CN103793883A - Principal component analysis-based imaging spectral image super resolution restoration method - Google Patents

Abstract

The invention discloses a principal component analysis-based imaging spectral image super resolution restoration method. The method includes the steps of principal component analysis, gray mapping and MAP-based first principal component super resolution restoration and all-band super resolution restoration of an imaging spectral image. According to the principal component analysis-based imaging spectral image super resolution restoration method, the effective information of the imaging spectral image is concentrated on a first principal component through PCA transform, with the super resolution restoration of the first principal component simply realized, the spatial resolution of all bands can be improved, and therefore, the amount of computation is small; mapping from panchromatic image high-frequency information to a first principal component image can be realized through establishing a gray mapping model and based on the correlation between the first principal component and a panchromatic image after the PCA transform, and the quality of a reconstructed high-frequency information can be further improved through MAP constrained optimization; and therefore, high-frequency information of the panchromatic image can be fully utilized, and the introduction of wrong information can be avoided, and the quality of a reconstructed high-resolution image can be ensured, and the problem of spectrum distortion caused by independent operation of each band can be effectively solved.

Description

A kind of imaging spectrum Super-Resolution method based on principal component analysis (PCA)

Technical field

The present invention relates to a kind of Super-Resolution method of imaging spectrum, particularly a kind of imaging spectrum Super-Resolution method based on principal component analysis (PCA) (Principal Component Analysis, PCA).

Background technology

Imaging spectral technology is a kind of new remote sensing technology developing rapidly the eighties in 20th century, it obtains atural object radiation information with nano level superelevation spectral resolution at dozens or even hundreds of wave band simultaneously, thereby can, in obtaining ground object target spatial information, its internal physical feature and formation be surveyed.Imaging spectral technology is all widely used in fields such as resource exploration, geologic prospect, disaster assistances.

Spatial resolution and spectral resolution are to weigh two important parameters of imaging spectrum image quality, be subject to the restriction of image-forming principle, the raising of spectral resolution, often with the cost that is reduced to of spatial resolution, makes the spatial resolution of imaging spectrum conventionally far below panchromatic image.And in practical application, remote-sensing flatform carries the panchromatic of different resolution and multispectral imaging equipment conventionally simultaneously, the high-frequency information of panchromatic image has important reference for the raising of multispectral image spatial resolution.

Imaging spectrum mainly contains following feature: spatial resolution is lower than panchromatic image; Spectral resolution is high, and spectral coverage is many, and data volume is large; Spectral correlation is strong, spatial coherence relatively a little less than; Similar atural object has the similar curve of spectrum.For these features, the method that improves at present imaging spectrum spatial resolution mainly contains following several:

Panchromatic image integration technology: extract the high-frequency information with scene high resolution spatial panchromatic image, incorporate the imaging spectrum of low resolution by image fusion technology, reach the effect that improves its spatial resolution.The method is mainly applicable to the less multispectral image of wave band, not too applicable for high spectrum image; And merge after image often there is certain spectrum distortion.

Super-Resolution Restoration from Image Sequences: the Super-Resolution Restoration from Image Sequences of normal image, successively for each wave band of imaging spectrum, is reached to the effect that improves spatial resolution.Because imaging spectrum has the correlativity between spectrum very by force, be between each wave band, to have a large amount of redundant informations, if use conventional methods successively each wave band carried out to Super-Resolution, correlativity between wave band can make to influence each other between the reconstructed results of each wave band, destroys original spectral signature; And also very large by the super-resolution rebuilding process operand of wave band.

Spectrum solution is mixed technology: regard low resolution picture dot as mixed pixel that the imaging simultaneously of multiple atural object forms, by the mixed technology of spectrum solution, be decomposed into the mixed form of multiple atural object, reached decomposition mixed pixel by solving the different proportion of each atural object, and then improved the effect of spatial resolution.Application number is that 201210051365.8 patent discloses a kind of high spectrum image super resolution ratio reconstruction method based on sub-pixel mapping, by the mixed Abundances of the every kind of atural object that forms mixed pixel in each picture dot that solve of spectrum solution, then be a certain atural object by each sub-pixel Random assignment, obtain initialized atural object distributed image; Finally, by iteration optimization, rebuild a high-resolution image.This is a kind of method that improves spatial resolution by excavating high spectrum image internal information, but fails to utilize the information of the high resolution spatial panchromatic image that Same Scene obtains, thereby the ability that its resolution improves is difficult to reach very high level.In the time there is high resolution spatial panchromatic image in Same Scene, by the inventive method, make full use of the high-frequency information of high resolution spatial panchromatic image, can reach better Super-Resolution effect.

Prior art does not take into full account the hold facility of spectrum dimension information in Super-Resolution process to the Super-Resolution of imaging spectrum, cause the high-definition picture of reconstruction often to have certain spectrum distortion.In addition, high spectrum image wave band is numerous, and all wave bands are carried out respectively to Super-Resolution, and its huge operand is also difficult to bear often.

Summary of the invention

For the above-mentioned problems in the prior art, the invention provides a kind of imaging spectrum Super-Resolution method based on principal component analysis (PCA), realize high-quality Super-Resolution, reduce the overall operand of algorithm.

For achieving the above object, the present invention adopts following technological means:

Completed the collection of imaging spectrometer data by imaging spectrometer, and the optical signalling of pending image is converted into data image signal, be stored in collecting device storer; Read in image by USB, infrared interface, in processor, carry out the imaging spectrum Super-Resolution based on principal component analysis (PCA).It is characterized in that: by principal component analysis (PCA), the main information of imaging spectrum is concentrated on to its 1st major component, by the Super-Resolution to the 1st major component, realize the full wave Super-Resolution of imaging spectrum.

1. principal component analysis (PCA)

Principal component analysis (PCA) (PCA) is the multi-dimensional orthogonal linear transformation on statistical nature basis, is also conventional a kind of converter technique during multiband, Multitemporal Remote Sensing Images application are processed.It has the data dependence of removal and assembles the effect of main information, thereby is being widely used aspect the dimensionality reduction of high dimensional signal and feature extraction.Imaging spectrum similarly is typical high dimensional signal, and has very strong Spectral correlation.In the present invention, the object of PCA conversion is exactly the useful information in original multiple band images will be focused in the 1st major component image, makes by the Super-Resolution of the 1st major component, reaches the effect that strengthens all band image spatial resolutions.Not only reduce by the huge operand of wave band Super-Resolution process, also avoid relevant information to repeat to restore the phenomenon of introducing spectrum distortion.

2. the 1st major component Super-Resolution based on grey scale mapping and MAP

The 1st major component image of imaging spectrum, has merged the important information of all wave bands of imaging spectrum, and its spectral wavelength coverage and panchromatic image have certain overlapping, and corresponding image detail has very strong similarity.The present invention utilizes this feature, extracts the high-frequency information of high resolution spatial panchromatic image, after certain grey scale mapping, incorporates the 1st major component image of imaging spectrum, realizes the Super-Resolution of major component image.

From the angle of frequency domain, imaging system is equivalent to a low-pass filter, has certain cutoff frequency.On the basis that the image low-frequency information that the Super-Resolution of image can be thought to obtain in to imaging system passband is restored, recover the process of the above high-frequency information of its cutoff frequency, the present invention is just as starting point, utilize the high-frequency information of high resolution spatial panchromatic image, the high-frequency information of reestablishment imaging spectrum picture major component.

No matter be panchromatic image or imaging spectrum, its record be all the reflection characteristic of atural object to respective wavelength light, different reflection characteristics is presented as the variation of gray-scale value on image.Imaging spectrum is after PCA conversion, often there is certain difference in the tonal range of its 1st major component and panchromatic image, for this reason, the present invention proposes a kind of method of high-frequency information grey scale mapping, only extract the high-frequency information of panchromatic image, after certain grey scale mapping, incorporate the 1st major component image of low resolution imaging spectrum, to utilize better the detailed information of panchromatic image, and reduce the impact of low frequency component.

In order further to improve the fidelity of rebuilding high resolving power major component image, the image quality decrease of avoiding mapping error to cause, further retrains and optimizes the high-definition picture of initial estimation.The high resolving power estimated image that the present invention rebuilds grey scale mapping method, as initial value, is introduced maximum a posteriori probability (Maximum a Posteriori, MAP) framework and is is further optimized and revised, and obtains the Super-Resolution image of the 1st major component image.

3. all band Super-Resolution of imaging spectrum

The 1st major component image after Super-Resolution, comprise the high-frequency information about each wave band of this imaging spectrum, the equal interpolation amplification of other each wave bands of imaging spectrum is arrived after identical resolution, through PCA inverse transformation, the high-frequency information that Super-Resolution process can be rebuild returns in all wave bands, realizes the full wave Super-Resolution of imaging spectrum.Experimental result shows, the Super-Resolution algorithm that the present invention proposes, not only can make the resolution of imaging spectrum be significantly improved, and keep the spectral signature of original image that distortion does not occur.

An imaging spectrum Super-Resolution method based on principal component analysis (PCA), comprises the steps:

Step 1, computing machine reads in imaging spectrum from memory device, and whole image represents by the form of a three-dimensional array X.

Step 2, carries out principal component analysis (PCA) to original image, extracts the 1st major component after its conversion, retains all the other compositions for subsequent use simultaneously.The method of original image being carried out to principal component analysis (PCA) is as follows:

Step 2.1, reads in imaging spectrum data X;

Step 2.2, calculates the related coefficient between the each wave band of imaging spectrum X, composition covariance matrix Σ _x;

Step 2.3, calculates covariance matrix Σ _xeigenwert, and its eigenwert is arranged by order from big to small;

Step 2.4, obtains each eigenwert characteristic of correspondence vector u _i;

Step 2.5, asks for PCA transformation matrix U according to proper vector;

Step 2.6, by imaging spectrometer data X and the transformation matrix U major component image Y after conversion that multiplies each other to obtain.

Step 3, carries out Super-Resolution to the 1st major component after PCA conversion, and method is as follows:

Step 3.1, estimates the grey scale mapping parameter of high resolution spatial panchromatic image to imaging spectrum;

(1) by down-sampled high resolution spatial panchromatic image z be z ^l(representing that with subscript l it is the low-resolution image after down-sampled), makes itself and image the 1st major component image y ₁there is identical spatial resolution;

(2) adopt Laplace operator to extract respectively z ^lhigh frequency details with y image, obtains corresponding detail pictures

with

(3) calculate average and the variance of each detail pictures, computing formula is:

$\mathrm{\μ}=\frac{1}{\mathrm{MN}}\underset{i=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}E(i,j)---\left(1\right)$

$\mathrm{\σ}=\frac{1}{\mathrm{MN}}\underset{i=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}{(E(i,j)-\mathrm{\μ})}^2---\left(2\right)$

In formula, E (i, j) expression high frequency detail pictures (i, j) is located the gray-scale value of pixel; μ and σ are corresponding average and variance; M, N be the length and width pixel count of presentation video respectively.

Step 3.2, the high resolving power initial estimate of generation the 1st major component image;

(1) adopt bilinear interpolation method that the 1st major component image is amplified to required size;

(2) high-frequency information of high resolution spatial panchromatic image is carried out to grey scale mapping, and in the 1st major component image being added to after interpolation amplification, obtain the high resolving power estimated image of the 1st major component image, formula is as follows:

${\hat{y}}_1^H={y_1}^B+{[(E\left(z\right)-{\mathrm{\μ}}_{E\left(2\right)})\×\frac{{\mathrm{\σ}}_{{\mathrm{Ey}}_1}}{{\mathrm{\σ}}_{{\mathrm{Ez}}^l}}+{\mathrm{\μ}}_{\mathrm{Ez}}\frac{{\mathrm{\μ}}_{{\mathrm{Ey}}_1}}{{\mathrm{\μ}}_{{\mathrm{Ez}}^l}}]}^{1/2}---\left(3\right)$

In formula,

for the estimated value of high resolving power major component image; y ₁ ^bfor low resolution major component image y ₁image through bilinear interpolation to high resolving power size gained, it provides the low-frequency information of estimating high-definition picture; μ _{e (z)}for the average of extracted panchromatic image high-frequency information E (z).

be respectively and utilize formula (1) and (2) to estimate the down-sampled rear panchromatic image of gained and average and the variance of the 1st major component image;

Step 3.3, the MAP that carries out the 1st major component image optimizes estimation;

(1) set up the maximum a posteriori probability estimation model of the 1st major component image:

${\hat{y}}_1=\arg \underset{y_1^H}{\max }\log \mathrm{Pr}\left(y_1^H\right|y_1)=\underset{y_1^H}{\arg \max }\{\log \mathrm{Pr}\left(y_1^H\right)+\log \mathrm{Pr}\left(y_1\right|y_1^H)\}---\left(4\right)$

In formula,

be illustrated in known low-resolution image y ₁time, high-definition picture

posterior probability.

for the prior distribution of high-definition picture, adopt Huber-Markov model description.Conditional probability

reflect

the low resolution estimated image of down-sampled rear gained and actual low-resolution image y ₁between error distribute, can think Gaussian distributed, that is:

$\mathrm{Pr}\left(y_1\right|y_1^H)=\frac{1}{{2\mathrm{\π}}^{\frac{N_1{N}_2}{2}}{\mathrm{\σ}}^{\mathrm{MN}}}\exp \{-\frac{1}{{2\mathrm{\σ}}^2}||y_1-{\mathrm{Dy}}_1^H|\left|\right\}---\left(5\right)$

In formula, M, N represent respectively low-resolution image y ₁ranks number of pixels.σ is the variance that error distributes.D is down-sampled matrix, and it has described ccd sensor averaging process on certain area in image acquisition procedures.That is:

${\hat{y}}_1=\frac{1}{q^2}\left(\underset{r=\mathrm{qi}-q+1}{\overset{\mathrm{qi}}{\mathrm{\Σ}}}\underset{s=\mathrm{qj}-q+1}{\overset{\mathrm{qj}}{\mathrm{\Σ}}}{y}_1^H\right)---\left(6\right)$

In formula, q is down-sampled coefficient.

(2) by the high resolving power estimated value of the 1st major component image

substitution formula (4), adopts method of Lagrange multipliers iterative, obtains the Super-Resolution result of the 1st major component image after the satisfied appointment condition of convergence

Step 4, carries out all band super-resolution rebuilding of imaging spectrum, and method is as follows:

Step 4.1, carries out bilinear interpolation successively to other the each wave band after PCA conversion;

Step 4.2 is carried out PCA inverse transformation together with other composition of the 1st major component after Super-Resolution and interpolation amplification, obtains all band image after Super-Resolution.

Step 5, the imaging spectrum after Super-Resolution outputs to buffer, for follow-up analysis and application;

Step 6, after above EO, closes imaging spectrum file.

Compared with prior art, the present invention has the following advantages:

The inventive method converts by PCA, and the effective information of imaging spectrum is concentrated on to the 1st major component, has only reached by the Super-Resolution of the 1st major component the effect that improves all wave band spatial resolutions, and operand is lower; Utilize the correlativity between rear the 1st major component of PCA conversion and panchromatic image, by setting up grey scale mapping model, realize the mapping of panchromatic image high-frequency information to the 1 major component image, and further improve the quality of rebuilding high-frequency information by MAP constrained optimization, both taken full advantage of the high-frequency information of panchromatic image, avoid again the introducing of error message, guaranteed to rebuild the quality of high-definition picture; The reconstruction of all band high-frequency information is deduced by the 1st major component image, the spectrum problem of dtmf distortion DTMF of effectively having avoided each wave band independently to produce.Experimental result shows, the high-resolution imaging spectrum picture that adopts the inventive method to obtain, and with compared with band dual linear interpolation method, its PSNR value improves 1～2dB; Compared with traditional HIS image interfusion method, each wave band PNSR value improves 5～7dB; Compared with PCA major component replacement method, PSNR value improves 3～4dB.From subjective quality, the spatial resolution of image has not only obtained significant lifting, and spectrum hold facility also is significantly better than contrasting algorithm.

Accompanying drawing explanation

Fig. 1 is the imaging spectrum Super-Resolution method structured flowchart based on principal component analysis (PCA);

Fig. 2 is algorithm of the present invention and the PSNR value comparison diagram that contrasts algorithm;

Fig. 3 is that algorithm of the present invention contrasts with the subjective quality of contrast algorithm: be (a) high resolution spatial panchromatic image of reference, (b) be the pseudo-color image of original high resolving power multiband, (c)～(f) be respectively the experimental result of bilinear interpolation, HIS method, PCA major component Shift Method and the method for the invention.

Embodiment

Below in conjunction with Figure of description, embodiments of the invention are described in detail.

First completed the collection of imaging spectrometer data by imaging spectrometer, the optical signalling of target image is converted into data image signal, be stored in collecting device storer; Computing machine reads in image by existing USB, the interface such as infrared, in processor, carry out the imaging spectrum Super-Resolution based on principal component analysis (PCA), acquired results is directly stored in local hard drive, for further analysis and processing to imaging spectrum.

Fig. 1 is shown in by general structure block diagram of the present invention, mainly comprises the steps:

Step 1, computing machine reads in imaging spectrum from memory device, and whole image represents with a three-dimensional array X;

Step 2, carries out PCA conversion to imaging spectrum, and method is as follows:

Step 2.1, reads in imaging spectrum data X;

Step 2.2, calculates the related coefficient between the each wave band of imaging spectrum X, composition covariance matrix Σ _x;

Step 2.3, separate secular equation:

(λI-Σ _x)u＝0 (7)

Obtain matrix Σ _xeigenvalue λ _i(i=0,1...n), in formula, λ is eigenwert, and I is unit matrix, and u is proper vector.And its eigenwert is arranged by order from big to small;

Step 2.4, obtains each eigenwert characteristic of correspondence vector u _i

u _i＝[u _1i,u _2i...u _ni] ^T （8）

Step 2.5, get transformation matrix:

$A=U^T=\left[\begin{array}{cccc}{u}_{11}& u_{12}& ...& u_{1n}\\ u_{21}& u_{22}& ...& u_{2n}\\ & & .& \\ & & .& \\ ...& ...& .& ...\\ u_{n1}& u_{n2}& ...& u_{\mathrm{nn}}\end{array}\right]---\left(9\right)$

Step 2.6, by imaging spectrometer data X and the transformation matrix U major component image Y after conversion that multiplies each other to obtain.

Obtain the expression of PCA conversion:

$Y=\left[\begin{array}{cccc}{u}_{11}& u_{12}& ...& u_{1n}\\ u_{21}& u_{22}& ...& u_{2n}\\ & & .& \\ & & .& \\ ...& ...& .& ...\\ u_{n1}& u_{n2}& ...& u_{\mathrm{nn}}\end{array}\right]X=U^{T}X---\left(10\right)$

In formula, Y represents the result after conversion.

After PCA, obtain one group of new image, they are called as the 1st major component successively, the 2nd major component ..., n major component.According to the principle of PCA conversion, each component of the image Y obtaining after conversion is actually the linear combination of each component information of original image X, it combines the information of original each feature rather than simply accepts or rejects, thereby makes new n n dimensional vector n can better react the feature of original image.

Step 3, carries out Super-Resolution to the 1st major component after PCA conversion, and method is as follows:

Step 3.1, estimates the grey scale mapping parameter of high resolution spatial panchromatic image to imaging spectrum;

(1) by down-sampled high resolution spatial panchromatic image z be z ^l, make itself and image the 1st major component image y ₁there is identical spatial resolution;

(2) adopt Laplace operator to extract respectively the high frequency details of each two field picture, obtain corresponding detail pictures

with

(3) utilize formula (1), (2) to calculate respectively average and the variance of each detail pictures.

Step 3.2, the high resolving power initial estimate of generation the 1st major component image;

(1) adopt bilinear interpolation method that the 1st major component image is amplified to required size;

(2) according to formula (3), the high-frequency information of high resolution spatial panchromatic image is carried out to grey scale mapping, and in the 1st major component image being added to after interpolation amplification, obtain the high resolving power estimated image of the 1st major component image.

Step 3.3, the MAP that carries out the 1st major component image optimizes estimation;

In order further to improve the fidelity of rebuilding high resolving power major component image, the image quality decrease of avoiding mapping error to cause, needs further the high-definition picture of initial estimation is retrained and optimized.The high resolving power estimated image that the present invention rebuilds said method, as initial value, is introduced maximum a posteriori probability framework and is is further optimized and revised, and concrete steps are as follows:

(1) set up the maximum a posteriori probability estimation model of the 1st major component image, as formula (4);

(2) by the high resolving power estimated value of the 1st major component image

substitution formula (4), adopts method of Lagrange multipliers iterative, obtains the Super-Resolution result of the 1st major component image after the satisfied appointment condition of convergence

Step 4, all band super-resolution rebuilding of imaging spectrum, method is as follows:

Step 4.1, carries out bilinear interpolation successively to other the each wave band after PCA conversion;

Step 4.2 is carried out PCA inverse transformation together with other composition of the 1st major component after Super-Resolution and interpolation amplification, obtains all band image after Super-Resolution.

Step 5, outputs to buffer by compressed bit stream, is directly stored in local hard drive, for follow-up imaging spectrum analysis and processing.

Step 6, closes original imaging spectrum file, closes Super-Resolution program.

Provide an application example of the present invention below.

Test pattern is one group of remote sensing image Brest that SPOT satellite high resolving power multiband scanner (HRV) obtains, and intercepts wherein three width subimage Brest1-Brest3 and is used for test.This image comprises two kinds of panchromatic and multibands.Wherein the spectral response range of panchromatic wave-band is 0.51～0.73 micron, and spatial resolution is 10 meters; Multiband responding range is respectively 0.50～0.59 micron (green), 0.61～0.68 micron (red) and 0.79～0.89 micron (near infrared), and spatial resolution is 20 meters.It is mainly to read in by existing USB interface or the network storage equipment image collecting that computing machine is processed, and is deposited into hard disk, and the Super-Resolution of multispectral image is realized by software.

For the objective reconstruction effect of verification algorithm, in experiment, first two groups of images are carried out respectively 2 times down-sampled, and then the high-frequency information that utilizes high resolving power panchromatic wave-band rebuilds high-resolution multi-band image, and Y-PSNR PSNR by image is as the objective indicator of measure algorithm performance.

Table 1 has provided the result that adopts the method for the invention and bilinear interpolation, PCA major component Shift Method, method based on IHS to test above-mentioned three width subimages, and its PSNR value correlation curve is shown in accompanying drawing 2.Experimental result shows, the PSNR value that the present invention rebuilds image is all rebuild the PSNR value of image higher than other several method, illustrate that the high-definition picture that the present invention rebuilds is more close with original down-sampled image before, there is better Super-Resolution performance, can rebuild better original high-definition picture.

Table 1 algorithms of different PSNR (dB) is worth relatively

Fig. 3 has provided subjective experiment result, the high resolution spatial panchromatic image that wherein Fig. 3 (a) is reference, Fig. 3 (b) is the pseudo-color image of original high resolving power multiband, and Fig. 3 (c)～(f) is respectively that bilinear interpolation, IHS, PCA major component are replaced and the experimental result of the method for the invention.From figure, can clearly be seen that, it is very fuzzy that two-wire interpolation amplification image is compared former figure, do not increase the details of image, and amplification effect is undesirable; Fig. 3 (d) is the result that the amplification based on HIS obtains, and can find out, although image detail has obtained increase, its color has significant variation, and change has occurred its spectral characteristic.Fig. 3 (e) is major component Shift Method, and panchromatic image is directly replaced the 1st major component after simple grey scale mapping, rebuilds image when details increases, and variation has also occurred color.And scheme the result that the inventive method shown in (f) obtains, and not only effectively increasing the detail of the high frequency of image, and retained well the spectral characteristic of original image, the color of pcolor does not change.

Claims (4)

1. the imaging spectrum Super-Resolution method based on principal component analysis (PCA), is completed the collection of imaging spectrometer data, and the optical signalling of pending image is converted into data image signal by imaging spectrometer, is stored in collecting device storer; Read in image by USB, infrared interface, in processor, carry out the imaging spectrum Super-Resolution based on principal component analysis (PCA); It is characterized in that: by principal component analysis (PCA), the main information of imaging spectrum is concentrated on to its 1st major component, by the Super-Resolution to the 1st major component, realize the full wave Super-Resolution of imaging spectrum; Comprise the following steps:

Step 1, computing machine reads in imaging spectrum from memory device, and whole image represents by the form of a three-dimensional array X;

Step 2, carries out principal component analysis (PCA) PCA to original image, extracts the 1st major component after its conversion, retains all the other compositions for subsequent use simultaneously; The method of original image being carried out to PCA conversion is as follows:

(1) read in imaging spectrum data X;

(2) calculate the related coefficient between the each wave band of imaging spectrum X, composition covariance matrix Σ _x;

(3) calculate covariance matrix Σ _xeigenwert, and its eigenwert is arranged by order from big to small;

(4) obtain each eigenwert characteristic of correspondence vector u _i;

(5) ask for PCA transformation matrix U according to proper vector;

(6) the major component image Y after conversion that imaging spectrometer data X and transformation matrix U multiplied each other to obtain;

Step 3, carries out Super-Resolution to the 1st major component after PCA conversion;

Step 3.1, estimates the grey scale mapping parameter of high resolution spatial panchromatic image to imaging spectrum;

Step 3.2, the high resolving power initial estimate of generation the 1st major component image;

Step 3.3, carries out the maximum a posteriori probability optimization of the 1st major component image and estimates;

Step 4, carries out all band super-resolution rebuilding of imaging spectrum;

Step 4.1, carries out bilinear interpolation successively to other the each composition after PCA conversion;

Step 4.2 is carried out PCA inverse transformation together with other composition of the 1st major component after Super-Resolution and interpolation amplification, obtains all band image after Super-Resolution;

Step 5, the imaging spectrum after Super-Resolution outputs to buffer, for follow-up analysis and application;

Step 6, after above EO, closes imaging spectrum file.

2. a kind of imaging spectrum Super-Resolution method based on principal component analysis (PCA) according to claim 1, is characterized in that, described step 3 high resolution spatial panchromatic image is as follows to the method for estimation of the grey scale mapping parameter of imaging spectrum:

(1) by down-sampled high resolution spatial panchromatic image z be z ^l, make itself and image the 1st major component image y ₁there is identical spatial resolution, z ^lsubscript l represent that it is the low-resolution image after down-sampled;

(2) adopt Laplace operator to extract respectively z ^lhigh frequency details with y image, obtains corresponding detail pictures

with

(3) calculate average and the variance of each detail pictures, computing formula is:

$\mathrm{\μ}=\frac{1}{\mathrm{MN}}\underset{i=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}E(i,j)---\left(1\right)$

$\mathrm{\σ}=\frac{1}{\mathrm{MN}}\underset{i=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}{(E(i,j)-\mathrm{\μ})}^2---\left(2\right)$

In formula, E (i, j) expression high frequency detail pictures (i, j) is located the gray-scale value of pixel; μ and σ are corresponding average and variance; M, N be the length and width pixel count of presentation video respectively.

3. a kind of imaging spectrum Super-Resolution method based on principal component analysis (PCA) according to claim 1, is characterized in that, the method for high resolving power initial estimate that described step 3 generates the 1st major component image is as follows:

(1) adopt bilinear interpolation method that the 1st major component image is amplified to required size;

(2) high-frequency information of high resolution spatial panchromatic image is carried out to grey scale mapping, and in the 1st major component image being added to after interpolation amplification, obtain the high resolving power estimated image of the 1st major component image, formula is as follows:

${\hat{y}}_1^H={y_1}^B+{[(E\left(z\right)-{\mathrm{\μ}}_{E\left(2\right)})\×\frac{{\mathrm{\σ}}_{{\mathrm{Ey}}_1}}{{\mathrm{\σ}}_{{\mathrm{Ez}}^l}}+{\mathrm{\μ}}_{\mathrm{Ez}}\frac{{\mathrm{\μ}}_{{\mathrm{Ey}}_1}}{{\mathrm{\μ}}_{{\mathrm{Ez}}^l}}]}^{1/2}---\left(3\right)$

In formula, for the estimated value of high resolving power the 1st major component image; y ₁ ^bfor low resolution the 1st major component image y ₁image through bilinear interpolation to high resolving power size gained, it provides the low-frequency information of estimating high-definition picture; μ _{e (z)}for the average of extracted panchromatic image high-frequency information E (z);

be respectively and utilize formula (1) and (2) to estimate the down-sampled rear panchromatic image of gained and average and the variance of the 1st major component image.

4. a kind of imaging spectrum Super-Resolution method based on principal component analysis (PCA) according to claim 1, is characterized in that, described step 3 carry out the 1st major component image maximum a posteriori probability optimization estimate method as follows:

(1) set up the maximum a posteriori probability estimation model of the 1st major component image:

${\hat{y}}_1=\arg \underset{y_1^H}{\max }\log \mathrm{Pr}\left(y_1^H\right|y_1)=\underset{y_1^H}{\arg \max }\{\log \mathrm{Pr}\left(y_1^H\right)+\log \mathrm{Pr}\left(y_1\right|y_1^H)\}---\left(4\right)$

In formula,

be illustrated in known low-resolution image y ₁time, high-definition picture

posterior probability;

for the prior distribution of high-definition picture, adopt Huber-Markov model description; Conditional probability

reflect

the low resolution estimated image of down-sampled rear gained and actual low-resolution image y ₁between error distribute, can think Gaussian distributed, that is:

$\mathrm{Pr}\left(y_1\right|y_1^H)=\frac{1}{{2\mathrm{\π}}^{\frac{N_1{N}_2}{2}}{\mathrm{\σ}}^{\mathrm{MN}}}\exp \{-\frac{1}{{2\mathrm{\σ}}^2}||y_1-{\mathrm{Dy}}_1^H|\left|\right\}---\left(5\right)$

In formula, M, N represent respectively low-resolution image y ₁ranks number of pixels; σ is the variance that error distributes; D is down-sampled matrix, and it has described ccd sensor averaging process on certain area in image acquisition procedures; That is:

${\hat{y}}_1=\frac{1}{q^2}\left(\underset{r=\mathrm{qi}-q+1}{\overset{\mathrm{qi}}{\mathrm{\Σ}}}\underset{s=\mathrm{qj}-q+1}{\overset{\mathrm{qj}}{\mathrm{\Σ}}}{y}_1^H\right)---\left(6\right)$

In formula, q is down-sampled coefficient;

(2) by the high resolving power estimated value of the 1st major component image

substitution formula (4), adopts method of Lagrange multipliers iterative, obtains the Super-Resolution result of the 1st major component image after the satisfied appointment condition of convergence

Images