CN101996396A - Compressive sensing theory-based satellite remote sensing image fusion method - Google Patents

Abstract

The invention discloses a compressive sensing theory-based satellite remote sensing image fusion method. The method comprises the following steps of: vectoring a full-color image with high spatial resolution and a multi-spectral image with low spatial resolution; constructing a sparsely represented over-complete atom library of an image block with high spatial resolution; establishing a model from the multi-spectral image with high spatial resolution to the full-color image with high spatial resolution and the multi-spectral image with low spatial resolution according to an imaging principle of each land observation satellite; solving a compressive sensing problem of sparse signal recovery by using a base tracking algorithm to obtain sparse representation of the multi-spectral color image with high spatial resolution in an over-complete dictionary; and multiplying the sparse representation by the preset over-complete dictionary to obtain the vector representation of the multi-spectral color image block with high spatial resolution and converting the vector representation into the image block to obtain a fusion result. By introducing the compressive sensing theory into the image fusion technology, the image quality after fusion can be obviously improved, and ideal fusion effect is achieved.

Description

A kind of satellite remote sensing images fusion method based on compression sensing theory

Technical field

The present invention relates to a kind of satellite remote sensing images fusion method, a kind of satellite remote sensing images fusion method of saying so more specifically based on compression sensing theory.

Background technology

Along with the fast development of remote sensing technology and the continuous appearance of novel sensor, the ability that people obtain remote sensing image data improves constantly.Yet most at present satellites still only provide panchromatic gray level image of high spatial resolution and the multispectral coloured image of low spatial resolution, and this makes and can be restricted when carrying out the data message analysis.Simple and the most frequently used remote sensing image fusion method comprises the color transformed method of IHS, principal component analysis (PCA), Gram-Schmidt converter technique etc.Its fusion process mainly comprises three steps: at first the remote sensing multispectral image is carried out the spectrum channel conversion, the realization monochrome information is separated with colouring information, secondly full-colour image is replaced going up the luminance picture that the step conversion obtains, last spectrum channel inverse transformation obtains fused images.These class methods can improve the spatial resolution and the spectral characteristic of fused images, but have twisted original spectral characteristic easily simultaneously, have produced the spectrum degradation phenomena.Another kind of exemplary process is based on the method for multiresolution analysis.Its basic thought is exactly to extract the detailed information of panchromatic gray level image by the multiresolution conversion, and be inserted in the multiresolution conversion coefficient of the multispectral coloured image of low spatial resolution, at last by the multiresolution inverse transformation to fused images.Multiresolution method commonly used comprises Laplacian pyramid decomposition, wavelet transform, small echo frame transform, " à trous " wavelet transformation or the like.These class methods are owing to spectral characteristic and the details characteristic considered simultaneously on the source images different resolution, make fused images can keep the detailed information of panchromatic gray level image and the multispectral coloured image spectral characteristic of original low spatial resolution, but fusion results image and desirable fused images still have than large deviation, have to a certain degree detailed information and the losing of spectral information.Additive method for example also is commonly used to realize the fusion of remote sensing images based on the Bayesian method with based on the method for markov random file etc., but these method computing complexity, and effect remains further to be improved.

Summary of the invention

In order to solve the above-mentioned technical matters that the satellite remote sensing images fusion method exists, the invention provides a kind of satellite remote sensing images fusion method based on compression sensing theory.The present invention will compress the sensing theory and apply in the satellite remote sensing images fusion method, panchromatic gray level image of high spatial resolution and the multispectral coloured image of low spatial resolution are merged, both can improve image resolution ratio, make fused image have color again, thereby provide the good basis data Layer for Geographic Information System.Safeguarding national defense safety, utilizing remote sensing images to carry out revision of topographic map, improving land identification of targets precision, very big effect has been brought into play in aspects such as the remote sensing soil utilizes dynamic monitoring, takes precautions against natural calamities, Geographic Information System.

The technical scheme that the present invention solves the problems of the technologies described above may further comprise the steps:

1) vectorization high spatial resolution full-colour image and low spatial resolution multispectral image;

2) the rarefaction representation over-complete dictionary of atoms of the image block of structure high spatial resolution;

3), set up from the high spatial resolution multi-spectral image to the high spatial resolution full-colour image and the model of low spatial resolution multispectral image according to the image-forming principle of each land observation satellite;

4) find the solution the compression sensing problem that this sparse signal recovers with basic tracing algorithm, obtain the rarefaction representation of multispectral coloured image in crossing complete dictionary of high spatial resolution, again with this rarefaction representation with preestablished the multispectral coloured image piece vector representation that complete dictionary multiplies each other and obtains high spatial resolution, this vector representation is converted into image block, obtains fusion results.

The concrete steps of above-mentioned step 1) image vectorization are:

1) moving window of a pair of fixed size of selection, comprise a big window, window size is 8 row, 8 row, a little window, window size are 2 row 2 row, and big window slides according to from top to bottom scanning sequency from left to right on the high spatial resolution full-colour image, the step-length of sliding is 4 pixels, wicket slides according to from top to bottom scanning sequency from left to right on the multispectral image of low spatial resolution, and the step-length of slip is 1 pixel, and the slip of big window and wicket is carried out simultaneously;

2) 8 row, the 8 row image blocks on the high spatial resolution full-colour image of the big moving window covering of collection, and with its type vectorization to connect;

3) gather 2 row, 2 column split rate image blocks on the low spatial resolution multispectral image that little moving window covers, and with its vectorization;

4) vector that the image block of the high spatial resolution full-colour image of correspondence position and low spatial resolution multispectral image is obtained connects into a vector.

Further, the method for described structure rarefaction representation over-complete dictionary of atoms is a random sampling methods.

Further, described image interfusion method adopts the strategy of moving window.

Because adopt technique scheme, technique effect of the present invention is: the image interfusion method that the present invention proposes is a kind of satellite remote sensing images fusion method based on compression sensing theory.This method is converted into the fusion problem of satellite remote sensing images the recovery problem of compressible signal, it has more sparse signal indication form, meets human vision property more, and on the basis of rarefaction representation, introduced sliding window technique, made it have translation invariance; Panchromatic gray level image of high spatial resolution and the multispectral coloured image of low spatial resolution are merged, both can improve image resolution ratio, make fused image have color again; And this method adopts the method for grab sample to construct the rarefaction representation over-complete dictionary of atoms, avoids the complexity of over-complete dictionary of atoms learning algorithm commonly used and shortcoming consuming time.

The present invention is further illustrated below in conjunction with accompanying drawing.

Description of drawings

Fig. 1 is the synoptic diagram that the present invention is based on the satellite remote sensing images fusion method of compression sensing theory;

Fig. 2 is the synoptic diagram that high spatial resolution full-colour image and low spatial resolution multispectral image produce model framework chart;

Embodiment

As shown in Figure 1 and Figure 2, Fig. 1 is the satellite remote sensing images fusion method synoptic diagram based on compression sensing theory of the present invention.Source images to be merged comprises a gray scale full-colour image and colored multispectral image, and full-colour image is 4: 1 with the ratio of the spatial resolution of colored multispectral image, and colored multispectral figure comprises red, green, blue and four Color Channels of near infrared.As shown in Figure 1, this method adopts the strategy of moving window to realize the fusion of entire image, each algorithm is all realized the fusion in a little corresponding moving window zone, after single treatment is finished, moving window is according to certain step-length sampling next window, the multispectral coloured image of step-length and the high spatial resolution of sampling than relevant, repeats above scanning window processing to the sampling of the multispectral coloured image of low spatial resolution then, all is scanned up to entire image.The concrete implementation detail of each several part is as follows:

1. with the video in window piece vectorization of high spatial resolution full-colour image and low spatial resolution multispectral image.Its concrete steps are:

1) moving window of a pair of fixed size of selection, comprise a big window, window size is 8 row, 8 row, a little window, window size is 2 row, 2 row, big window slides according to from top to bottom scanning sequency from left to right on the high spatial resolution full-colour image, the step-length of sliding is 4 pixels, wicket slides according to from top to bottom scanning sequency from left to right on the multispectral image of low spatial resolution, the step-length of sliding is 1 pixel, the slip of big window and wicket is carried out simultaneously, because full-colour image is 4: 1 with the ratio of the spatial resolution of colored multispectral image, the big window content corresponding identical with wicket after so each window slides, but the resolution ratio is 4: 1.

8 row, 8 row image blocks on the high spatial resolution full-colour image of the moving window covering that 2) collection is big, and with its type vectorization that connects with row, the secondary series that is piece is connected to first back that is listed as, the 3rd row are connected to the back of the previous column that has just connected, and the like, it is 64 vector that image block is become a dimension.Detail is used P as shown in Figure 2 _iI size of expression sampling is the image block of 8 row, 8 row

Y wherein _1,1The pixel value of representing the 1st row the 1st row respective pixel in the image block of 8 row 8 row, y _1,2The pixel value of representing the 1st row the 2nd row respective pixel, y by that analogy _8,8The pixel value of expression eighth row the 8th row respective pixel.By P _iThe vector that obtains is

Length is 64, wherein $y_{\mathrm{pan}}^i={[{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA0000026402840000012.png"\; state="\{\{state\}\}">\; <figure-callout\; id="1"\; label="y"\; filenames="HDA0000026402840000012.png"\; state="\{\{state\}\}">y</figure-callout>\; </figure-callout>}}_{\mathrm{1,1}},{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA0000026402840000012.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{2,1},...,}{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA0000026402840000012.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{8,1}},{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA0000026402840000012.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,2}},y_{\mathrm{2,2},...,}{y}_{\mathrm{8,2}},...,y_{\mathrm{1,8}},y_{\mathrm{2,8},...,}{y}_{\mathrm{8,8}}]}^T.$

3) little moving window acts on the low spatial resolution multispectral image, and its sample mode is with the big sample mode of window on full-colour image.With the size of window correspondence is the 4 passage coloured image piece vectorizations of 2 row, 2 row, and four channel image pieces of coloured image piece are used respectively

With

Expression, by the mode of row respectively vectorization to obtain four length be 4 vector, establish

M wherein _1,1It is the 1st row the 1st row pixel corresponding pixel value in 2 row, the 2 row image blocks.Define vectorial r _i=[m _1,1m _2,1m _1,2, m _2,2] ^TIdentical method from With

Obtain g _i, b _iAnd n _i, then by r _i, g _i, b _iAnd n _iStructure

Length be 16.

4) correspondence position is connected into a vector from the vector that the image block of the multispectral coloured image of the panchromatic gray level image of high spatial resolution and low spatial resolution obtains The length of vector is 80.

2. construct the rarefaction representation over-complete dictionary of atoms of high spatial resolution images piece.For avoiding using the complexity of over-complete dictionary of atoms learning algorithm and shortcoming consuming time always, the present invention adopts the method for grab sample to construct the rarefaction representation over-complete dictionary of atoms.At first, select 20 width of cloth spatial resolutions the same with panchromatic gray level image and with treating the fused images statistical property the close multispectral coloured image of natural color; The bigger image window of using in 10000 the coloured image pieces of therefrom sampling at random then, image block size and the first step big or small the same, i.e. 8 row, 8 row, 4 passages are at last with all vectorizations of each image block.The method of vectorization is identical with the method for image block in the first step, and the image block corresponding pixel value with each color channel generates a vector by being linked in sequence of row earlier, and again with the loud connection of each passage correspondence, the length that generates vector is 256 vector.10000 pairing vectors of coloured image are arranged, and the formation size is 256 * 10000 matrix D, and this matrix is over-complete dictionary of atoms.

3. according to the image-forming principle of each land observation satellite, set up multispectral coloured image from high spatial resolution to the panchromatic gray level image of high spatial resolution and the multispectral coloured image degradation model of low spatial resolution.Regard the data of vectorization as compress in the sensing theory sampled data, the degradation model matrix of being constructed is regarded the sensing matrix in the compression sensing theory as, and the problem that satellite remote sensing images is merged is converted into the compression sensing problem that sparse signal recovers.Detailed process is:

1) the panchromatic gray level image of structure high spatial resolution produces model.Because the wavelength coverage of the wavelength coverage of panchromatic gray level image and all passages of multispectral coloured image is overlapped, so the panchromatic gray level image of high spatial resolution can be regarded the weighted linear combination of multispectral each passage of coloured image as.Wherein weighting coefficient obtains by the spectral response characteristic of analyzing the satellite image sensor, and is red among the present invention, high post, and weighting coefficient blue and the near infrared correspondence is respectively w ₁=0.2308, w ₂=0.2315, w ₃=0.1139, w ₄=0.4239.This model can represent that the form of matrix is relevant with the spectral response characteristic of satellite image sensor with matrix.Fig. 2 is the synoptic diagram that the multispectral coloured image of the panchromatic gray level image of high spatial resolution and low spatial resolution produces model framework chart.As shown in Figure 2, use

$x_i={(x_{\mathrm{1,1}}^R,x_{\mathrm{1,2}}^R,...,x_{\mathrm{1,8}}^R,x_{1,2}^R,...,x_{\mathrm{8,8}}^R,...,x_{1,1}^{\mathrm{NIR}},x_{\mathrm{1,2}}^{\mathrm{NIR}},...,x_{\mathrm{1,8}}^{\mathrm{NIR}},x_{\mathrm{1,2}}^{\mathrm{NIR}},...,x_{\mathrm{8,8}}^{\mathrm{NIR}})}^T---\left(1\right)$

Represent that desirable high-resolution multi-spectral image pulls into the form of vector, R wherein, G, B and NIR represent red respectively, high post, blue and near infrared passage,

The pixel value of the 1st row the 1st row pixel correspondence position in the red channel passage correspondence image piece in the presentation graphs 2, then:

$y_{\mathrm{PAN}}^i=M_1{x}_i+v,---\left(2\right)$

Wherein, M ₁=(w ₁I w ₂I w ₃I w ₄I), I ∈ R ^{64 * 64}Unit matrix, v represents the additive zero Gaussian noise.

2) the multispectral coloured image of structure low spatial resolution produces model.Because the light intensity on the ccd array of low-resolution image pixel value correspondence equals the mean value of the desirable high score rate pixel value of its corresponding neighborhood to the light intensity on the deserved ccd array, therefore, the low-resolution image pixel value can be regarded as in the mean value of the desirable high score rate pixel value of its corresponding neighborhood.The panchromatic gray level image of high spatial resolution can be regarded as the weighted mean value of desirable each passage of high spatial resolution coloured image, and its weights can obtain by the spectrum reflection characteristic of corresponding satellite optical sensor is analyzed.Because the sampling rate of desirable high spatial resolution coloured image and low spatial resolution coloured image is 4, so each pixel value of a passage of multispectral coloured image of low spatial resolution can be regarded the mean value of its 4 * 4 neighborhood territory pixel in corresponding ideal high spatial resolution coloured image as, promptly

$y_{\mathrm{MS}}^i=M_2{x}_i+v,---\left(3\right)$

M wherein ₂Be that size is the sampling matrix of 16 row, 256 row.M ₂Building method be

I wherein _{8 * 8}∈ R ^{8 * 8}Unit matrix, 1 ∈ R ^{4 * 1}Complete 1 matrix, I _{2 * 2}∈ R ^{2 * 2}Unit matrix, v additive zero Gaussian noise.

3) data of vectorization are regarded as the sampled data of compressing in the sensing theory, the degradation model matrix of being constructed is regarded the sensing matrix in the compression sensing theory as.The problem that satellite remote sensing images is merged is converted into the compression sensing problem that sparse signal recovers.

At first, formula (2) and (3) merging are obtained

y ⁱ＝Mx _i+v， (4)

Wherein

Here the purpose of image co-registration is exactly by known y ⁱAsk x with M _iBecause the line number of M so problem (4) is an irreversible problem, that is to say a plurality of x less than columns _iCan obtain identical y by formula (4) ⁱHere this problem is regarded as compression sensing problem, wherein y ⁱBe sampled data, M is a sensing matrix, x _iBe the signal that will recover.This problem is converted into the optimization problem under the constraint of sparse property

$\min {\left|\right|\mathrm{\&alpha;}\left|\right|}_{1}s.t.{\left|\right|y^i-\mathrm{\&Phi;\&alpha;}\left|\right|}_2^2\&le;\mathrm{\&epsiv;},---\left(5\right)$

Φ=MD wherein, D was complete sparse dictionary, and ε represents reconstructed error, and its value is relevant with the degree of noise in the original image, and when not having noise in the acquiescence original image, it is very little that its value can be provided with, and ε=1 is set in the present invention.

4. with basic tracing algorithm (the specific implementation details reference Scott Shaobing Chen of basic tracing algorithm, David L.Donoho and Michael A.Saunders are published in paper S.Chen on the SIAM REVIEW in calendar year 2001, D.Donoho, and M.Saunders, " Atomic Decomposition by Basis Pursuit; " SIAM Rev., vol.43, no.1, pp.129-159,2001) finding the solution the compression sensing problem (5) that this sparse signal recovers, obtain the rarefaction representation α of the multispectral coloured image of high spatial resolution, is x with this rarefaction representation with preestablishing the dictionary multispectral coloured image that obtains high spatial resolution that multiplies each other _i=D α.Again with x _iBe converted into the form of image block, the process of conversion is the inverse process of formula (1).At last the image block that reconstructs is put into the relevant position of fused images.Repeat above scanning window and handle, all be scanned, obtain final fusion results image up to entire image.

Method provided by the present invention with compare based on the method for support vector conversion with based on these two kinds of up-to-date remote sensing image fusion methods of method of genetic algorithm.Watch 1 and watch 2 have been listed the objective evaluation result. the objective evaluation of watch 1 fast bird satellite image fusion results.The objective evaluation of table 2IKONOS satellite image fusion results.Here used mark related coefficient, root-mean-square error, SAM, ERGAS and Q4 as evaluation criterion.Wherein the big more expression syncretizing effect of related coefficient and Q4 value is good more, and the more little expression syncretizing effect of the value of root-mean-square error, SAM and ERGAS is good more.From experimental result as can be seen, the method for the present invention's proposition obtains best fusion results.

Table 1

Table 2

Claims (3)

1. satellite remote sensing images fusion method based on compression sensing theory may further comprise the steps:

1) with high spatial resolution full-colour image and the vectorization of low spatial resolution multispectral image;

2) the rarefaction representation over-complete dictionary of atoms of the image block of structure high spatial resolution;

3), set up from the high spatial resolution multi-spectral image to the high spatial resolution full-colour image and the model of low spatial resolution multispectral image according to the image-forming principle of each land observation satellite;

4) find the solution the compression sensing problem that this sparse signal recovers with basic tracing algorithm, obtain the rarefaction representation of multispectral coloured image in crossing complete dictionary of high spatial resolution, again with this rarefaction representation with preestablished the multispectral coloured image piece vector representation that complete dictionary multiplies each other and obtains high spatial resolution, this vector representation is converted into image block, obtains fusion results.

2. the satellite remote sensing images fusion method based on compression sensing theory according to claim 1 is characterized in that the concrete steps of described step 1) image vectorization are:

1) moving window of a pair of fixed size of selection, comprise a big window, window size is 8 row, 8 row, a little window, window size is 2 row, 2 row, big window slides according to from top to bottom scanning sequency from left to right on the high spatial resolution full-colour image, the step-length of sliding is 4 pixels, wicket slides according to from top to bottom scanning sequency from left to right on the multispectral image of low spatial resolution, the step-length of sliding is 1 pixel, and the slip of big window and wicket is carried out simultaneously;

2) 8 row, the 8 row image blocks on the high spatial resolution full-colour image of the big moving window covering of collection, and with its type vectorization to connect;

3) gather 2 row, 2 column split rate image blocks on the low spatial resolution multispectral image that little moving window covers, and with its vectorization;

4) vector that the image block of the high spatial resolution full-colour image of correspondence position and low spatial resolution multispectral image is obtained connects into a vector.

3. the satellite remote sensing images fusion method based on compression sensing theory according to claim 1 is characterized in that described step 2) method of structure rarefaction representation over-complete dictionary of atoms is random sampling methods.

Images