CN103426167A - Hyperspectral real-time detection method based on recursive analysis - Google Patents

Abstract

The invention relates to a hyperspectral real-time detection method based on recursive analysis. The method is characterized by including 1, establishing a spectral vector related matrix R(n) of hyperspectral image pixels; 2, establishing a state equation for the related matrix R(n), and updating an estimated value of current state according to an observed value rn of current state and an estimated value R(n-1) of previous state; 3, updating an inverse matrix R(n)-1 of the related matrix R(n) by a Woodbury identical equation; 4, detecting a hyperspectral image in real time by anomaly detection operators. In the state equation, R(n-1) refers an estimated value of the previous state, and rn refers to an observed value of the current state.

Description

A kind of high spectrum real-time detection method based on recursive analysis

Technical field

The present invention relates to a kind of high spectrum real-time detection method based on recursive analysis.

Background technology

The appearance of high-spectrum remote-sensing is a revolution of remote sensing technology.Along with the raising of spectral resolution, it is surveyed the atural object that originally can't effectively survey in multispectral remote sensing, thereby is widely used.Under a lot of actual conditions, the researcher does not always have enough prioris to characterize other statistical information of target class, for example the cancer cell in the vehicle in the abnormal migration in the specialized species of agronomy, ecology, the rare mineral in geology, the toxic waste excretion in environmental monitoring and Oil spills, battlefield or aircraft, medical diagnosis or tumour etc.Therefore, the hyperspectral image abnormal detection without priori has obtained paying close attention to more and more widely.

In actual abnormality detection, detect in real time particularly importantly, this is because many abnormal objects, moving target for example, its residence time is very short, can occur suddenly then disappearing soon.Therefore, want to realize the detection of this abnormal object, its processing procedure must be real-time.Yet, existing detection method is to utilize single order and second-order statistics, as sample average and covariance matrix etc. design high spectral singularity and detect operator, need complete high-spectral data information and calculate these statistical properties, thereby can not realize real-time detection.On the other hand, along with the develop rapidly of modern Remote Sensing Technical, high-spectrum remote-sensing is when obtaining and more enriching terrestrial object information, and its a large amount of data volume also to line number under data storage, satellite, passes and subsequent treatment has been brought huge pressure.

Summary of the invention

The object of the invention is to provide a kind of high spectrum real-time detection method based on recursive analysis, can realize accurately and effectively the real-time detection to high spectrum image, and can effectively reduce the storage space of data.

Realize the object of the invention technical scheme:

A kind of high spectrum real-time detection method based on recursive analysis is characterized in that:

Step 1: the spectrum vector correlation matrix R (n) that sets up the high spectrum image pixel;

Step 2: set up the state equation of correlation matrix R (n),

$R\left(n\right)=\frac{n-1}{n}R(n-1)+\frac{1}{n}{r}_n{r_n}^T$

In formula, R (n-1) is the estimated value of a upper moment state, r _nThe observed reading of current state,

Observed reading r according to current state _nWith the estimated value R (n-1) of a upper moment state, upgrade the estimated value of current state;

Step 3: utilize the Woodbury identical relation to upgrade the inverse matrix R (n) of correlation matrix R (n) ^-1

Step: 4: high spectrum image is detected in real time in conjunction with the abnormality detection operator.

Preferably, in step 3, utilize the Woodbury identical relation to derive, inverse matrix R (n) ^-1Computing formula as follows:

R(n) ^-1＝n[(n-1)R(n-1)+r _nr _n ^T] ^-1；

$R{\left(n\right)}^{-1}=\frac{n}{n-1}{R(n-1)}^{-1}-\frac{{\mathrm{nR}(n-1)}^{-1}{r}_n{r_n}^T{R(n-1)}^{-1}}{{(n-1)}^2+(n-1){r_n}^T{R(n-1)}^{-1}{r}_n}$

In formula, R (n-1) ^-1Inverse matrix for a upper correlation matrix.

Preferably, in step 1, correlation matrix

In formula, r _nCurrent pixel n to be detected ^ThThe spectrum vector, r _i=[r _1i, r _2i..., r _Li] ^TI ^ThThe spectrum vector of pixel, wherein, L is the number of wave band.

Preferably, in step 4, the abnormality detection operator adopts the RX operator, and formula is as follows:

${\mathrm{\δ}}^{\mathrm{RTC}-R-\mathrm{RXD}}\left(r_n\right)=r_n^T[\frac{n}{n-1}{R(n-1)}^{-1}-\frac{\mathrm{nR}{(n-1)}^{-1}{r}_n{r_n}^T{R(n-1)}^{-1}}{{(n-1)}^2+{{(n-1)r}_n}^T{R(n-1)}^{-1}{r}_n}]r_n.$

The beneficial effect that the present invention has:

The present invention is applied to the high spectrum image Data processing by kalman filtering theory, utilize the recurrence thought of kalman filtering theory to draw correlation matrix R (n) recurrence formula, thereby can be only with the pixel of current transmission before information surveyed, and information after not needing to use realizes the real-time process that process on transmission limit, data limit.The present invention draws correlation matrix R (n) inverse matrix R (n) by the Woodbury identical relation ^-1Recurrence express, upgrade the inverse matrix R (n) of correlation matrix ^-1, and, without preserving existing information and recalculating existing information, when reducing the required storage space of data, greatly improved the algorithm travelling speed, more effectively realize detecting in real time.The present invention can not only be combined with classical RX operator, also can be combined with other operators that hyperspectral image abnormal detects simultaneously, has very strong portability, more easily meets the demand that high spectrum image detects.

Advantage of the present invention is specific as follows:

1) because R (n) only needs current pixel r _nInformation in the past, and therefore image element information after not using can realize the real-time process that process on transmission limit, data limit;

2) without double counting R (n) and R (n) ^-1Can greatly reduce the operation time of algorithm, improve operator speed;

3) owing to calculating R (n) ^-1Only need R (n-1) ^-1And r _n, therefore only need storage R (n-1) ^-1With record current input pixel r _nAnd, without the existing image element information of storage, can greatly reduce the required storage space of operator.

The accompanying drawing explanation

Fig. 1 is the real high spectrum image data of a width;

Fig. 2 is synthetic high spectrum image data;

Fig. 3 is the testing result gray-scale map after the classical R-RXD abnormality detection operator of employing;

Fig. 4 is the testing result gray-scale map after the high spectrum real-time detection algorithm adopted based on recursive analysis;

Fig. 5 is algorithm flow chart.

Embodiment

Step 1: the spectrum vector correlation matrix R (n) that sets up the high spectrum image pixel.The spectrum vector of supposing to have the high spectrum image pixel of L wave band can be expressed as a L dimensional vector r _i=[r _1i, r _2i..., r _Li] ^T, correlation matrix is expressed as follows:

$R\left(n\right)=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{r}_i{r_i}^T---\left(1\right)$

Wherein, r _nCurrent pixel (n to be detected ^Th) the spectrum vector, r _i=[r _1i, r _2i..., r _Li] ^TI ^ThThe spectrum vector of pixel, wherein, L is the number of wave band.

Step 2: set up the state equation of correlation matrix R (n),

$R\left(n\right)=\frac{n-1}{n}R(n-1)+\frac{1}{n}{r}_n{r_n}^T---\left(2\right)$

In formula, R (n-1) is the estimated value of a upper moment state, r _nThe observed reading of current state,

Observed reading r according to current state _nWith the estimated value R (n-1) of a upper moment state, upgrade the estimated value of current state;

Kalman filtering theory is a kind of recursive analysis, as long as know that the observed reading of the upper estimated value once moment state and current state can calculate the estimated value of current state, does not therefore need the historical information of hourly observation or estimation,

According to this theory, the iteration that obtains above-mentioned correlation matrix R is new formula (2) more.

Step 3: utilize the Woodbury identical relation to upgrade the inverse matrix R (n) of correlation matrix R (n) ^-1.

In mathematics, especially in linear algebra, the Woodbury identical relation points out, some inverse of a matrix battle array with k rank modifying factor can mean by original matrix inverse matrix and k rank modifying factor thereof.This criterion is called again the lemma of matrix inverse matrix, Sherman-Morrison-Woodbury lemma or directly be referred to as Woodbury lemma, and this lemma can be expressed as follows:

(A+UCV) ^-1＝A ^-1-A ^-1U(C ^-1+VA ^-1U) ^-1VA ^-1 (3)

Wherein, A, U, C and V are the matrixes with specific size, and A is n * n matrix, and U is n * k matrix, and C is k * k matrix, V is k * n matrix.At this, if the dimension of Matrix C is far smaller than matrix A, the efficiency of this equation will be far away higher than directly calculating the inverse matrix of (A+UCV).Especially when C be 1 * 1 unit matrix formula, equation (3) can be simplified to the Sherman-Morrison identical relation, is expressed as follows

(A+UV) ^-1＝A ^-1-A ^-1U(1+VA ^-1U) ^-1VA ^-1 (4)

Utilize Woodbury identical relation (4) can effectively avoid the calculating of correlation matrix and covariance matrix inverse matrix, the recurrence of realization matrix inverse matrix is upgraded.

Utilize Woodbury identical relation (4), the recurrence of correlation matrix inverse matrix is expressed as

R(n) ^-1＝n[(n-1)R(n-1)+r _nr _n ^T] ^-1 (5)

By lemma (4), make A=(n-1) R (n-1), u=v=r again _n, the correlation matrix inverse matrix can further be expressed as

${R\left(n\right)}^{-1}=\frac{n}{n-1}{R(n-1)}^{-1}-\frac{\mathrm{nR}{(n-1)}^{-1}{r}_n{r_n}^T{R(n-1)}^{-1}}{{(n-1)}^2+{{(n-1)r}_n}^T{R(n-1)}^{-1}{r}_n}---\left(6\right)$

Can be according to the inverse matrix R (n-1) of previous correlation matrix by formula (6) ^-1With current new pixel r _nUpgrade R (n) ^-1, realize R (n) ^-1Recursive calculation.

Step: 4: high spectrum image is detected in real time in conjunction with the abnormality detection operator.In the present embodiment, the abnormality detection operator adopts the RX operator, and formula is as follows:

${\mathrm{\δ}}^{\mathrm{RTC}-R-\mathrm{RXD}}\left(r_n\right)=r_n^T[\frac{n}{n-1}R{(n-1)}^{-1}-\frac{\mathrm{nR}{(n-1)}^{-1}{r}_n{r_n}^{T}R{(n-1)}^{-1}}{{(n-1)}^2+{{(n-1)r}_n}^T{R(n-1)}^{-1}{r}_n}]r_n.---\left(7\right)$

Below in conjunction with concrete experiment, further the inventive method is described.With reference to Fig. 1, be the real high spectrum image data of a width, a certain mining area that experimental data is the state of Nevada, taken in 1997.This AVIRIS hyperspectral imager has 224 wave bands, and the view data size is 350 * 350.Removing 1-3, the water absorption bandses such as 105-115 and 150-170 are the low signal-to-noise ratio wave band, and the 189-wave band data is for follow-up test.In the figure of Fig. 1 (b), provided the geographic distribution of five kinds of atural objects: A, B, C, K, M.Provide the spectral information of five kinds of atural objects and the spectral information of background mean value in figure (c), utilized these spectral characteristics, designed generated data as shown in Figure 1.

With reference to Fig. 2, this figure is synthetic by the true high spectrum image data of Fig. 1.This generated data size is 200 * 100, and 5 * 3=15 abnormity point arranged.These 15 abnormal objects generate as follows: with figure's (c) in Fig. 1

Five kinds of abnormal objects of spectral characteristic simulation of five kinds of materials, every row abnormal object consists of material of the same race.The pure picture dot that wherein first row is 4 * 4 by five kinds of sizes forms, the pure picture dot that secondary series is 2 * 2 by five kinds of sizes forms, the 3rd classifies the mixed pixel that size is 1 * 1 as, the background spectrum characteristic of 70% abnormal picture dot spectral characteristic+30% wherein, as shown in Table 1 below.Fig. 2 can be used for detecting anomaly detection and the detection of inferior picture dot of different sizes.

Table 1

With reference to Fig. 3, it is the testing result gray-scale map after the classical R-RXD abnormality detection operator of employing.With classical R-RXD abnormality detection operator the time, correlation matrix R adopts overall correlation matrix R, thereby can't realize real-time detection.

With reference to Fig. 4, for the ease of analyzing relatively, the real-time detection that Fig. 4 has provided the high spectrum real-time detection algorithm based on recursive analysis is gray-scale map as a result.Detect operator and adopt the RX operator.Wherein the figure in Fig. 4 (a) is the real-time detection gray-scale map of the operator that not yet notes abnormalities, figure (b) detects first row abnormal object (abnormal object consisted of substance A), figure (c) detects secondary series abnormal object (abnormal object consisted of substance B), figure (d) detects the 3rd row abnormal object (abnormal object consisted of substance C), figure (e) detects the 4th row abnormal object (abnormal object consisted of material K), figure (f) detects the 5th row abnormal object (abnormal object consisted of material M), thereby obtain the net result gray-scale map detected in real time.

Claims (4)

1. the high spectrum real-time detection method based on recursive analysis is characterized in that:

Step 1: the spectrum vector correlation matrix R (n) that sets up the high spectrum image pixel;

Step 2: set up the state equation of correlation matrix R (n),

$R\left(n\right)=\frac{n-1}{n}R(n-1)+\frac{1}{n}{r}_n{r_n}^T$

In formula, R (n-1) is the estimated value of a upper moment state, r _nThe observed reading of current state,

Observed reading r according to current state _nWith the estimated value R (n-1) of a upper moment state, upgrade the estimated value of current state;

Step 3: utilize the Woodbury identical relation to upgrade the inverse matrix R (n) of correlation matrix R (n) ^-1

Step: 4: high spectrum image is detected in real time in conjunction with the abnormality detection operator.

2. the high spectrum real-time detection method based on recursive analysis according to claim 1, is characterized in that: in step 3, utilize the Woodbury identical relation to derive, inverse matrix R (n) ^-1Computing formula as follows:

R(n) ^-1＝n[(n-1)R(n-1)+r _nr _n ^T] ^-1；

$R{\left(n\right)}^{-1}=\frac{n}{n-1}{R(n-1)}^{-1}-\frac{{\mathrm{nR}(n-1)}^{-1}{r}_n{r_n}^T{R(n-1)}^{-1}}{{(n-1)}^2+(n-1){r_n}^T{R(n-1)}^{-1}{r}_n}$

In formula, R (n-1) ^-1Inverse matrix for a upper correlation matrix.

3. the high spectrum real-time detection method based on recursive analysis according to claim 2 is characterized in that: in step 1, and correlation matrix

In formula, r _nCurrent pixel n to be detected ^ThThe spectrum vector, r _i=[r _1i, r _2i..., r _Li] ^TI ^ThThe spectrum vector of pixel, wherein, L is the number of wave band.

4. the high spectrum real-time detection method based on recursive analysis according to claim 3 is characterized in that: in step 4, the abnormality detection operator adopts the RX operator, and formula is as follows:

${\mathrm{\δ}}^{\mathrm{RTC}-R-\mathrm{RXD}}\left(r_n\right)=r_n^T[\frac{n}{n-1}{R(n-1)}^{-1}-\frac{\mathrm{nR}{(n-1)}^{-1}{r}_n{r_n}^T{R(n-1)}^{-1}}{{(n-1)}^2+{{(n-1)r}_n}^T{R(n-1)}^{-1}{r}_n}]r_n.$

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