CN105224915A - A kind of mixed pixel of hyper-spectral image decomposition method - Google Patents

Abstract

The invention discloses a kind of mixed pixel of hyper-spectral image decomposition method.The method is decomposed in the process of mixed pixel at application NMF algorithm, SC-SVM algorithm is used to the end member quantity in mixed pixel and solving of spectral vector, its can initiative recognition end member quantity and mark the vector of endmember spectra, thus the basis matrix solved in NMF algorithm, then design factor matrix (i.e. abundance matrix) is carried out by Algorithms of Non-Negative Matrix Factorization, by minimizing the process progressive alternate of objective function to convergence, thus calculate the result wanted, finally reach the object of Decomposition of Mixed Pixels.

Description

A kind of mixed pixel of hyper-spectral image decomposition method

Technical field

The present invention relates to a kind of method that hyperspectral remote sensing image mixed pixel decomposes, the method that the mixed pixel of hyper-spectral image being specially a kind of NMF algorithm based on SC-SVM decomposes, belong to high-spectrum remote sensing processing technology field.

Background technology

Remote sensing technology (RemoteSensing, RS), refer to and start from nineteen sixties, from the comprehensive observation technology that remote space (space flight) or outer space space (aviation) is carried out earth surface, by certain device, remote sensing, namely from remote or outer space indirect observation monitoring, not contact target, the relevant information to target, phenomenon and region is obtained from optical angle, thus carry out convergence analysis and the deduction of data, finally reach a kind of means of the target information needed for acquisition, technology and science.High spectrum image remote sensing technology (Hyper-spectralGraphicRemoteSensing), being a kind of remote sensing stood in the technical foundation of hyperspectral technique, is a kind ofly merge novel spectrographic detection technology, micro-signal Detection Techniques, optical precision optical machinery, signal high-speed processing technology, computer treatmenting information technology advance together, comprehensive, scientific technology.This technology is simultaneously owing to having influence on the gordian technique of numerous scientific domains such as geonomy, environmental protection, field biology, infotech, spatiography; the progress of its technology enjoys strongly attracting attention of Chinese scholars; be widely used in the aspects such as greening vegetation, soil analysis, precision agriculture management, atmosphere environment supervision, monitoring water environment, exploration mineral resource distribution at present, fully illustrate the Potential & advantage of high spectrum resolution remote sensing technique.

Usually can think like this in global remote sensing circle: multispectral remote sensing (Multi-spectralRemoteSensing) refers to spectrum discrimination rate 1 ~ 9.9 × 10 ^-1remote sensing in the spectral range of λ, is only distributed in little wave band number of visible region and nearly mid-infrared light spectral region in the remote sensor in this scope; High-spectrum remote-sensing (Hyper-spectralRemoteSensing) refers to spectrum discrimination rate 1 ~ 9.9 × 10 ^-2remote sensing technology in the spectral range of λ; Ultraspectral remote sensing (Ultra-spectralRemoteSensing) then refers to after the progress of more hi-tech, and spectrum discrimination rate reaches 1 ~ 9.9 × 10 ^-3remote sensing technology in the spectral range of λ.Remote sensing technology, its development course is after panchromatic (i.e. black and white) photography with chromatic image stage, multispectral remote sensing develops the period second half in twentieth century rapidly, achieve larger progress, and applied to environment and re-sources field of detecting, but its resolution is still in the wavelength coverage of order of magnitude spectrum, only has relatively less sampled point, along with the development of science and technology, people are more and more deep to earth resource and environment understanding, it uses precision more and more can not satisfy the demands, the demand for development more deep to resolution is more urgent, be mainly reflected in the deep and raising of spatial resolution and spectral resolution.Referring between two terrain and its features adjacent in remote sensing image in spatial resolution in picture can by the minimum length distinguished, namely usually said picture know degree, can be used for the visual interpretation to image data.And the wavelength of the minimum spectrum interval that can distinguish that the spectral reflectance referred in spectral detection in spectral resolution in picture goes out, more specifically, be exactly the performance of detection zone spectral.Relative to the direct vision of spatial resolution, spectrum observation technology can more directly and the structure and properties of effective reaction atural object, especially investigates at become more meticulous planning, exploration mineral products of ocean detection monitoring, animals and plants research classification, agricultural and have better effect and speed faster in modernization Military application.Along with making rapid progress of science and technology, the develop rapidly of aerospace industries, the continuous renewal progress upgrading of remote-sensing flatform and optical sensor, that improves Remote Spectra resolution is in swift and violent growth momentum, and the development of high spectrum resolution remote sensing technique has become the study hotspot of current remote sensing technology researchers.Because the different material of kind character is under the spectral illumination of certain wavelength, there is the absorption of respective different proportion and the characteristic of reflection, by contrasting the difference between its reflectance spectrum (or absorb) spectrum, can derive its material constituent and physically between difference.How could extract the particular attribute (feature) of material and clear understanding and periphery material and the relation in configuration from the image of data complexity, become the problem mainly solved in research.

Target in hyperspectral remotely sensed image (Hyper-spectralRemoteSensingImages), refer in the mid and far infrared spectrum in electromagnetic wave spectrum, near infrared spectrum, visible light and ultraviolet spectral region, under the effect of optical spectrum imagers, a lot of spectral distribution obtained continuously and the very little image information data of SPECTRAL REGION scope.Along with developing rapidly and progress of imaging spectrometer, the target in hyperspectral remotely sensed image that can get is compared to the remote sensing images of traditional two-dimensional imaging technique, it has tens so that the spectrogram of up to a hundred band overlappings, each basic pixel structure is wherein from tens so that the spectrum picture obtained obtained individual waveband channels continuously up to a hundred, the reflection characteristic of its positive corresponding spectrum material object, finally all can obtain a comparatively complete curve of spectrum.High-spectrum remote sensing is no longer two-dimensional imaging technique, is organically combined by the spectral theory of uniqueness with remotely sensed image technology, the continuous print object spectrum curve of formation, makes to utilize hyperspectral technique can the details of successful inverting terrain and its features.

In today of high-spectrum remote sensing development, obtain in multiple field and used widely, and achieved gratifying effect.High spectrum resolution remote sensing technique, its spectral resolution is 10 ^-2in the scope of the spectral wavelength of the λ order of magnitude, relative to 10 of traditional multispectral romote sensing technology ^-1the λ order of magnitude has had great lifting, and utilization there has also been matter must be progressive.In high-spectrum remote sensing, the division of pixel has two kinds: pure pixel and mixed pixel.Pure pixel refer to using the curve of spectrum of the curve of spectrum in image pixel elements as single clutter reflections, this kind of method obviously can simplify calculating and be convenient to use, but, even spectral resolution has had huge progress like this, due to the complicacy of atural object and the technical limitation of sensor element, pixel in high-spectrum remote sensing and the curve of spectrum are normally mixed, Here it is mixed pixel by the reflectance spectrum of multiple atural object.The reflection spectrum curve of each the single atural object in mixed pixel is referred to as end member.The existence of mixed pixel affects and plays the effect of high-spectrum remote sensing technology, how just can better carry out Decomposition of Mixed Pixels and become top priority.

Summary of the invention

Goal of the invention: the existence of mixed pixel affects and plays, in order to better carry out Decomposition of Mixed Pixels the effect of high-spectrum remote sensing technology.The invention provides a kind of method that mixed pixel of hyper-spectral image decomposes, the intelligent classification method of high-spectrum remote sensing, is a kind of method that mixed pixel of hyper-spectral image of the NMF algorithm based on SC-SVM decomposes.

Technical scheme: a kind of method of mixed pixel of hyper-spectral image decomposition of the NMF algorithm based on SC-SVM newly.The method is decomposed in the process of mixed pixel at application NMF algorithm, SC-SVM algorithm is used to the end member quantity in mixed pixel and solving of spectral vector, its can initiative recognition end member quantity and mark the vector of endmember spectra, thus the basis matrix solved in NMF algorithm, then design factor matrix (i.e. abundance matrix) is carried out by Algorithms of Non-Negative Matrix Factorization, by minimizing the process progressive alternate of objective function to convergence, thus calculate the result wanted, finally reach the object of Decomposition of Mixed Pixels.Specifically comprise the steps:

Step 1: high spectrum image is carried out pre-service, comprise radiant correction and geometry correction etc., by the correction to the geometry deformation produced in image acquisition procedures, distortion and noise, thus acquisition penetrates real image at geometry and good fortune as far as possible, the wave band that removal effect is bad, image storage format is changed into the second-order matrix V of convenient operation, namely in V, the curve of spectrum of the corresponding mixed pixel of each column vector is vectorial.

Step 2: obtain the number K of end member and the spectral vector of corresponding end member according to SC-SVM method.In SC-SVM method, select radial kernel function, wherein ask K to ask Laplace operator corresponding v _jbe exactly the spectral vector of end member, make given training sample set { x _i, i=1,2 ..., n, x _i∈ R ⁿ, v ∈ (0,1] be the parameter estimation set

Step 3: utilize NMF algorithm, solves matrix of coefficients H, adopts the iteration of unidirectional amount in the calculation, more can simplify the calculating of iterative process, reduces calculated amount and complexity.

SC-SVM method is utilized just singly to classify to spectral information, by spectral information through radial kernel Function Projective in high-dimensional feature space, seek best lineoid make mapping (enum) data sample point and origin interval maximum, thus find out end member quantity and projection vector corresponding to each endmember spectra information, can obtain NMF decompose the basis matrix for asking.

If the second-order matrix V={v of high-spectrum remote sensing _i, i=1,2 ..., n, is made up of n pixel, v _ibe a column vector, represent the curve of spectrum in a mixed pixel; Utilize NMF method, require to characterize the basis matrix W of end member feature and the matrix of coefficients H of each end member abundance in each pixel, i.e. V ≈ WH; In SC-SVM method, be selected in kernel function suitable in Hyperspectral imagery processing is radial kernel function, namely original image V is passed through mapping function map in higher dimensional space I, it can thus be appreciated that:

For radial kernel function; SC-SVM is as common svm classifier machine, and object is searching optimal hyperlane, but this lineoid makes the sample point mapped be separated with initial point, and maximizes the Euclidean distance of initial point and lineoid, makes the equation of lineoid be wherein w is the normal vector of lineoid, and ρ is biased; Lineoid is ρ/‖ w ‖ to the Euclidean distance of initial point, and maximize the interval of initial point and sample mapping point, namely max (ρ/‖ w ‖), constructs quadratic programming problem, and then calculate, solve Laplace operator { α _i, i=1,2 ..., n, finds out in this operator and identified out, the number of j is exactly the number K of the end member required by us, the x that each j is corresponding _jbe exactly the endmember spectra vector that we require, we can in the hope of arriving basis matrix W={x thus _j.

After obtaining basis matrix W, use the method for NMF, solve matrix of coefficients (i.e. abundance matrix) H;

By the known V=WH of NMF, make H={h _i, i=1,2 ..., n, h _ifor the column vector of K element, namely abundance vector, meets element non-negative and abundance and be, i.e. h _ij>=0 and

Establishing target function is:

$F(W,H)=\frac{1}{2}\left|\right|V-WH|{|}^2---\left(2\right)$

Function basis matrix W before solving determines thus, does not need again as NMF method, iteration two matrixes, only have now a matrix of coefficients H to be unknown, computationally quantity and difficulty all can reduce greatly; By formula (2), H is differentiated:

$\frac{\∂F}{\∂H}=-W^{T}V+W^{T}WH---\left(3\right)$

Adopt gradient descent method, obtain:

$H\←H-{\mathrm{\μ}}_H\frac{\∂F}{\∂H}---\left(4\right)$

μ _hfor learning rate, here get obtain iterative formula:

$H\←H.*\frac{W^{T}V}{W^{T}WH}---\left(5\right)$

In formula .* represents corresponding element and is multiplied.In this computation, we can solve separately abundance vector with each pixel, thus obtain whole abundance matrix, and namely objective function becomes:

$F(W,h_i)=\frac{1}{2}\left|\right|v_i-{\mathrm{Wh}}_i|{|}^2---\left(6\right)$

Thus iterative formula becomes:

$h_i\←h_i.*\frac{W^T{v}_i}{W^T{\mathrm{Wh}}_i}---\left(7\right).$

Accompanying drawing explanation

Fig. 1 is SVM principle schematic;

Fig. 2 is linearly inseparable algorithm schematic diagram;

Fig. 3 is SVM process flow diagram;

Fig. 4 is SC-SVM model schematic;

Fig. 5 is USGS data pictures;

Fig. 6 (1) for NMF algorithm is to the abundance of 6 kinds of Endmember extraction, a, talcum, b, water ammonium feldspar, c, almandine, d, alunite, e, smalite, f, acmite;

Fig. 6 (2) for CNMF algorithm is to the abundance of 6 kinds of Endmember extraction, a, talcum, b, water ammonium feldspar, c, almandine, d, alunite, e, smalite, f, acmite;

Fig. 6 (3) for SC-SVMNMF algorithm is to the abundance of 6 kinds of Endmember extraction, a, talcum, b, water ammonium feldspar, c, almandine, d, alunite, e, smalite, f, acmite;

Fig. 7 is certain city picture in HYDICE database;

Fig. 8 (1) is that three kinds of methods are estimated the abundance on meadow, a, NMF, b, CNMF, c, SC-SVMNMF;

Fig. 8 (2) is that three kinds of methods are estimated the abundance of bituminous pavement, a, NMF, b, CNMF, c, SC-SVMNMF;

Fig. 8 (3) is that three kinds of methods are estimated the abundance of trees, a, NMF, b, CNMF, c, SC-SVMNMF;

Fig. 8 (4) three kinds of methods are estimated the abundance on roof, a, NMF, b, CNMF, c, SC-SVMNMF.

Embodiment

Below in conjunction with specific embodiment, illustrate the present invention further, these embodiments should be understood only be not used in for illustration of the present invention and limit the scope of the invention, after having read the present invention, the amendment of those skilled in the art to the various equivalent form of value of the present invention has all fallen within the application's claims limited range.

Based on the method that the mixed pixel of hyper-spectral image of the NMF algorithm of SC-SVM decomposes, comprising:

Step 1: high spectrum image is carried out pre-service, comprise radiant correction and geometry correction etc., by the correction to the geometry deformation produced in image acquisition procedures, distortion and noise, thus acquisition penetrates real image at geometry and good fortune as far as possible, the wave band that removal effect is bad, image storage format is changed into the second-order matrix V of convenient operation, namely in V, the curve of spectrum of the corresponding mixed pixel of each column vector is vectorial.

Step 2: obtain the number K of end member and the spectral vector of corresponding end member according to SC-SVM method.In SC-SVM method, select radial kernel function, wherein ask K to ask Laplace operator corresponding v _jbe exactly the spectral vector of end member, make given training sample set { x _i, i=1,2 ..., n, x _i∈ R ⁿ, v ∈ (0,1] be the parameter estimation set.

Step 3: utilize NMF algorithm, solves matrix of coefficients H, adopts the iteration of unidirectional amount in the calculation, more can simplify the calculating of iterative process, reduces calculated amount and complexity.

Techniques and methods involved for a better understanding of the present invention, is introduced the theory that the present invention relates at this.1.SVM rudimentary algorithm

Support vector machine (SVM) is a kind of novel Data classification machine learning method, and its initial object is classified for two class samples of linear separability.As shown in Figure 1.

Square sample and circular sample represent two kinds of samples that we will separate respectively, classify respectively with+1 and-1, and the target of SVM is the best lineoid that searching one can realize largest interval.

Make sample set { (x _i, y _i), i=1,2 ..., n, x _i∈ R, y _i∈-1 ,+1}, if classifying face equation is:

w·x+ρ＝0(8)

Wherein w is the normal vector of lineoid, and ρ is biased.Then can release and be spaced apart 2/ ‖ w ‖, now, we require that best lineoid will make interval maximum, namely be equivalent to so draw and be equivalent to quadratic programming problem:

$\left\{\begin{array}{c}\min \frac{1}{2}\left|\right|w|{|}^2\\ s.t.\→y_i\left(\right(w\·x_i)+\mathrm{\ρ})\≥1,i=1,2,...,n\end{array}\right.---\left(9\right)$

Easy for calculating, we introduce Lagrange (Lagrange) function:

$L(w,\mathrm{\ρ},\mathrm{\α})=\frac{1}{2}\left|\right|w|{|}^2-\underset{i=1}{\overset{n}{\Σ}}{\mathrm{\α}}_i\left(\right(y_i\left(w\·x_i\right)+\mathrm{\ρ})-1)---\left(10\right)$

Wherein for Lagrange multiplier, ask w and ρ local derviation to formula (10), ask minimum by extreme value, namely

$\left\{\begin{array}{c}w=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i{x}_i\\ \underset{i=1}{\overset{n}{\Σ}}{y}_i{\mathrm{\α}}_i=0\end{array}\right.---\left(11\right)$

Thus push type (12) is converted into dual problem, for:

$\left\{\begin{array}{c}\underset{\mathrm{\α}}{\min }\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\α}}_j{y}_i{y}_j\left(x_i\·x_j\right)-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i\\ \begin{array}{ccc}s.t.\→\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i{\mathrm{\α}}_i=0,& {\mathrm{\α}}_i\≥0,& i=1,2,\mathrm{...},n\end{array}\end{array}\right.---\left(12\right)$

At higher dimensional space, adopt kernel function K (x ₁, x ₂) replace inner product (x ₁x ₂), then obtain:

$\left\{\begin{array}{c}\underset{\mathrm{\α}}{\min }\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\α}}_j{y}_i{y}_{j}K\left(x_i,x_j\right)-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i\\ \begin{array}{ccc}s.t.\→\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i{\mathrm{\α}}_i=0,& {\mathrm{\α}}_i\≥0,& i=1,2,\mathrm{...},n\end{array}\end{array}\right.---\left(13\right)$

Separate this linear convex quadratic programming, draw optimum solution { α ^*, then solve optimum solution w by formula (11) ^*and ρ ^*, then best lineoid equation is: (w ^*x)+ρ ^*=0, thus draw final we want the decision-making equation asked:

$f\left(x\right)=\mathrm{sgn}\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i^{*}{y}_{i}K\right(x,x_i)+{\mathrm{\ρ}}^{*})---\left(14\right)$

Wherein sgn () is sign function, namely $\mathrm{sgn}\left(x\right)=\left\{\begin{array}{cc}+1,& x\&GreaterEqual;0\\ -1,& x<0\end{array}\right..$

Above SVM algorithm is the situation of two class sample linear separabilities, if linearly inseparable, then above method can not be suitable for again, and we can introduce slack variable ξ _i>=0 to weaken border, namely removes the impact of outliers point, thus continue the situation of the sample " conversion " of linearly inseparable to linear separability.As shown in Figure 2.

This optimization problem becomes:

$\left\{\begin{array}{c}\min \left(\frac{1}{2}\left|\right|w|{|}^2+C\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&xi;}}_i\right)\\ \begin{array}{cc}s.t.\&RightArrow;y_i\left(w\&CenterDot;x+\mathrm{\&rho;}\right)+{\mathrm{\&xi;}}_i\&GreaterEqual;1,& i=1,2,\mathrm{...},n\end{array}\end{array}\right.---\left(15\right)$

Wherein C is error penalty coefficient, for constant and C > 0, to weigh empiric risk and the complexity of SVM classifier.C is larger, represent larger to the punishment degree of outlier, precision will be made higher, but its extensive degree will reduce.

SVM process flow diagram is as shown in Figure 3:

2.SC-SVM algorithm

Svm classifier machine is divided into two classification, many classification and classifier of singly classifying, usually said SVM two classification classifiers mainly, its vital role is classified by two class samples, kernel function is in fact used to build suitable high-dimensional feature space, under structure space minimization principle, make two class samples classify, many classification can use two classification to classify repeatedly, seriatim a class sample and residue sample are classified, finally reach the object of all carrying out classifying, and used herein to SVM mainly singly to classify SVM (Single-ClassSVM, SC-SVM).First use SC-SVM algorithm to carry out single classification to each mixed pixel in algorithm, draw end member number and endmember spectra vector, then use NMF algorithm to carry out Decomposition of Mixed Pixels, thus reach the object of Decomposition of Mixed Pixels.

SC-SVM is an important branch of SVM development, it can be equivalent to two special classification, based on Optimal Separating Hyperplane and classification largest interval inwardly, the optimal classification surface (best lineoid or hypersphere) maximizing interval between initial point and sample is sought.

Make given training sample set { x _i, i=1,2 ..., n, x _i∈ R ⁿ, in the higher dimensional space mapped, set up point that lineoid makes sample map and initial point is separated, make lineoid equation be:

w·φ(x)-ρ＝0(16)

Wherein w is hyperplane method vector, and φ (x) is mapping function, and ρ is lineoid intercept.Lineoid is ρ/‖ w ‖ to the distance of initial point, and the object of classification is the interval maximizing initial point and sample mapping point, i.e. max (ρ/‖ w ‖).As shown in Figure 4.

In algorithm, introduce a relaxation factor ξ _i>=0 to add the generalization of strong algorithms, and now SC-SVM is equivalent to convex quadratic programming problem:

Wherein v ∈ (0,1] be the parameter estimation of setting, can find by observing contrast (17) and formula (15) with the punishment parameter C effect comparing class in former SVM method seemingly.

Introduce Lagrange (Lagrange) function, obtain:

Respectively local derviation is asked to w, ρ and ξ, minimize w, ρ and ξ, namely solve $\frac{\&part;L}{\&part;\mathrm{\&xi;}}=0:$

Bring kernel function into thus, pair type quadratic programming problem can be released:

$\left\{\begin{array}{c}\min \frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{\mathrm{\&alpha;}}_{j}K\left(x_i,x_j\right)\\ s.t.\&RightArrow;\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i=1,0\&le;{\mathrm{\&alpha;}}_i\&le;\frac{1}{vn}\end{array}\right.---\left(20\right)$

Solve this planning equation and can obtain Laplace operator { α _i, i=1,2 ..., n, now solves intercept $\mathrm{\&rho;}=\underset{i=1}{\overset{n}{\&Sigma;}}{\mathrm{\&alpha;}}_{i}K(x_i,x_j),$ Thus decision function is:

$f\left(x\right)=\mathrm{sgn}\left(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{i}K\left(x_i,x\right)-\mathrm{\&rho;}\right)---\left(21\right)$

Wherein sgn () is sign function.

3. Algorithms of Non-Negative Matrix Factorization (NMF)

NMF algorithm solves basis matrix and matrix of coefficients under being intended to non-negative condition, by minimizing the process progressive alternate of objective function to convergence, thus calculates the result wanted.The nonnegativity restrictions of NMF algorithm meets the actual physics meaning of most signal, and thus paying attention to very widely appears just receiving in one.Analysis of complexity algorithm is the redundancy for generally depositing in natural sign, if be all used for computational analysis, a large amount of manpower and materials will certainly be wasted, by to the recompile of signal to compress the length reducing message code, carrying out computational analysis on this basis again can be more effectively terse.

The simulation experiment result is analyzed

1. experimental image

This part experiment adopts USGS database picture, and this picture size is 395 × 350 pixels, totally 224 wave bands (wave band that removal effect is bad).As shown in Figure 5 (through dimensionality reduction display).Through using the extraction of virtual dimension algorithm, the end member number of this part is 12 kinds, in Endmember extraction, we ignore shade and bring interactional interference between the error of the curve of spectrum and end member, illustrate with regard to talcum, water Chang'an stone, almandine, alunite, smalite and acmite 6 kinds of typical end members below, to the abundance of end member, three kinds of methods estimate that schematic diagram is as shown in Fig. 6 (1)-6 (4):

2. interpretation

From figure, comparatively significantly can find out that the estimation effect of the end member abundance that SC-SVMNMF algorithm and CNMF algorithm extract than NMF algorithm is much better, herein algorithm SC-SVMNMF algorithm estimates all to have a good effect to the extraction of end member and abundance.

This experiment adopts HYDICE database, and this image is certain urban parts EO-1 hyperion picture, as shown in Figure 7 (through dimension-reduction treatment).

This picture size is 320 × 240 pixels, i.e. mixed pixel, wherein comprises 210 wave bands, wave band (1-4,45,76 that removal effect is bad, 87,98,101-112,136-152,198-210), get the spectrum picture of remaining 160 wave bands, through checking computations, pixel main in this figure has 4 kinds, and respectively: meadow, bituminous pavement, trees and roof, experimental result image is as shown in Fig. 8 (1)-8 (4).

Can find out that the demeanour estimation of CNMF and SC-SVMNMF algorithm can significantly better than NMF algorithm from experimental result Fig. 8 (1)-8 (4), and slightly difference list between CNMF and SC-SVMNMF algorithm is not too obvious.

Claims (4)

1., based on the method that the mixed pixel of hyper-spectral image of the NMF algorithm of SC-SVM decomposes, it is characterized in that, specifically comprise the steps:

Step 1: high spectrum image is carried out pre-service, changes into the second-order matrix V of convenient operation by image storage format, namely in V, the curve of spectrum of the corresponding mixed pixel of each column vector is vectorial;

Step 2: obtain the number K of end member and the spectral vector of corresponding end member according to SC-SVM method; In SC-SVM method, select radial kernel function, wherein ask K to ask Laplace operator corresponding v _jit is exactly the spectral vector of end member;

Step 3: utilize NMF algorithm, solves matrix of coefficients H, adopts the iteration of unidirectional amount in the calculation, more can simplify the calculating of iterative process, reduces calculated amount and complexity.

2. as claimed in claim 1 based on the method that the mixed pixel of hyper-spectral image of the NMF algorithm of SC-SVM decomposes, it is characterized in that, SC-SVM method is utilized just singly to classify to spectral information in step 2, by spectral information through radial kernel Function Projective in high-dimensional feature space, seek best lineoid make mapping (enum) data sample point and origin interval maximum, thus find out end member quantity and projection vector corresponding to each endmember spectra information, can obtain NMF decompose the basis matrix for asking.

3., as claimed in claim 2 based on the method that the mixed pixel of hyper-spectral image of the NMF algorithm of SC-SVM decomposes, it is characterized in that, if the second-order matrix V={v of high-spectrum remote sensing _i, i=1,2 ..., n, is made up of n pixel, v _ibe a column vector, represent the curve of spectrum in a mixed pixel; Utilize NMF method, require to characterize the basis matrix W of end member feature and the matrix of coefficients H of each end member abundance in each pixel, i.e. V ≈ WH; In SC-SVM method, be selected in kernel function suitable in Hyperspectral imagery processing is radial kernel function, namely original image V is passed through mapping function map in higher dimensional space I, it can thus be appreciated that:

For radial kernel function; SC-SVM is as common svm classifier machine, and object is searching optimal hyperlane, but this lineoid makes the sample point mapped be separated with initial point, and maximizes the Euclidean distance of initial point and lineoid, makes the equation of lineoid be wherein w is the normal vector of lineoid, and ρ is biased; Lineoid to the Euclidean distance of initial point be ρ/|| w||, maximizes the interval of initial point and sample mapping point, and namely max (ρ/|| w||), constructs quadratic programming problem, and then calculate, solve Laplace operator { α _i, i=1,2 ..., n, finds out in this operator and identified out, the number of j is exactly the number K of the end member required by us, the x that each j is corresponding _jbe exactly the endmember spectra vector that we require, we can in the hope of arriving basis matrix W={x thus _j.

4. as claimed in claim 2 based on the method that the mixed pixel of hyper-spectral image of the NMF algorithm of SC-SVM decomposes, it is characterized in that, after obtaining basis matrix W, use the method for NMF, solve matrix of coefficients (i.e. abundance matrix) H;

By the known V=WH of NMF, make H={h _i, i=1,2 ..., n, h _ifor the column vector of K element, namely abundance vector, meets element non-negative and abundance and be, i.e. h _ij>=0 and

Establishing target function is:

$F(W,H)=\frac{1}{2}\left|\right|V-WH|{|}^2---\left(2\right)$

Function basis matrix W before solving determines thus, does not need again as NMF method, iteration two matrixes, only have now a matrix of coefficients H to be unknown, computationally quantity and difficulty all can reduce greatly; By formula (2), H is differentiated:

$\frac{\&part;F}{\&part;H}=-W^{T}V+W^{T}WH---\left(3\right)$

Adopt gradient descent method, obtain:

$H\&LeftArrow;H-{\mathrm{\&mu;}}_H\frac{\&part;F}{\&part;H}---\left(4\right)$

μ _hfor learning rate, here get obtain iterative formula:

$H\&LeftArrow;H.*\frac{W^{T}V}{W^{T}WH}---\left(5\right)$

In formula .* represents corresponding element and is multiplied.In this computation, we can solve separately abundance vector with each pixel, thus obtain whole abundance matrix, and namely objective function becomes:

$F(W,h_i)=\frac{1}{2}\left|\right|v_i-{\mathrm{Wh}}_i|{|}^2---\left(6\right)$

Thus iterative formula becomes:

$h_i\&LeftArrow;h_i.*\frac{W^T{v}_i}{W^T{\mathrm{Wh}}_i}---\left(7\right).$