CN103440502A - Infrared small-target detection method based on mixing Gauss and sparse representation - Google Patents

Abstract

The invention provides an infrared small-target detection method based on mixing Gauss and sparse representation. The method comprises the following steps: constructing an overcomplete morphological dictionary of an image in a self-adaptive mode by adopting a K cluster singular value decomposition K_SVD method; according to the characteristic that object signals are usually distributed in a Gauss mode, dividing the atoms of the self-adaptive overcomplete morphological dictionary into target atoms representing target forms and background atoms representing background noise components by using a Gauss overcomplete dictionary, and forming a self-adaptive mixing Gauss overcomplete dictionary having a target morphological dictionary and a background morphological dictionary; performing sparse representation on an original image block in the mixing Gauss overcomplete dictionary and extracting the sparse representation coefficient of an image signal; and when the rarefication degree represented by the sparse representation coefficient is greater than a threshold, determining that the image block contains a target, otherwise determining that the image block is a background. By using the method provided by the invention, defects can be overcome that it is difficult for a conventional Gauss sparse dictionary to be adaptive to non-Gaussian distributed target forms and judging whether a target is contained by Gauss atom sparse representation coefficients, and thus the detection performance of small and weak targets can be improved.

Description

Infrared small target detection method based on the mixed Gaussian rarefaction representation

Technical field

The invention belongs to deep space Spacecraft TT&C field, be specifically related to survey infrared weak moving target detection, be a core technology of infrared imaging acquisition and tracking system, targeted surveillance system, satellite remote sensing system, safety check system etc., all can be widely used in all kinds of military, civilian systems.

Background technology

In various imaging detection trackers, requirement can be intercepted and captured and the locking tracking target as soon as possible.When distant between detector and target, target shows as the little target that only accounts for several pixels in imaging, and is easy to be submerged in various clutter backgrounds and very noisy, and this has brought great difficulty to object detecting and tracking.

Current, the Method of Target Detection in Infrared based on single frames can be divided into detection algorithm and detection algorithm two classes based on study based on image filtering.At first albefaction picture signal of detection algorithm based on image filtering, then adopt threshold process to obtain target location, as Top-Hat, TDLMS and wavelet transformation etc.Detection algorithm based on study is that target detection problems is converted into to the pattern classification problem, it is trained object module and background model, and similarly be the no target that contains according to regular process decision chart, as Principal Component Analysis Method (Principal Component Analysis, PCA) and the series of algorithms developed out, sparse theoretical detection algorithm etc.This class algorithm obtains testing result by building the little weak target signature of the little weak target sample collection extraction of Gauss, and sample set commonly used comprises Gauss's dictionary, Gabor dictionary, discrete Gabor perception multicomponent dictionary etc.Gauss's sample and the sparse dictionary with Gauss model are suitable for the little weak target of Gaussian distribution, and little weak target morphology dynamic change, Gauss model is difficult to adapt to the non-structural forms such as non-Gaussian distribution, and adaptability and detectability remain further to be strengthened.

Summary of the invention

For Gauss's dictionary and adaptive morphology dictionary in the deficiency that means and extract echo signal, the present invention be take target and is presented different morphological differencess from background signal as starting point in image, has proposed a kind of infrared small target detection method based on the mixed Gaussian rarefaction representation.The present invention solves the problems of the technologies described above by the following technical solutions.

The present invention proposes a kind of infrared small target detection side based on the mixed Gaussian rarefaction representation, relate to the observation and control technology field.The present invention adopts the super complete form dictionary of K cluster singular value decomposition method K_SVD self-adaptation design of graphics picture; Based target signal informal dress is from the characteristics of Gaussian distribution, adopt the super complete dictionary of Gauss that the atom of the super complete form dictionary of self-adaptation is divided into to the target atoms that means target morphology and the background atom that means the ground unrest composition, and then form the super complete dictionary of mixed Gaussian with target morphology dictionary and background form dictionary; The original image piece is carried out to Its Sparse Decomposition or rarefaction representation in the super complete dictionary of mixed Gaussian, extract the rarefaction representation coefficient of picture signal at the super complete dictionary of mixed Gaussian; The sparse degree that adopts degree of rarefication tolerance image block to decompose at the target morphology dictionary, carry out threshold process by degree of rarefication, be greater than threshold value image block contain target, otherwise be background.

The super complete dictionary of described Gauss is to take Gaussian function as model, the expansion Gaussian function $I(i,j)=I_{\max }\exp (-\frac{1}{2}[\frac{{(i-x_0)}^2}{{\mathrm{\σ}}_x^2}\text{+}\frac{{(j-y_0)}^2}{{\mathrm{\σ}}_y^2}\left]\right)$ In parameter obtain a large amount of atoms, and then form the super complete dictionary of Gauss.Particularly, take the upper left corner of sample image is initial point, by regulating the point (x of target's center ₀, y ₀), the pixel value I of central point _max, the horizontal dispersion parameter s _xwith the vertical dispersion parameter s _yfour parameters generate diverse location, different brightness, difform infrared small target sample image, i.e. super complete Gauss's dictionary D _gaussian.

The super complete adaptive morphology composition dictionary of described K_SVD training comprises sparse coding and two steps of dictionary updating.In the sparse coding stage, an at first given initial dictionary D, the sparse coefficient of employing tracing algorithm computed image, solve

in formula, || γ || ₀mean l ₀norm, the i.e. number of element in rarefaction representation coefficient vector γ.In the dictionary updating stage, upgrade the row of dictionary D at every turn, upgrade an atom d _k, find the image block of using this atom in image f, the error after this atom rarefaction representation of definition figure image subtraction

utilize SVD to decompose obtain one group of best approximation (d _k, g _k).Due to the coefficient g tried to achieve _kfull vector, it and g _kmiddle non-zero number and position are inconsistent, Divergent Phenomenon occurs.For head it off, remove g _kin all neutral elements, only retain nonzero value, then utilize Singular Value Decomposition Using SVD to upgrade (d _k, g _k), try to achieve the d after renewal _kwith sparse coefficient g _k.Each atom is repeated to the dictionary updating stage, upgraded all atoms and completed once whole dictionary updating, repeatedly upgrade dictionary until meet algorithm convergence E _k￡ e, can train the sparse dictionary D adapted with original image f.

The assorting process of described super complete adaptive morphology composition dictionary comprises the steps: 1) solve the atom d of super complete adaptive morphology composition dictionary _kat Gauss's dictionary D _gaussianthe rarefaction representation coefficient

? $\widehat{\mathrm{\α}}=\underset{\mathrm{\α}}{\arg \min }{\left|\right|d_k-D_{\mathrm{gaussian}}a\left|\right|}_2^{2}s.t.{\left|\right|\mathrm{\α}\left|\right|}_0=n,$ Wherein, d _kd (k 1...m) is each atom in adaptive morphology composition dictionary D, D _gaussianfor Gauss's dictionary, after n time is decomposed, obtain the sparse coefficient that comprises n nonzero value

; 2) solve atom d after rarefaction representation _kresidual amount of energy r (d _k) be r (d _k)=|| d _k-D _gaussianα || ₂; 3) by r (d _k) with threshold value δ, compare, as residual amount of energy r (d _k) be greater than threshold value δ and judge atom d _kfor the background atom, on the contrary, d _kit is target atoms.The background atom classifies as background dictionary D _b, target atoms classifies as target dictionary D _t.

Described image block is at the super complete dictionary D=[D of mixed Gaussian _bd _t] in Its Sparse Decomposition be that greedy algorithm (matching pursuit algorithm) by iteration extracts the rarefaction representation coefficient gamma of picture signal at mixed Gaussian target morphology dictionary, solve its Approximating Solutions in certain allowable error σ

$\widehat{\mathrm{\γ}}=\arg \min {\left|\right|\mathrm{\γ}\left|\right|}_{0}s.t.{\left|\right|D\widehat{\mathrm{\γ}}-f\left|\right|}_{2}s.$

Described degree of rarefication index S I quantitative description signal is at target dictionary D _tthe sparse degree of expression factor beta,

in formula, the n signal is at target dictionary D _tits Sparse Decomposition coefficient non-zero number, i=1,2 ..., n, d _i(β) mean to belong in β the coefficient of i position.The SI of the image block that contains target (β) value is close to 1, and not containing SI (β) value of the background sub-block of target close to 0.

The accompanying drawing explanation

Fig. 1 is principle of work block diagram of the present invention;

Fig. 2 original image;

Fig. 3 is the super complete dictionary of Gauss;

Fig. 4 is super complete adaptive morphology composition dictionary;

Fig. 5 is mixed Gaussian target morphology dictionary;

Fig. 6 is mixed Gaussian rarefaction representation coefficient.

Embodiment

For Gauss's dictionary and adaptive morphology dictionary in the deficiency that means and extract echo signal, the present invention be take target and is presented different morphological differencess from background signal as starting point in image, has proposed a kind of infrared small target detection method based on the mixed Gaussian rarefaction representation.

In order to understand better technical scheme of the present invention, below in conjunction with accompanying drawing, embodiments of the present invention are further described.

The principle of work block diagram that Fig. 1 is the initial flight path detection method of the infrared small and weak moving target of the present invention.The present invention adopts the super complete form dictionary of K cluster singular value decomposition method K_SVD self-adaptation design of graphics picture; Based target signal informal dress is from the characteristics of Gaussian distribution, adopt the super complete dictionary of Gauss that the atom of the super complete form dictionary of self-adaptation is divided into to the target atoms that means target morphology and the background atom that means the ground unrest composition, and then form the super complete dictionary of mixed Gaussian with target morphology dictionary and background form dictionary; The original image piece is carried out to Its Sparse Decomposition or rarefaction representation in the super complete dictionary of mixed Gaussian, extract the rarefaction representation coefficient of picture signal at the super complete dictionary of mixed Gaussian; The sparse degree that adopts degree of rarefication tolerance image block to decompose at the target morphology dictionary, carry out threshold process by degree of rarefication, be greater than threshold value image block contain target, otherwise be background.The Infrared cloud image of low contrast of take discusses the concrete implementation detail of each several part following (in Fig. 2, center, square frame place, as little weak target, is submerged among cloud layer) in detail as example:

1. the super complete dictionary of Gauss

The super complete dictionary of Gauss is to take Gaussian function as model, the expansion Gaussian function $I(i,j)=I_{\max }\exp (-\frac{1}{2}[\frac{{(i-x_0)}^2}{{\mathrm{\σ}}_x^2}\text{+}\frac{{(j-y_0)}^2}{{\mathrm{\σ}}_y^2}\left]\right)$ In parameter obtain a large amount of atoms, and then form the super complete dictionary of Gauss.Particularly, take the upper left corner of sample image is initial point, by regulating the point (x of target's center ₀, y ₀), the pixel value I of central point _max, the horizontal dispersion parameter s _xwith the vertical dispersion parameter s _yfour parameters generate diverse location, different brightness, difform infrared small target sample image, i.e. super complete Gauss's dictionary D _gaussian.Fig. 3 is parameter { I for a change _max, (x ₀, y ₀), s _x, s _ygauss's dictionary D of obtaining of value _gaussian.

2. super complete adaptive morphology composition dictionary

Utilize the super complete adaptive morphology composition dictionary of K_SVD training to comprise sparse coding and two steps of dictionary updating.In the sparse coding stage, an at first given initial dictionary D, the sparse coefficient of employing tracing algorithm computed image, solve

in formula, || γ || ₀mean l ₀norm, the i.e. number of element in rarefaction representation coefficient vector γ.In the dictionary updating stage, upgrade the row of dictionary D at every turn, upgrade an atom d _k, find the image block of using this atom in image f, the error after this atom rarefaction representation of definition figure image subtraction

utilize SVD to decompose

obtain one group of best approximation (d _k, g _k).Due to the coefficient g tried to achieve _kfull vector, it and g _kmiddle non-zero number and position are inconsistent, Divergent Phenomenon occurs.For head it off, remove g _kin all neutral elements, only retain nonzero value, then utilize Singular Value Decomposition Using SVD to upgrade (d _k, g _k), try to achieve the d after renewal _kwith sparse coefficient g _k.Each atom is repeated to the dictionary updating stage, upgraded all atoms and completed once whole dictionary updating, repeatedly upgrade dictionary until meet algorithm convergence E _k￡ e, can train the sparse dictionary D adapted with original image f.The super complete adaptive morphology composition dictionary that Fig. 4 is the cloudy background image.The size of each atom is the 16x16 pixel, has 1024 atoms.The adaptive morphology dictionary has comprised many effective anatomic elements in infrared image, and target atoms has been reacted the morphological feature of little weak target more realistically than Gauss atom.

3. mixed Gaussian target morphology dictionary

Classified and formed mixed Gaussian target morphology dictionary by low super complete adaptive morphology composition dictionary.Mixed Gaussian target morphology dictionary process of establishing comprises the steps: 1) solve the atom d of super complete adaptive morphology composition dictionary _kat Gauss's dictionary D _gaussianthe rarefaction representation coefficient

? $\widehat{\mathrm{\α}}=\underset{\mathrm{\α}}{\arg \min }{\left|\right|d_k-D_{\mathrm{gaussian}}a\left|\right|}_2^{2}s.t.{\left|\right|\mathrm{\α}\left|\right|}_0=n,$ Wherein, d _kd (k1...m) is each atom in adaptive morphology composition dictionary D, D _gaussianfor Gauss's dictionary, after n time is decomposed, obtain the sparse coefficient that comprises n nonzero value 2) solve atom d after rarefaction representation _kresidual amount of energy r (d _k) be r (d _k)=|| d _k-D _gaussianα || ₂; 3) by r (d _k) with threshold value δ, compare, as residual amount of energy r (d _k) be greater than threshold value δ and judge atom d _kfor the background atom, on the contrary, d _kit is target atoms.The background atom classifies as background dictionary D _b, target atoms classifies as target dictionary D _t.The super complete dictionary of mixed Gaussian is both orderly combinations, i.e. D=[D _bd _t].Fig. 5 is cloud layer image blend Gauss target morphology dictionary, and figure (a) means target dictionary D _t, figure (b) means background dictionary D _b.The target atoms that the mixed Gaussian classifying dictionary is isolated in the adaptive morphology dictionary is preferably separated with the background atom, has guaranteed little weak target detection performance.

4. mixed Gaussian rarefaction representation

Image block is at the super complete dictionary D=[D of mixed Gaussian _bd _t] in rarefaction representation be that greedy algorithm (matching pursuit algorithm) by iteration extracts the rarefaction representation coefficient gamma of picture signal at mixed Gaussian target morphology dictionary, solve its Approximating Solutions in certain allowable error σ

fig. 6 is target image and the background image Its Sparse Decomposition coefficient at mixed Gaussian target dictionary Dt, and wherein figure (a) means that the sparse coefficient of target only has 2 atoms to have larger decomposition sparse, and other Atomic Decomposition sparse be zero substantially; Figure (b) means the sparse coefficient of background, has the sparse coefficient of some non-zeros, and its degree of rarefication is little a lot of than the coefficient degree of target, shows whether the target dictionary contains target to image and have stronger discrimination.Rarefaction representation and degree of rarefication thereof by comparison signal at the target dictionary, carry out threshold process by degree of rarefication, be greater than threshold value image block contain target, otherwise be background.

The present invention takes full advantage of target and present different morphological differencess from background signal in image, and self-adaptation builds super complete anatomic element dictionary, strengthens target and the background feature difference at sparse dictionary, detects little weak echo signal; The anatomic element dictionary is decomposed into to target dictionary and the background dictionary that means respectively echo signal and background information, can overcome the target morphology that the sparse dictionary of Gauss is difficult to adapt to non-Gaussian distribution, can improve again the adaptive morphology dictionary and express the degree of rarefication of infrared image signal, greatly improve little weak target echo detection performance.

Claims (9)

1. the infrared small target detection method based on the mixed Gaussian rarefaction representation, is characterized in that, described detection method comprises step:

1) based target signal informal dress, from the characteristics of Gaussian distribution, builds the super complete dictionary of Gauss;

2) adopt the super complete form dictionary of self-adaptation of K cluster singular value decomposition method K_SVD design of graphics picture;

3) adopt the super complete dictionary of Gauss that the atom of the super complete form dictionary of self-adaptation is divided into to the target atoms that means target morphology and the background atom that means the ground unrest composition, and then formation target morphology dictionary and background form dictionary, the i.e. sparse super complete dictionary of mixed Gaussian;

4) the original image piece is carried out to Its Sparse Decomposition or rarefaction representation at the sparse super complete dictionary of mixed Gaussian, extract the rarefaction representation coefficient of picture signal at the sparse super complete dictionary of mixed Gaussian;

5) the sparse degree that adopts degree of rarefication tolerance image block to decompose at the target morphology dictionary, carry out threshold process by degree of rarefication, be greater than threshold value image block contain target, otherwise be background.

2. the infrared small target detection method based on the mixed Gaussian rarefaction representation according to claim 1, is characterized in that, described typoiogical classification dictionary reconstructed image signal f=D _bα+D _tβ, wherein D _b, D _tmeaning respectively can Its Sparse Decomposition target composition and the super complete sub-dictionary of background composition, i.e. target dictionary and background dictionary, D _bα>>f _b, D _tβ>>f _tmean respectively the sparse reconstruct of echo signal and ambient noise signal.

3. the infrared small target detection method of mixed Gaussian rarefaction representation according to claim 1, is characterized in that, Gauss is super, and complete dictionary is described as Gauss model

$I(i,j)=I_{\max }\exp (-\frac{1}{2}[\frac{{(i-x_0)}^2}{{\mathrm{\σ}}_x^2}\text{+}\frac{{(j-y_0)}^2}{{\mathrm{\σ}}_y^2}\left]\right)$

Wherein, I (i, j) is positioned at the pixel value at (i, j) coordinate place, I for target _maxfor (the x of target's center ₀, y ₀) pixel value, σ _xfor horizontal dispersion parameter, σ _yfor the vertical dispersion parameter.S _xand s _ythese two parameters are being controlled the dispersion characteristic of object pixel.Take the upper left corner of sample image is initial point, by regulating (x ₀, y ₀), I _max, s _xand s _yfour parameters generate diverse location, different brightness, difform infrared small target sample image, i.e. super complete Gauss's dictionary D _gaussian.

4. the infrared small target detection method based on the mixed Gaussian rarefaction representation according to claim 1, it is characterized in that, it is training sample that described K cluster singular value decomposition method (K_SVD) is chosen image block at random, the complete adaptive morphology composition of training excess of export dictionary.

5. the infrared small target detection method based on the mixed Gaussian rarefaction representation according to claim 4, is characterized in that, the super complete adaptive morphology composition dictionary of described K_SVD training comprises step:

1) sparse coding: an at first given initial dictionary D, the sparse coefficient of employing tracing algorithm computed image, solve $\arg \min {\left|\right|\mathrm{\γ}\left|\right|}_{0}s.t.{\left|\right|f-\mathrm{D\γ}\left|\right|}_2^{2}e,$ In formula, || γ || ₀mean l ₀norm, the i.e. number of element in rarefaction representation coefficient vector γ.

2) dictionary updating: upgrade the row of dictionary D at every turn, upgrade an atom d _k, find the image block of using this atom in image f, the error after this atom rarefaction representation of definition figure image subtraction

Utilize SVD to decompose

obtain one group of best approximation (d _k, g _k).To each atom repeated execution of steps 2), upgrade all atoms and completed once whole dictionary updating, repeatedly upgrade dictionary until meet algorithm convergence, can train the sparse dictionary D adapted with original image f.

6. the infrared small target detection method based on the mixed Gaussian rarefaction representation according to claim 1, is characterized in that, the assorting process of described super complete adaptive morphology composition dictionary comprises the steps:

1) solve the atom d of super complete adaptive morphology composition dictionary _kat Gauss's dictionary D _gaussianthe rarefaction representation coefficient

? $\widehat{\mathrm{\α}}=\underset{\mathrm{\α}}{\arg \min }{\left|\right|d_k-D_{\mathrm{gaussian}}a\left|\right|}_2^{2}s.t.{\left|\right|\mathrm{\α}\left|\right|}_0=n,$ Wherein, d _kd (k1...m) is each atom in adaptive morphology composition dictionary D, D _gaussianfor Gauss's dictionary, after n time is decomposed, obtain the sparse coefficient that comprises n nonzero value

2) solve atom d after rarefaction representation _kresidual amount of energy r (d _k) be r (d _k)=|| d _k-D _gaussianα || ₂;

3) by r (d _k) with threshold value δ, compare, as residual amount of energy r (d _k) be greater than threshold value δ and judge atom d _kfor the background atom, on the contrary, d _kit is target atoms.The background atom classifies as background dictionary D _b, target atoms classifies as target dictionary D _t.

7. the infrared small target detection method based on the mixed Gaussian rarefaction representation according to claim 1, is characterized in that, by the original image piece at mixed Gaussian target morphology dictionary D=[D _bd _t] carry out Its Sparse Decomposition or rarefaction representation, extract the rarefaction representation coefficient gamma of picture signal at mixed Gaussian target morphology dictionary, the greedy algorithm (matching pursuit algorithm) by iteration solves its Approximating Solutions in certain allowable error σ

? $\widehat{\mathrm{\γ}}=\arg \min {\left|\right|\mathrm{\γ}\left|\right|}_{0}s.t.{\left|\right|D\widehat{\mathrm{\γ}}-f\left|\right|}_{2}s.$

8. the infrared small target detection method based on the mixed Gaussian rarefaction representation according to claim 1, is characterized in that, the present invention adopts degree of rarefication level index (Sparse Index, SI) quantitative description signal at target dictionary D _tthe sparse degree of expression factor beta,

in formula, the n signal is at target dictionary D _tits Sparse Decomposition coefficient non-zero number, i=1,2 ..., n, d _i(β) mean to belong in β the coefficient of i position.Obviously, the SI of the image block that contains target (β) value is close to 1, and not containing SI (β) value of the background sub-block of target close to 0.

9. the infrared small target detection method based on the mixed Gaussian rarefaction representation according to claim 1, it is characterized in that, the sparse level index SI (β) that extracts each image subblock carries out threshold process, be greater than threshold value image block contain target, otherwise be background.

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