∝∫p(G|Θ,β)p(Θ|Ω)p(Ω)p(β)dΩ(10)

Wherein,For all of noise precision, it is assumed that the element independent same distribution in β and Ω, then p (β) and p (Ω) is as follows respectively:

Adopt the Markov monte carlo method based on gibbs sampler, be similar to, by being distributed sample drawn from corresponding condition, the Posterior distrbutionp needing predictor；θ_s,jiGibbs sampler as follows:

Wherein, other parameters needed in the distribution of～expression condition, Φ_jRepresent Φ_jIn jth row；

(5) sampling noiset precision β_i；Sample distribution meets following gamma distribution:

(6) sampling hyper parameterConcrete sample distribution is as follows:

Wherein, 1 (x) is 1 when x is genuine, is otherwise 0；

(7) circulating execution (4), (5), (6) three steps successively for each wavelet coefficient in Θ to sample, until meeting the condition of convergence or end condition, obtaining the wavelet coefficient of final estimationM_sFor total number of sampling,For the result sampled each time；The end condition used is iterations, wherein, sampler stable process 400 times, sampling process 200 times；

Step 4, according to linear mixed model (1) obtain rebuild high-spectral data