CN106326926A - Hyperspectral image target spectrum learning method - Google Patents

Abstract

The invention belongs to the technical field of remote sensing image processing, and particularly provides a target spectrum learning method for the problem of hyperspectral image target detection. The method is formed by two parts of a target spectrum learning algorithm based on the self-adaptive weight and a self-complete dictionary construction method. As for the content of the former part, learning of the target spectrum is optimized through a sparse coding and gradient descent algorithm under the condition of existence of a complete background dictionary; and as for the content of the latter part, the completeness of the dictionary is ensured by continuous expansion of the background dictionary so as to guarantee the accuracy of the learning algorithm. The accurate target spectrum is extracted so that the effect of the hyperspectral remote sensing image target detection algorithm can be effectively enhanced, and the method has important value in the actual application.

Description

A kind of high spectrum image target optical spectrum learning method

Technical field

The invention belongs to technical field of remote sensing image processing, be specifically related to a kind of for high-spectrum remote sensing target acquisition The target optical spectrum learning method of problem.

Background technology

High-spectrum remote sensing has higher spectral resolution, its observation wavelength cover electromagnetic spectrum ultraviolet, can Seeing light, near-infrared and mid infrared region, each pixel in image is a continuous spectrum being made up of hundreds of wave bands Curve, contains detailed object spectrum information.And the atural object of each kind suffers from corresponding spectral signature curve, because of This high-spectrum remote sensing has the advantage of uniqueness in ground object target field of detecting, receives the extensive weight of researchers in recent years Depending on [1].

Target acquisition algorithm is broadly divided into two classes: have supervision and without supervision.The method having supervision refers to the mesh with priori Mark spectral information, is detected the pixel with this target information, thus realizes target acquisition by all kinds of algorithms.Unsupervised side Method is mainly used in the situation that target optical spectrum is unknown, and target to be looked for is exactly to differ from the pixel in field around in image, because of This this kind of method is the most often referred to as abnormality detection.Proposed algorithm is primarily directed to the feelings of priori target optical spectrum Condition, i.e. has supervision target acquisition.

Traditional target acquisition algorithm include bound energy minimize (Constrained Energy Minimization, CEM) algorithm [2], self adaptation cosine compliance evaluation device (Adaptive Coherence/Cosine Estimator, ACE) are calculated Method [3], adaptive matched filter (Adaptive Matched Filter, AMF) algorithm [4] etc., these algorithms are all based on Statistical principle, has a wide range of applications.In the last few years, some innovatory algorithm, such as multi-layer C EM (hierarchical CEM, hCEM) algorithm [5], and some target acquisitions algorithm [6] based on sparse theory, [7] the also studied persons of priority propose, There is preferable Effect on Detecting.

But, the Effect on Detecting of above method is the most relevant to the accuracy of the target optical spectrum of priori.When priori target light When composing inaccurate, algorithm above cannot obtain gratifying effect.Generally there are following three kinds of methods at present to obtain target ground The spectral information of thing: (1) Laboratory Spectra data base；(2) pixel in high spectrum image or the average of multiple pixel [8]；(3) Endmember extraction algorithm [9].But the mode that the spectrum in library of spectra typically uses laboratory or field measurement obtains, Affected by observation geometry, illumination, air, noise of instrument etc. so that it is poor to exist between the spectrum in measure spectrum and true picture Different [10].Meanwhile, " the different spectrum of jljl " phenomenon makes same atural object have a plurality of corresponding Laboratory Spectra.Additionally Owing to the spatial resolution of high-spectrum remote sensing is relatively low, image exists substantial amounts of mixed pixel, be difficult under normal circumstances protect Some pixel on card image belongs to pure goal pels, and carrying out careful judgement needs again bigger cost of labor.And hold Unit's extraction algorithm needs to there is pure goal pels in image, requires that the target detected has higher probability of occurrence simultaneously, when When conditions above is unsatisfactory for, Endmember extraction algorithm is also difficult to obtain target optical spectrum accurately.

Therefore, in a practical situation, the accuracy of priori target optical spectrum is difficult to be guaranteed, has the effect of target acquisition Large effect.In the recent period, for this problem, T.Wang, et al proposes the ACE that a kind of iteration self-adapting is weighed surely (reweighted ACE, rACE) algorithm [11], this algorithm carrys out optimization aim spectrum by multilamellar ACE algorithm, thus obtains more Excellent result.But this algorithm cannot tackle relative complex background [5].S.Yang, et al proposes a kind of robust CEM (CEM using a inequality constrain, CEM-IC) algorithm [12], does not wait constraint to replace CEM with one Middle equality constraint so that the target detected is the envelope constituted near priori target optical spectrum.But the method is promoting Increasing false alarm rate in the case of detectivity, additionally the selection of parameter is the most relatively difficult the most simultaneously.In sum, priori target light Compose inaccurate problem still without being well solved.

Related to the present invention some concepts are described below

Sparse coding and dictionary learning

Based on sparse representation model, existing dictionary matrixWhereinIndicate N_bIndividual The background dictionary of atom,Indicate N_tThe target dictionary of individual atom, each pixel x on image_i∈R^L×1, can To be expressed as:

x_i=D γ_i+ν (1)

Whereinα_iAnd β_iFor the sparse vector that background dictionary is corresponding with target dictionary, v is error term.

Sparse vector γ_iCan obtain by solving following optimization problem:

$\begin{array}{ccc}{\mathrm{\γ}}_i=\underset{{\mathrm{\γ}}_i}{\mathrm{argmin}}\left|\right|x_i-{\mathrm{D\γ}}_i|{|}_2^2& s.t.& \left|\right|{\mathrm{\γ}}_i|{|}_0\≤K_0\end{array}---\left(2\right)$

Wherein | | | |₀Represent l₀Norm, refers to the number of nonzero element, K in matrix₀Represent γ_iDegree of rarefication.But ask Topic (2) is a non-convex problem, is generally relaxed to l₁Norm solves:

${\mathrm{\γ}}_i=\underset{{\mathrm{\γ}}_i}{\mathrm{argmin}}\left|\right|x_i-{\mathrm{D\γ}}_i|{|}_2^2+\mathrm{\λ}|\left|{\mathrm{\γ}}_i\right|{|}_1---\left(3\right)$

Wherein | | | |₁Represent l₁Norm, each element absolute value sum in representing matrix, λ is weighting factor.Solve problems (3) process is referred to as sparse coding, and this problem is a convex problem, can return (Least angle by minimum angular convolution Regression, LARS) algorithm [14] solves.

When dictionary matrix D the unknown when, the problem of dictionary learning can be expressed as:

$\{D,\{{\mathrm{\γ}}_i\left\}\right\}=\underset{D,\left\{{\mathrm{\γ}}_i\right\}}{\mathrm{argmin}}\underset{i=1}{\overset{N}{\Σ}}\left(\right||x_i-{\mathrm{D\γ}}_i|{|}_2^2+\mathrm{\λ}\left|\right|{\mathrm{\γ}}_i\left|{|}_1\right)---\left(4\right)$

Wherein N is number of samples.Can be optimized by a loop iteration following two step and obtain study dictionary: 1) Sparse vector in Solve problems (3)；2) by following formula gradient updating dictionary matrix:

$D^{(n+1)}=D^{\left(n\right)}-\mathrm{\μ}\underset{i=1}{\overset{N}{\Σ}}(D^{\left(n\right)}{\mathrm{\γ}}_i-x_i){\mathrm{\γ}}_i^T---\left(5\right)$

Wherein μ is for updating step-length.

Summary of the invention

It is an object of the invention to propose the mesh for high-spectrum remote sensing target acquisition problem of a kind of excellent effect Mark spectroscopy learning method.

The target optical spectrum learning method that the present invention proposes, by target optical spectrum learning algorithm based on adaptive weighting with from complete Standby background dictionary building method two parts form.Front portion content is in the case of the most complete background dictionary, passes through Sparse coding and gradient descent algorithm carry out Optimization Learning target optical spectrum；Rear portion content is the continuous expansion by background dictionary Guarantee the completeness of this dictionary, thus ensure the accuracy of learning algorithm.The present invention, can by extracting target optical spectrum accurately To be effectively improved the effect of high-spectrum remote sensing target acquisition algorithm.Particular content is described below:

One, target optical spectrum learning algorithm based on adaptive weighting (Adaptive weighted learned method, AWLM)

The thinking of target optical spectrum learning algorithm is derived from dictionary learning algorithm [13], and different is, it is assumed that obtained One complete background dictionary D_bWith initial priori target optical spectrum d, fixed background dictionary D_b, target optical spectrum d accurately_tPermissible Obtain by solving following optimization problem:

$\begin{array}{cc}\{d_i,\{{\mathrm{\α}}_i\},\{{\mathrm{\β}}_i\left\}\right\}=\underset{d_t,\left\{{\mathrm{\α}}_i\right\},\left\{{\mathrm{\β}}_i\right\}}{\arg \min }\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\left(\right||x_i-\[D_b,d_t\]\×\left[\begin{array}{c}{\mathrm{\α}}_i\\ {\mathrm{\β}}_i\end{array}\right]|{|}_2^2+\mathrm{\λ}\left|\right|\left[\begin{array}{c}{\mathrm{\α}}_i\\ {\mathrm{\β}}_i\end{array}\right]\left|{|}_1\right)& \\ =\underset{d_t,\left\{{\mathrm{\α}}_i\right\},\left\{{\mathrm{\β}}_i\right\}}{\arg \min }\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\left(\right||x_i-D_b{\mathrm{\α}}_i-{\mathrm{\β}}_i{d}_t|{|}_2^2+\mathrm{\λ}\left|\right|\left[\begin{array}{c}{\mathrm{\α}}_i\\ {\mathrm{\β}}_i\end{array}\right]\left|{|}_1\right)& s.t.d_t^0=d,\end{array}---\left(6\right)$

Wherein,Represent d_tInitial setting up, remaining pa-rameter symbols implication is the same.It should be noted that the purpose of algorithm It is to obtain target optical spectrum accurately from high spectrum image learning, therefore to should sparse coefficient β of target optical spectrum_iIt it is a mark Amount.First pass through sparse coding Algorithm for Solving sparse vector:

$\left\{\right\{{\mathrm{\α}}_i\},\{{\mathrm{\β}}_i\left\}\right\}=\underset{\left\{{\mathrm{\α}}_i\right\},\left\{{\mathrm{\β}}_i\right\}}{\arg \min }\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\left(\right||x_i-D\×\left[\begin{array}{c}{\mathrm{\α}}_i\\ {\mathrm{\β}}_i\end{array}\right]|{|}_2^2+\mathrm{\λ}\left|\right|\left[\begin{array}{c}{\mathrm{\α}}_i\\ {\mathrm{\β}}_i\end{array}\right]\left|{|}_1\right)---\left(7\right)$

Then, d_tBeing optimized by gradient descent algorithm, its more new formula is as follows:

$d_t^{k+1}=d_t^k+\mathrm{\μ}\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\β}}_i{x}_t^i,x_t^i=x_i-D_b{\mathrm{\α}}_i---\left(8\right)$

Wherein,Can be regarded as pixel x in cyclic process_iRemove the target residual after background component.Constantly more than circulation Two steps can be with solving-optimizing problem (6).

Such as dictionary learning algorithm, updating d every time_tAfterwards, tackle it and carry out two norm normalization operations.

But the accuracy of above-mentioned optimization method greatly relies on the accuracy of initial background dictionary, and background word accurately Allusion quotation is generally difficult to obtain.Simultaneously according to optimization problem (6), all of pixel has a same weight, but in a practical situation, The probability of occurrence of target sample is the least, gives the identical weight of all of pixel unreasonable.Proposed algorithm introduces certainly Adapt to weight, overcome problem above by giving different weights to each pixel.In theory, corresponding to each pixel Weight should be relevant to the accounting of target in this pixel, and the weight of the pixel that target accounting is the biggest is bigger, otherwise, then weight is relatively Little.In iterative optimization procedure, pixel x_iAccounting t of middle target_iIt is expressed from the next:

$t_i=\frac{\left|\right|{\mathrm{\β}}_i{d}_t|{|}_2}{\left|\right|x_i|{|}_2}=\frac{{\mathrm{\β}}_i}{\left|\right|x_i|{|}_2}---\left(9\right)$

Wherein, d_tTwo norms be fixed as 1.Then the weight obtaining each pixel with minor function is used:

$g\left(t_i\right)=\frac{1}{1+e^{-\mathrm{\κ}*(t_i-\mathrm{\τ})}}---\left(10\right)$

Wherein, κ and τ is two parameters controlling g (t), specifically can be fixed to 30 and 0.5.Concrete function shape Shape is shown in Fig. 1.It can be seen that the pixel that target accounting is more than τ has bigger weight.Then by each weight of following formula normalization:

${\mathrm{\ω}}_i=\frac{g\left(t_i\right)}{\underset{i=1}{\overset{N}{\Σ}}g\left(t_i\right)}---\left(11\right)$

After introducing adaptive weighting, optimization problem (6) becomes:

$\begin{array}{cc}\{d_i,\{{\mathrm{\α}}_i\},\{{\mathrm{\β}}_i\left\}\right\}=\underset{d_t,\left\{{\mathrm{\α}}_i\right\},\left\{{\mathrm{\β}}_i\right\}}{\arg \min }\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i\left(\right||x_i-\[D_b,d_t\]\×\left[\begin{array}{c}{\mathrm{\α}}_i\\ {\mathrm{\β}}_i\end{array}\right]|{|}_2^2+\mathrm{\λ}\left|\right|\left[\begin{array}{c}{\mathrm{\α}}_i\\ {\mathrm{\β}}_i\end{array}\right]\left|{|}_1\right)& \\ =\underset{d_t,\left\{{\mathrm{\α}}_i\right\},\left\{{\mathrm{\β}}_i\right\}}{\arg \min }\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_i\left(\right||x_i-D_b{\mathrm{\α}}_i-{\mathrm{\β}}_i{d}_t|{|}_2^2+\mathrm{\λ}\left|\right|\left[\begin{array}{c}{\mathrm{\α}}_i\\ {\mathrm{\β}}_i\end{array}\right]\left|{|}_1\right)& s.t.d_t^0=d,\end{array}---\left(12\right)$

Correspondingly, d_tGradient Iteration formula be:

$d_t^{k+1}=d_t^k+\mathrm{\μ}\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\ω}}_i{\mathrm{\β}}_i{x}_t^i,x_t^i=x_i-D_b{\mathrm{\α}}_i---\left(13\right)$

Significantly, since adaptive weighting ω_iWith β_iRelevant, optimization problem (12) is a non-convex problem, may The problem having local optimum, but test result indicate that afterwards, this algorithm still can be restrained and achieve desired results.

The flow process of target optical spectrum learning algorithm based on adaptive weighting is:

For observation data matrix X ∈ R^b×N, priori target optical spectrum d ∈ R^b×1, background dictionaryWherein b table Registration is according to wave band number, and N represents the number of samples in data, N_bRepresent the atom number in background dictionary；

Algorithm initialization:

Circulation below performing:

(1.2a), integration background dictionary and target dictionary:

$D=\[D_b,d_t^k\].$

(1.2b), each pixel x is solved_iSparse vector { the α of corresponding dictionary_i},{β_i}:

$\left\{\right\{{\mathrm{\α}}_i\},\{{\mathrm{\β}}_i\left\}\right\}=\underset{\left\{{\mathrm{\α}}_i\right\},\left\{{\mathrm{\β}}_i\right\}}{\arg \min }\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\left(\right||x_i-D\×\left[\begin{array}{c}{\mathrm{\α}}_i\\ {\mathrm{\β}}_i\end{array}\right]|{|}_2^2+\mathrm{\λ}\left|\right|\left[\begin{array}{c}{\mathrm{\α}}_i\\ {\mathrm{\β}}_i\end{array}\right]\left|{|}_1\right)$

Wherein, | | | |₂Represent l₂Norm, | | | |₁Represent l₁Norm, each element absolute value sum in representing matrix, {α_i},{β_iIt is pixel x_iThe sparse vector of corresponding dictionary D, λ is weighting factor；

(1.2c), calculate the adaptive weighting that each pixel is corresponding, pass sequentially through calculating below equation and obtain:

$t_i=\frac{\left|\right|{\mathrm{\β}}_i{d}_t|{|}_2}{\left|\right|x_i|{|}_2}=\frac{{\mathrm{\β}}_i}{\left|\right|x_i|{|}_2}$

$g\left(t_i\right)=\frac{1}{1+e^{-\mathrm{\κ}*(t_i-\mathrm{\τ})}}$

${\mathrm{\ω}}_i=\frac{g\left(t_i\right)}{\underset{i=1}{\overset{N}{\Σ}}g\left(t_i\right)}$

Wherein, t_iRepresent pixel x_iThe component of middle target, g (t_i) it is a projection function, wherein κ Yu τ is to control this function Two parameters of shape, κ controls g (t_i) slope of interlude, τ controls g (t_i) center value, work as t_iDuring=τ, g (t_i)= 0.5；

(1.2d), target optical spectrum is updated:

$d_t^{k+1}=d_t^k+\mathrm{\μ}\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\ω}}_i{\mathrm{\β}}_i{x}_t^i,x_t^i=x_i-D_b{\mathrm{\α}}_i$

Wherein, μ is for updating step-length；

(1.2e), normalization target optical spectrum:

$d_t^{k+1}=d_t^{k+1}/\left|\right|d_t^{k+1}|{|}_2^2$

(1.2f), more row iteration number of times:

k←k+1

(1.2g), when meetingTime, jump out circulation；

Wherein, ε represents the threshold value of iteration ends；

Output study spectral results

Two, from complete background dictionary building method (SCBD)

AWLM algorithm solves background dictionary D by introducing adaptive weighting_bInaccurate brought problem, from certain journey Ensure on degree that algorithmic statement is to actual target optical spectrum.But work as D_bTime the most complete, the effectiveness of algorithm still existing problems. Consider the situation of a kind of worst, i.e. D_bIt is an empty set, the now target residual x in iterative formula (13)_t ⁱValue be exactly picture Element spectral vector itself.According to formula (13), d_tCertain atural object endmember spectra that in image, accounting is maximum can be converged to.Therefore may be used D is worked as to be concluded that_bTime incomplete, the result of AWLM convergence is probably certain background spectrum.Here, it is proposed that one Plant background dictionary constructing plan so that after AWLM converges to certain spectral vector, first this spectral vector is judged, if It is judged to background spectrum, then makes D_bA new atom, then restart to take turns AWLM learning algorithm, if it is decided that For target, then this spectrum is required accurate target spectrum.During such a, D_bConstantly expand complete until accurate Standby target optical spectrum is learnt to obtain, and therefore this dictionary is referred to as from complete background dictionary.

Proposed algorithm utilizes two features of target to judge convergence result d of AWLM_tWhether belong to target: (1) its Distance between the target optical spectrum d of spectrum and priori is within the specific limits；(2) probability of occurrence of target is low.The information of d may not Enough accurate, but also can have certain target information, work as d_tWith d apart from excessive, it is believed that learning outcome is a bias light Spectrum.Due to d_tTwo norm normalization have the most been carried out, it is possible to use simple Euclidean distance weighs distance between the two with d, When | | d_t-d||₂≤ η, d_tMay be target optical spectrum, otherwise be then background spectrum.η is decision threshold, specifically can be fixed as 0.2. In the ordinary course of things, object pixel accounting in whole high spectrum image is the lowest, and its threshold value is set as 0.5%.In AWLM mistake Cheng Zhong, the target accounting pixel more than τ has bigger weight, utilizes the number of greater weight pixel, be denoted as sum (t_i>=τ), Weigh d_tProbability of occurrence.

Work as d_tMeet simultaneously | | d_t-d||₂≤ η and sum (t_i>=τ) two conditions of≤0.005N time, d_tIt is judged as reality Target optical spectrum, is otherwise judged to background spectrum, starts new AWLM circulation as a new background dictionary atom.

From the flow process of complete background dictionary building method it is:

For observation data matrix X ∈ R^b×N, priori target optical spectrum d ∈ R^b×1；

Algorithm initialization: D_b=[]；

Circulation below performing:

(2.2a), target optical spectrum learning algorithm based on adaptive weighting is utilized to obtain learning outcome d_t∈R^b×1；

(2.2b), when meeting less than two conditions simultaneously, circulation is jumped out, otherwise D_b=[D_b,d_t]:

Condition 1:| | d_t-d||₂≤η；Wherein η is judgment threshold；

Condition 2: adaptive weighting t_iPixel number more than τ is less than 0.005N；

Output is from complete background dictionary

The beneficial effects of the present invention is: utilize hyperspectral image data, obtained supervision mesh from real image learning Priori target optical spectrum required for mark detection, utilizes this learning outcome can obtain more preferable target as priori target optical spectrum and visits Survey effect, have important using value in the target acquisition field of high-spectrum remote sensing.

Emulation and the experiment of actual high-spectral data show, the spectrum being learnt to obtain more is kissed with actual target optical spectrum Closing, utilize this learning outcome as priori target optical spectrum, traditional CEM, ACE algorithm can obtain more preferably and more robust Effect on Detecting.

Accompanying drawing explanation

Fig. 1 adaptive weighting shape graph.

Fig. 2 algorithm flow illustrates.

The curve of spectrum of white mica in Fig. 3 US Geological Survey library of spectra.

Fig. 4 Cuprite data set.Wherein, (a) Cuprite intuitively shows figure；B () atural object is true.

Fig. 5 target optical spectrum based on Cuprite data set learning outcome.Wherein, (a) is using wherein three spectrum as priori The learning outcome of target optical spectrum；B () whole 10 spectrum are as the learning outcome of priori target optical spectrum.

Fig. 6 is based on Cuprite data set, the ROC curve of each method under utilization difference priori target optical spectrum.Wherein, (a) White mica _ 107；(b) white mica _ 108；(c) white mica _ 119.

Fig. 7 airport data set.Wherein, (a) intuitively shows figure；(b) all Aircraft Targets curve of spectrum.

Fig. 8 target optical spectrum based on airport data set learning outcome.Wherein, (a) is using wherein three aircraft spectrum as elder generation Test the learning outcome of target optical spectrum；B () whole 73 spectrum are as the learning outcome of priori target optical spectrum.

Fig. 9 based on airport data set, utilizes the ROC curve of each method under the priori target optical spectrum of diverse location.Wherein, A () position is (10,91)；B () position is (22,71)；C () position is (35,53).

Target optical spectrum learning outcome under Figure 10 difference noise.Wherein, (a) 10dB；(b)20dB；(c)30dB.

The algorithm that Figure 11 difference CEM is correlated with ROC curve under different noises.Wherein, (a) 10dB；(b)20dB；(c) 30dB。

The algorithm that Figure 12 difference ACE is correlated with ROC curve under different noises.Wherein, (a) 10dB；(b)20dB；(c) 30dB。

Time on the data set of Figure 13 airport using the pixel spectrum on diverse location as priori target optical spectrum, AWLM_SCBD's Convergence curve.Wherein, (a) position is (10,91)；B () position is (22,71)；C () position is (35,53).

Detailed description of the invention

Below, respectively by the specific embodiment that the present invention is described as a example by analog data and actual remote sensing image data.

First pass through AWLM_SCBD Algorithm Learning and obtain target optical spectrum accurately, then utilize this target optical spectrum by passing System CEM algorithm and ACE algorithm obtain result of detection, by this result with directly utilize CEM algorithm, ACE algorithm and up-to-date proposition The result of detection of hCEM algorithm [5], rACE algorithm [11] and CEM-IC algorithm [12] compare, verify AWLM_SCBD Algorithm effectiveness in terms of extracting accurate target spectrum.

The target optical spectrum learning method that the present invention uses, is made up of AWLM and SCBD two parts, and invention algorithm is called for short AWLM_ SCBD, its algorithm flow framework flow process is as in figure 2 it is shown, specific algorithm is described as follows:

Algorithm: AWLM_SCBD

Input: primary data matrix X ∈ R^b×N, the target optical spectrum d ∈ R of priori^b×1

Output: target optical spectrum d accurately_t∈R^b×1

Initialize installation: λ=0.5, η=0.2, κ=30, τ=0.5, μ=0.1, ε=10^-5,

Step 1. initializes interior cycle-index: k=0；

Step 2. performs following circulation (AWLM):

1.2a)

Formula (3) 1.2b) is utilized to solve sparse vector；

Formula (9), (10) and (11) 1.2c) is utilized to calculate each pixel weight；

1.2d) update iteration by formula (13)

1.2e) two norm normalization

1.2f) when meetingTime, jumping out circulation, AWLM exports

Step 3. is when meeting | | d_t-d||₂≤ η and sum (t_i>=τ) two conditions of≤0.005N time, terminate AWLM_SCBD calculate Method, exports d_t；Otherwise, D_b=[D_b,d_t] and return step 1.

Under recipient's operating characteristic curve (Receiver operating characteristic, ROC) and ROC curve Area (Area under ROC curve, AUC) is used as the evaluation criterion of detection performance in experiment.ROC is by drawing false alarm rate (False Alarm Rate, FAR) and detectivity (Probability of Detection, PD) relation represent, wherein FAR It is expressed as with the computing formula of PD:

$FAR=\frac{N_f}{N},PD=\frac{N_c}{N_t}---\left(14\right)$

Wherein, N_fRepresenting and be mis-marked the background dot number into impact point, N represents the sum of all background dots, N in image_c Represent the number of the impact point successfully detected, N_tRepresent the total number of impact point.

Experiment 1, analog data experiment

Tu3Shi US Geological Survey (United States Geological Survey, USGS) spectra database [15] curve of spectrum of white mica in, includes altogether 10 curves of spectrum, and jljl different spectrum phenomenon is extensively deposited it can be seen It is in hyperspectral image data.When in employing USGS, the curve of spectrum of white mica is as priori target optical spectrum, its spectrum is very Likely different from the curve of spectrum of white mica in real image, the result of detection of all kinds of target algorithm there is is bigger shadow Ring.Extract the target optical spectrum of reality thereby through AWLM_SCBD algorithm, then recycling other target acquisition algorithm can obtain Obtain gratifying effect.In order to verify the effectiveness of AWLM_SCBD algorithm, have employed the mode buried a little and carry out constructive simulation number According to.Emulation experiment has used Cuprite data set³, Cuprite data set is by airborne visible ray and Infrared Imaging Spectrometer (Airborne Visible/Infrared Imaging Spectrometer, AVIRIS) was shot on June 19th, 1997 The data in Nevada, USA Cuprite area, these data have 224 wave bands, and picture size is 250 × 191, its pseudocolour picture As shown in Fig. 4 (a).Before the use, the 1st～3,104～115 and 150～170 wave bands are owing to signal to noise ratio is too low or inhales for water Receive wave band and be rejected, stay 188 wave bands to be further processed.Pixel spectra z of embedment impact point is by following formula meter Obtain:

Z=f t+ (1-f) b (15)

Wherein, f is the abundance of target, and t is target optical spectrum, and b is the spectrum of current pixel.Position such as Fig. 4 (b) institute of embedment Show, wherein above two row be size be the target sample of 2 × 2, next two columns is simple target pixel, respective abundance f such as table 1 Shown in.In Fig. 3, the spectrum of numbered white mica _ 111 is as the target optical spectrum t of embedment, adds the Gaussian noise of 30dB simultaneously. Owing to white mica has 10 spectrum in library of spectra, then using these 10 spectrum as priori target optical spectrum, use AWLM_ SCBD algorithm extracts target optical spectrum.

The Abundances of target imbedded by table 1

Fig. 5 is target optical spectrum learning outcome based on Cuprite data set, and wherein Fig. 5 (a) is to make with wherein three spectrum

For the learning outcome of priori target optical spectrum, Fig. 5 (b) combines as priori target optical spectrum of whole 10 spectrum Practise result.In figure, AWLM_SCBD (white mica _ 107) expression is using the spectrum of numbered white mica _ 107 as priori target optical spectrum, Then utilize AWLM_SCBD algorithm to extract and obtain target optical spectrum curve accurately.It can be seen that extract the result obtained with actual The curve of spectrum of embedment is sufficiently close to, and is close to and overlaps, and illustrates that AWLM_SCBD can efficiently extract out the target optical spectrum of reality.

When Fig. 6 is using wherein three different white mica spectrum as priori target optical spectrum, the ROC corresponding to each method Curve.Table 2 is the AUC area corresponding to each method.Result shows, other kinds method, calculates including traditional CEM algorithm, ACE Method and new rACE algorithm, hCEM algorithm and the CEM-IC algorithm proposed are all by the inaccurate impact of target optical spectrum.And it is the most logical Cross AWLM_SCBD algorithm to extract accurately after target optical spectrum, utilize traditional CEM and ACE method can obtain more preferably and More stable result of detection.

The AUC area (%) of all kinds of algorithms on table 2Cuprite data set

Experiment 2, truthful data experiment

Truthful data experiment has used a width by AVIRIS airborne hyperspectral imaging spectrometer at California, USA Shooting high-spectrum remote sensing data above airport, Santiago, as shown in Fig. 7 (a), this picture size is 180 × 180, makes With before, the 1st～6,33～35,97,107～113,153～166 and 221～224 wave bands are owing to signal to noise ratio is too low or be water Absorption bands and be rejected, stay 189 wave bands to be further processed.In figure, one has three airplanes, contains 73 Individual Aircraft Targets pixel, shown in its spectrum such as Fig. 7 (b).

Truthful data experiment is tested using these 73 aircraft spectrum as priori target optical spectrum.AWLM_SCBD calculates The target optical spectrum result of calligraphy learning is as shown in Figure 8.Fig. 8 (a) is using the pixel spectrum of three positions in image as target light spectroscopy The example practised, shown in particular location such as Fig. 7 (a).Fig. 8 (b) combines the result that 73 target spectroscopy are practised.Fig. 9 is with three When the pixel spectrum of position is as priori target optical spectrum, the ROC curve that each method is corresponding.Table 3 is the AUC face that each method is corresponding Long-pending.Compared to emulation data experiment, truthful data experimental result the most more dissipates, this is because true picture number According to increasingly complex.It should be noted that wherein have that 3 aircraft spectrum are obtained by AWLM_SCBD Algorithm Learning is certain in figure The spectrum on one class roof.This is because these 3 aircraft spectrum are actually the mixed spectra of aircraft and ground, its curve of spectrum with The spectrum on that class roof extremely approximates, and this material being possibly due to this type of roof has similarity with aircraft materials.With This simultaneously, this type of roof spectrum meets and judges goal condition, and proposed algorithm terminates in study acquisition roof light time spectrum Iteration.But as a whole, the target optical spectrum that AWLM_SCBD is extracted is obviously improved for result of detection.

The AUC area (%) of all kinds of algorithms on the data set of table 3 airport

Experiment 3, noise robustness experiment

On Cuprite data set, analyze the noise impact on proposed algorithm by adding the noise of varying strength. Figure 10 is using the curve of spectrum of numbering white mica _ 108 as priori target optical spectrum, the target optical spectrum study knot under different noises Really.Result shows, the target optical spectrum curve that study obtains is close, wherein at 20dB and 30dB with the curve of spectrum of actual embedment In the case of the most identical with actual spectrum curve.In the case of noise is relatively big (10dB), learning outcome is the most crude, and this is main Less because of the number of target sample in image.Owing to CEM algorithm and ACE algorithm are affected by noise different, in order to Preferably representing experimental result, corresponding ROC curve is divided into two classes: CEM related algorithm and ACE related algorithm, respectively such as Figure 11 Shown in Figure 12.It can be seen that AWLM_SCDB algorithm can extract preferable target light under the noise of varying strength Spectrum so that the effect of target acquisition is obviously improved.

Experiment 4, convergence experiment

The introducing of adaptive weighting makes optimization problem (12) become a non-convex problem, thus convergence result there may be Local minimum problem, but experiment all shows, proposed algorithm all can be restrained well.Figure 13 is a difference on the data set of airport When the pixel spectrum of position is as priori target optical spectrum, the convergence curve of AWLM_SCBD.Wherein the longitudinal axis isWhen This value is less than 10^-5Time, loop convergence in one group of AWLM, then judge whether the result of AWLM belongs to target, when this result is judged to When being set to background spectrum, circulate in starting next round AWLM as the new atom of background dictionary.In figure, lower section transverse axis represents total Iterations, top transverse axis represents the number of background dictionary Atom.Figure 13 (a) represents that this target optical spectrum learning process experiences altogether 11 AWLM circulations, and Figure 13 (b) and (c) only experienced by 6 AWLM circulations, this is because position is the picture on (10,91) Unit's spectrum and actual aircraft spectral differences are away from relatively big, and this point can be as seen from Figure 7, it is therefore desirable to the most complete background word Actual target light spectroscopy could be gone out by allusion quotation.From here it can also be seen that proposed from complete background dictionary non-traditional meaning Complete dictionary in justice, actually refers to a background dictionary that can learn out required target optical spectrum.

In summary, for simulation and actual high-spectral data, the algorithm that the present invention proposes can be effectively from height Spectrum picture extracts target optical spectrum, significantly increases the effect of target acquisition algorithm, the algorithm pair that the present invention proposes simultaneously Noise robustness, has preferable convergence property, also has important value in the middle of reality application.

List of references:

[1]Nasrabadi Nasser M.Hyperspectral target detection:an overview of current and future challenges[J].IEEE Signal Process.Mag.,2014,31(1):34-44.

[2]Farrand William H.,Harsanyi Joseph C.Mapping the distribution of mine tailings in the Coeur d’Alene River Valley,Idaho,through the use of a constrained energy minimization technique[J].Remote Sens.Environ.,1997,59(1): 64–76.

[3]Kraut Shawn,Scharf Louis L.,McWhorter L.Todd.Adaptive subspace detectors[J].IEEE Trans.Signal Process.,2001,49(1):1-16.

[4]Robey Frank C.,Fuhrmann Daniel R.,Kelly Edward J.,et al.A CFAR adaptive matched filter detector[J].IEEE Trans.Aerosp.Electron.Syst.,1992,28 (1):208-216.

[5]Zou Zheng-Xia,Shi Zhen-Wei.Hierarchical suppression method for hyperspectral target detection[J].IEEE Trans.Geosci.Remote Sens.,2016,54(1): 330-342.

[6]Chen Yi,Nasrabadi Nasser M.,Tran Trac D.Sparse representation for target detection in hyperspectral imagery[J].IEEE J.Sel.Topics Signal Process.,2011,5(3):629-640.

[7]Zhang Yu-Xiang,Du Bo,Zhang Liang-Pei.A sparse representation-based binary hypothesis model for target detection in hyperspectral images[J].IEEE Trans.Geosci.Remote Sens.,2015,53(3):1346-1354.

[8]Zhang Le-Fei,Zhang Liang-Pei,Tao Da-Cheng,et al.Sparse transfer manifold embedding for hyperspectral target detection,[J].IEEE Trans.Geosci.Remote Sens.,2014,52(2):1030-1043.

[9]Winter Michael E.N-FINDR:an algorithm for fast autonomous spectral endmember determination in hyperspectral data[C].In Proc.SPIE,1999,3753:266– 275.

[10]Shaw Gary A.,Burke Hsiao-Hua.Spectral imaging for remote sensing [J].Lincoln Lab.J.,2003,14(1):3–28.

[11]Wang Ting,Du Bo,Zhang Liang-Pei.An automatic robust iteratively reweighted unstructured detector for hyperspectral imagery[J].IEEE J.Sel.Topics Appl.Earth Observ.Remote Sens.,2014,7(6):2367-2382.

[12]Yang Shuo,Shi Zhen-Wei,Tang Wei.Robust hyperspectral image target detection using an inequality constraint[J].IEEE Trans.Geosci.Remote Sens., 2015,53(6):3389-3404.

[13]Aharon Michal,Elad Michael,Bruckstein Alfred.K-SVD:an algorithm for designing overcomplete dictionaries for sparse representation[J].IEEE Trans.Signal Process.,2006,54(11):4311–4322.

[14]Zou Hui,Hastie Trevor,Tibshirani Robert.Sparse principal component analysis[J].J.Comp.Graph.Statist.,2006,15(2):265-286.

[15]Clark R.N.,Swayze G.A.,Gallagher A.J.,et al.The U.S.geological survey digital spectral library:Version 1:0.2 to 3.0μm[J].U.S.Geol.Surv., Denver,CO,USA,Open File Rep.93-592,1993.

[16]Mairal Julien,Bach Francis,Ponce Jean,et al.Online learning for matrix factorization and sparse coding[J].J.Mach.Learn.Res.,2010,vol.11(1): 19–60.。

Claims (6)

1. a high spectrum image target optical spectrum learning method, it is characterised in that include target optical spectrum based on adaptive weighting Learning algorithm, from complete background dictionary building method；Wherein:

One, the flow process of target optical spectrum learning algorithm based on adaptive weighting is:

For observation data matrix, priori target optical spectrum, background dictionary；Its In,Represent data wave hop count,Represent the number of samples in data,Represent the atom number in background dictionary；

Algorithm initialization:, iterations；

Circulation below performing:

(1.2a), integration background dictionary and target dictionary:

(1)

(1.2b) sparse vector of each pixel correspondence dictionary, is solved:

(2)

Wherein,Representl ₂Norm,Representl ₁Norm, each element absolute value sum in representing matrix,For pixel Corresponding dictionarySparse vector,It it is weighting factor；

(1.2c), the adaptive weighting that each pixel is corresponding is calculated, pass sequentially through calculating below equation and obtain:

(3)

(4)

(5)

Wherein,Represent pixelThe component of middle target,It is a projection function, whereinWithIt it is the shape controlling this function Two parameters,ControlThe slope of interlude,ControlCenter value, whenTime,；

(1.2d), target optical spectrum is updated:

(6)

Wherein,For updating step-length；

(1.2e), normalization target optical spectrum:

(7)

(1.2f), more row iteration number of times:

(8)

(1.2g), when meetingTime, jump out circulation；

Wherein,Represent the threshold value of iteration ends；

Output study spectral results；

Two, the flow process from complete background dictionary building method is:

For observation data matrix, priori target optical spectrum；

Algorithm initialization:；

Circulation below performing:

(2.2a), target optical spectrum learning algorithm based on adaptive weighting is utilized to obtain learning outcome；

(2.2b), when meeting less than two conditions simultaneously, circulation is jumped out, otherwise:

Condition 1:；WhereinFor judgment threshold；

Condition 2: adaptive weightingIt is more thanPixel number less than 0.005N；

Output is from complete background dictionary。

Learning method the most according to claim 1, it is characterised in that in step (1.2b)It is fixed as 0.5.

Learning method the most according to claim 1, it is characterised in that in step (1.2c)WithIt is fixed to 30 With 0.5.

Learning method the most according to claim 1, it is characterised in that in step (1.2d)It is fixed as 0.1.

Learning method the most according to claim 1, it is characterised in that in step (1.2g)It is fixed as 10^-5。

Learning method the most according to claim 1, it is characterised in that in step (2.2b)It is fixed as 0.2.