CN104036509A - Method for unmixing hyperspectral mixed pixel based on compressed sensing - Google Patents

Abstract

The invention relates to a method for unmixing a hyperspectral mixed pixel based on compressed sensing, and relates to the compressed sensing field and the hyperspectral remote sensing field. The method is used for solving the problem of low mixed pixel unmixing speed during hyperspectral image data acquisition by use of the traditional Nyquist sampling theorem. The method comprises the steps of firstly, inputting a measurement matrix Phi and a compressed measurement matrix Y and establishing a spectral mixing model Y=PhiXT=Phi(AS)T by use of the compressed sensing theory, secondly, performing iterative processing on the estimated value S^ of an end member abundance matrix S and the estimated value A^ of an end member spectrum matrix A, and if the difference of absolute values of every corresponding element in the estimated values A^ of the end member spectrum matrix A obtained by two adjacent times of iterative processing is smaller than 0.1, stopping iteration and outputting the end member abundance matrix S^ and completing the unmixing of the hyperspectral mixed pixel, otherwise, continuing the iterative processing. The method is mainly applied to unmixing the hyperspectral mixed pixels.

Description

A kind of method that high spectral mixing pixel based on compressed sensing decomposes

Technical field

The present invention relates to compressed sensing field and high-spectrum remote-sensing field.

Background technology

High light spectrum image-forming technology is a kind of novel earth observation technology that remote sensing field grows up, and typical hardware device is imaging spectrometer.Imaging spectrometer, by light splitting technology, is decomposed into many small, adjacent wave bands by electromagnetic wave signal, and the energy on corresponding wave band is received by different sensors.Therefore compare with traditional remotely sensed image technology, high light spectrum image-forming technology has that collection of illustrative plates unification, spectral band are many, spectral resolution high, and has larger advantage at aspects such as terrestrial materials identification and classification, feature extractions.The spatial resolution of high spectrum image is lower, therefore inevitably can produce mixed pixel, and the existence of mixed pixel becomes the obstacle further developing of high-spectrum remote-sensing application.If the Decomposition of Mixed Pixels of high spectrum image is obtained to the corresponding abundance of each end member, high-spectrum remote sensing data being carried out to " blind " decomposition will have very important meaning.

Blind source separate technology refers to the in the situation that of source signal and the equal the unknown of hybrid mode, according to the statistical property of source signal, only by the mixed signal observing, is recovered the process of source signal." blind " has two kinds of explanations: a kind of is except observation signal, and other information is all unknown, is called " total blindness "; Another kind is that some prior imformation of signal or commingled system is known, is called " half-blindness ".For the problem of Decomposition of Mixed Pixels, blind source separate technology obtains end member spectrum and end member abundance simultaneously, realizes the blind decomposition of mixed pixel.Before processing Decomposition of Mixed Pixels problem, need to set up spectral mixing model.Spectral mixing mode mainly comprises linear hybrid and non-linear mixing, and Areca trees model is current most widely used Pixel Unmixing Models, and its expression formula is:

$X=\underset{i=1}{\overset{P}{\mathrm{\Σ}}}{A}_i{s}_i=\mathrm{AS}---(1-1)$

In formula, X=[x ₁... x _l... x _l] ^t∈ R ^{l * 1}being the mixed pixel spectrum of a pixel L wave band, is known observed quantity; A ∈ R ^{l * P}for end member spectrum matrix, wherein the spectrum of the corresponding end member of each row is vectorial; P is end member number, S ∈ R ^{p * 1}abundance vector for this mixed pixel.Abundance vector need to meet two constraint conditions: non-negativity constraint and be 1 constraint.

s _i≥0,i∈{1,2,...,P} (2-1)

$\underset{i=1}{\overset{P}{\mathrm{\Σ}}}{s}_i=1,i\∈\{\mathrm{1,2},...,P\}---(3-1)$

If high spectrum image has N pixel, formula (1-1) can extend further to formula (4-1).

X＝AS (4-1)

X ∈ R in formula (4-1) ^{l * N}, its column vector represents that each pixel is at the mixed spectra vector of L wave band, S ∈ R ^{p * N}formed end member abundance matrix.End member abundance matrix meets following constraint condition:

s _i,j≥0,i∈{1,2,...,P},j∈{1,2,...,N} (5-1)

$\underset{i=1}{\overset{P}{\mathrm{\Σ}}}{s}_{i,j}=1,j\∈\{\mathrm{1,2},...,N\}---(6-1)$

Mixed pixel of hyper-spectral image resolution problem based on blind source separate technology in the situation that of end member matrix and the equal the unknown of abundance matrix, utilizes the observed reading of mixed pixel spectrum to recover end member spectrum and end member abundance.

The many features of wave band number of high spectrum image make the data volume of high spectrum image huge, if adopt traditional nyquist sampling theorem to data acquisition, will produce huge pressure to the sample rate of hardware, transmission speed and storage capacity.The proposition of compressive sensing theory has solved this difficult problem, and this theory is pointed out to meet sparse property or when compressible, can to signal, carry out overall situation observation with the speed far below nyquist sampling rate when signal, then adopts compressed sensing restructing algorithm to recover source signal.High spectrum image is sparse in wavelet field, therefore compressive sensing theory can be applied to in the sampling of high spectrum image.Concrete sampling process can be expressed as following formula:

Y＝ΦX ^T＝Φ(AS) ^T

In above-mentioned formula, Φ ∈ R ^{m * N}for observing matrix, X ∈ R ^{l * N}for mixed pixel spectrum matrix, Y ∈ R ^{m * L}for compression observing matrix.

Summary of the invention

The present invention is when solving the traditional nyquist sampling theorem of existing employing to high spectrum image data acquisition, and the slow-footed problem of Decomposition of Mixed Pixels the invention provides a kind of method that high spectral mixing pixel based on compressed sensing decomposes.

The method that high spectral mixing pixel based on compressed sensing decomposes, the method is,

Step 1, input observing matrix Φ and compression observing matrix Y, utilize compressive sensing theory, sets up spectral mixing model:

Y＝ΦX ^T＝Φ(AS) ^T (1)

Φ ∈ R ^{m * N}for the observing matrix of M * N, R is real number,

X ∈ R ^{l * N}for the mixed pixel spectrum matrix of L * N,

Y ∈ R ^{m * L}for the compression observing matrix of M * L,

S ∈ R ^{p * N}for the end member abundance matrix of P * N,

A ∈ R ^{l * P}for the end member spectrum matrix of L * P,

Step 2, initialization, chooses an end member spectrum matrix A at random as the estimated value of end member spectrum matrix A and for the matrix of L * P,

Make the estimated value of end member abundance matrix S:

$\hat{S}={\left[\begin{array}{ccc}0& ...& 0\\ & ...& \\ 0& & 0\end{array}\right]}_{N\×P}---\left(2\right)$

Wherein, for the matrix of N * P,

Step 3, the initial value that makes iterations variable t is 1;

Step 4, the estimated value to end member abundance matrix S estimated value with end member spectrum matrix A carry out iterative processing;

Step 5 is multiplied by formula (1) both sides simultaneously pseudoinverse, formula (1) is deformed into

Y ₁＝ΦS ^T (3)，

Step 6, establishing wavelet basis is Θ, and Σ is the sparse coefficient of end member abundance, and formula (3) is deformed into

Y ₁＝Φ(ΘΣ) ^T (4)，

Adopt BP Algorithm for Solving following formula:

argmin||Σ|| ₁ s.t. Y ₁＝Φ(ΘΣ) ^T (5)，

Obtain the estimated value of end member abundance matrix S

$\hat{S}=---\mathrm{\Θ\Σ}\left(6\right),$

Step 7 is P (S at probability density function _k) ∝ α exp (α | S _k|) condition under, the estimated value of normalization end member spectrum matrix A column vector, upgrade the estimated value of end member spectrum matrix A ,

$\hat{A}=A_1+\mathrm{\λ}\{-A_1(B{\hat{S}}^T+I)\}---\left(7\right),$

Wherein, A ₁the estimated value of the end member spectrum matrix obtaining for last iteration, λ is iteration step length, and I is unit matrix, and B is vector set, and B={B ₁, B ₂, B ₃... B _k, be the prior probability distribution of k source signal, k is integer, and α is greater than zero real number,

Step 8, if the estimated value of the end member spectrum matrix A of adjacent twice acquisition the difference of the absolute value of each element of middle correspondence is less than at 0.1 o'clock, stops iteration, execution step nine, otherwise, make t=t+1, and return to step 4;

Step 9, output end member abundance matrix complete the decomposition to high spectral mixing pixel.

The beneficial effect that the present invention brings is that the evaluation index of end member abundance matrix S is adopted to average signal-to-noise ratio SNR _avgrealize,

${\mathrm{SNR}}_{\mathrm{avg}}=\frac{1}{P}\underset{k=1}{\overset{P}{\mathrm{\Σ}}}20\×{\log }_{10}\left(\frac{\left|\right|S_k{\left|\right|}_2}{{\left|\right|S_k-{\hat{S}}_k\left|\right|}_2}\right)---\left(8\right)$

End member number P=3 of the high spectrum image adopting in experiment, wave band is counted L=40, and the pixel of high spectrum is counted N=32 * 32.When compressed sensing is sampled, compressibility is 0.8, to the average signal-to-noise ratio of the end member abundance matrix of Decomposition of Mixed Pixels, is 17.78dB, can realize preferably separation, and Decomposition of Mixed Pixels speed has been improved more than 40%.

Embodiment

Embodiment one: the method that a kind of high spectral mixing pixel based on compressed sensing described in present embodiment decomposes, the method is,

Step 1, input observing matrix Φ and compression observing matrix Y, utilize compressive sensing theory, sets up spectral mixing model:

Y＝ΦX ^T＝Φ(AS) ^T (1)

Φ ∈ R ^{m * N}for the observing matrix of M * N, R is real number,

X ∈ R ^{l * N}for the mixed pixel spectrum matrix of L * N,

Y ∈ R ^{m * L}for the compression observing matrix of M * L,

S ∈ R ^{p * N}for the end member abundance matrix of P * N,

A ∈ R ^{l * P}for the end member spectrum matrix of L * P,

Step 2, initialization, chooses an end member spectrum matrix A at random as the estimated value of end member spectrum matrix A and for the matrix of L * P,

Make the estimated value of end member abundance matrix S:

$\hat{S}={\left[\begin{array}{ccc}0& ...& 0\\ & ...& \\ 0& & 0\end{array}\right]}_{N\×P}---\left(2\right)$

Wherein, for the matrix of N * P,

Step 3, the initial value that makes iterations variable t is 1;

Step 4, the estimated value to end member abundance matrix S estimated value with end member spectrum matrix A carry out iterative processing;

Step 5 is multiplied by formula (1) both sides simultaneously pseudoinverse, formula (1) is deformed into

Y ₁＝ΦS ^T (3)，

Step 6, establishing wavelet basis is Θ, and Σ is the sparse coefficient of end member abundance, and formula (3) is deformed into

Y ₁＝Φ(ΘΣ) ^T (4)，

Adopt BP Algorithm for Solving following formula:

argmin||Σ|| ₁ s.t. Y ₁＝Φ(ΘΣ) ^T (5)，

Obtain the estimated value of end member abundance matrix S

$\hat{S}=---\mathrm{\Θ\Σ}\left(6\right),$

Step 7 is P (S at probability density function _k) ∝ α exp (α | S _k|) condition under, the estimated value of normalization end member spectrum matrix A column vector, upgrade the estimated value of end member spectrum matrix A

$\hat{A}=A_1+\mathrm{\λ}\{-A_1(B{\hat{S}}^T+I)\}---\left(7\right),$

Wherein, A ₁the estimated value of the end member spectrum matrix obtaining for last iteration, λ is iteration step length, and I is unit matrix, and B is vector set, and B={B ₁, B ₂, B ₃... B _k, be the prior probability distribution of k source signal, k is integer, and α is greater than zero real number,

Step 8, if the estimated value of the end member spectrum matrix A of adjacent twice acquisition the difference of the absolute value of each element of middle correspondence is less than at 0.1 o'clock, stops iteration, execution step nine, otherwise, make t=t+1, and return to step 4;

Step 9, output end member abundance matrix complete the decomposition to high spectral mixing pixel.

Claims (1)

1. the method that the high spectral mixing pixel based on compressed sensing decomposes, is characterized in that, the method is,

Step 1, input observing matrix Φ and compression observing matrix Y, utilize compressive sensing theory, sets up spectral mixing model:

Y＝ΦX ^T＝Φ(AS) ^T (1)

Φ ∈ R ^{m * N}for the observing matrix of M * N, R is real number,

X ∈ R ^{l * N}for the mixed pixel spectrum matrix of L * N,

Y ∈ R ^{m * L}for the compression observing matrix of M * L,

S ∈ R ^{p * N}for the end member abundance matrix of P * N,

A ∈ R ^{l * P}for the end member spectrum matrix of L * P,

Step 2, initialization, chooses an end member spectrum matrix A at random as the estimated value of end member spectrum matrix A and for the matrix of L * P,

Make the estimated value of end member abundance matrix S:

$\hat{S}={\left[\begin{array}{ccc}0& ...& 0\\ & ...& \\ 0& & 0\end{array}\right]}_{N\×P}---\left(2\right)$

Wherein, for the matrix of N * P,

Step 3, the initial value that makes iterations variable t is 1;

Step 4, the estimated value to end member abundance matrix S estimated value with end member spectrum matrix A carry out iterative processing;

Step 5 is multiplied by formula (1) both sides simultaneously pseudoinverse, formula (1) is deformed into

Y ₁＝ΦS ^T (3)，

Step 6, establishing wavelet basis is Θ, and Σ is the sparse coefficient of end member abundance, and formula (3) is deformed into

Y ₁＝Φ(ΘΣ) ^T (4)，

Adopt BP Algorithm for Solving following formula:

argmin||Σ|| ₁ s.t. Y ₁＝Φ(ΘΣ) ^T (5)，

Obtain the estimated value of end member abundance matrix S

$\hat{S}=---\mathrm{\Θ\Σ}\left(6\right),$

Step 7 is P (S at probability density function _k) ∝ α exp (α | S _k|) condition under, the estimated value of normalization end member spectrum matrix A column vector, upgrade the estimated value of end member spectrum matrix A

$\hat{A}=A_1+\mathrm{\λ}\{-A_1(B{\hat{S}}^T+I)\}---\left(7\right),$

Wherein, A ₁the estimated value of the end member spectrum matrix obtaining for last iteration, λ is iteration step length, and I is unit matrix, and B is vector set, and B={B ₁, B ₂, B ₃... B _k, be the prior probability distribution of k source signal, k is integer, and α is greater than zero real number,

Step 8, if the estimated value of the end member spectrum matrix A of adjacent twice acquisition the difference of the absolute value of each element of middle correspondence is less than at 0.1 o'clock, stops iteration, execution step nine, otherwise, make t=t+1, and return to step 4;

Step 9, output end member abundance matrix complete the decomposition to high spectral mixing pixel.