CN102592269B - Compressive-sensing-based object reconstruction method - Google Patents

Abstract

The invention discloses a compressive-sensing-based object reconstruction method. The main problem of incapability of detecting an object in image reconstruction in the prior art is solved. The method is implemented by the following steps of: 1) performing hybrid Gaussian modeling on the object to obtain the probability density of the object by using a mixed factor analysis model; 2) blocking the whole image to be reconstructed; 3) reconstructing each image block by utilizing the learnt probability density of the object as the priori knowledge of the object; and 4) splicing the reconstructed image blocks to recover an original integral image to obtain the whole reconstructed image. The object detection and image reconstruction are realized at the same time, so that the method has the advantages of resource saving and high efficiency, and can be used for object detection.

Description

Object reconstruction method based on compressed sensing

Technical field

The invention belongs to technical field of image processing, relate to the reconstruct of natural image, is exactly a kind of compressed sensing object reconstruction method that adds target priori specifically, can be used for target detection.

Background technology

Compressed sensing (Compressive Sensing) is a new direction between mathematics and information science, is proposed by people such as Candes, Terres Tao, challenges traditional sample code technology, i.e. Nyquist sampling thheorem.Compressive sensing theory is that Signal Collection Technology has been brought revolutionary breakthrough, it adopts non-self-adapting linear projection to carry out the prototype structure of holding signal, far below nyquist frequency, signal is sampled, accurately reconstruct original signal by numerical optimization problem.Single pixel camera that rice university of the U.S. has designed according to compressive sensing theory, advanced project research administration of U.S. Department of Defense is supporting the research of compressed sensing technology, in the presence of General Electric (GE) Medical Group, a research group of winconsin university is combined compressed sensing technology with HYPR and VIPR technology, to improve the speed of particular types magnetic resonance imaging, can reach under certain conditions several thousand times of original speed.

Signal or Image Reconstruction are the key problems of compressive sensing theory, and current existing compressed sensing reconstructing method has: interior point method, gradient projection method, matching pursuit algorithm MP, orthogonal matching pursuit method OMP, Bayes's compressed sensing Byes.These compressed sensing reconstructing methods have the following disadvantages:

1) owing to not adding the priori of target in restructuring procedure, therefore these methods can only be used for the reconstruct of whole scene, the function of target in not outstanding scene, cannot find interested target in scene, staff need to process the position that could determine target again to the entire image reconstructing;

2) sampling rate is had to higher requirement, bring very large burden therefore to sampling hardware device.

Summary of the invention

The object of the invention is to for above-mentioned existing methods deficiency, a kind of object reconstruction method based on compressed sensing is proposed, to reconstruct the target in scene in the situation that sampling rate is lower, and make target clear and distinctive with respect to background, in reconstructed image, detect target.

Realizing the object of the invention ground technical thought is: first pass through hybrid cytokine analytical model to Target Modeling, obtain the probability density function of target, again to wanting the entire image piecemeal of reconstruct, then each small images is carried out respectively to compressed sensing reconstruct, the probability density function of the target that training is obtained joins restructuring procedure as the priori of target.Concrete steps comprise as follows:

(1) by hybrid cytokine analytical model, target is carried out to Gaussian Mixture modeling, obtains the probability density of target:

Wherein: x ° of be target training sample, χ _tfor the average of each Gaussian distribution of comprising in gauss hybrid models, Ω _tfor the covariance of each Gaussian distribution of comprising in gauss hybrid models, λ _tfor the weight of each Gaussian distribution in gauss hybrid models, T is the number of the Gaussian distribution that comprises in gauss hybrid models;

(2) entire image at target place is evenly divided into the identical fritter of size, the size of the size of fritter and the training image of target is identical and guarantee target is complete on a certain fritter;

(3) each small images is reconstructed respectively:

(3a) each small images x is carried out respectively random observation and is obtained its random observation vector y:

y＝Φx+v

Wherein: x is the small images for the treatment of reconstruct, its dimension is N, the random observation vector that y is small images, and the gaussian random observing matrix that Φ is, the noise producing when v is observation is obeyed the Gaussian distribution of zero-mean, and its dimension is N, wherein N=1024;

(3b) from random observation vector y, recover small images x according to following Bayesian formula:

Wherein: p (x/y) is posterior probability density, the probability density that p (x °) is the target that trains, p (y/x) is conditional probability density, for the weights of each Gaussian distribution in gauss hybrid models, for the covariance of each Gaussian distribution in gauss hybrid models, the inverse of the covariance of the noise producing when R is observation, for the average of each Gaussian distribution in gauss hybrid models, this average be the reconstructed image of small images x;

(4) small images reconstructing in step (3) is pieced together and is reduced to original complete image, the entire image that obtains reconstructing output.

The present invention compared with prior art has the following advantages:

1) the present invention is because the priori using the probability density of target as target joins restructuring procedure, thus can be in the situation that sampling rate be lower by target clearly reconstruct out, alleviate the burden of sampling hardware device, saving resource and expense;

2) the present invention is due to entire image piecemeal, then to each small images reconstruct, improved reconstruct speed, saved the time.

The simulation experiment result shows, thus the present invention can be in the situation that sampling rate be lower by the clearly out target in outstanding scene of reconstruct of target, reach the object that detects target.

Brief description of the drawings

Fig. 1 realization flow figure of the present invention;

The former figure that Fig. 2 emulation experiment of the present invention is used;

Fig. 3 uses the present invention and the reconstruction result figure of existing weighting two Norm Methods to Fig. 2 in the time that sampling rate is 20%;

Fig. 4 uses invention and the existing weighting two result figures of norm reconstructing method to Fig. 2 reconstruct in the time that sampling rate is 40%.

Embodiment

With reference to Fig. 1, specific embodiment of the invention step is as follows:

Step 1. is carried out Gaussian Mixture modeling by hybrid cytokine analytical model to target, obtains the probability density of target:

(1a) photographic subjects is at the image n of different angles width, and using these images as training image, by arest neighbors interpolation method, training image being unified into size is 32 × 32 pixels, 1000≤n≤1600;

(1b), by Beta process, obtain the order J of the covariance matrix of following Gaussian distribution:

x _i～N(Aw _i+μ，α ^-1I _N)；

Wherein: x _ifor training sample dimension is N, A represents the matrix that one group of base is N × J in hybrid cytokine analytical model, a being aligned temper space, w _ifor the coefficient of the linear subspaces that A opened in hybrid cytokine analytical model, its dimension is J, and μ is that average dimension is N, I _nbe the unit matrix of N × N, α is accuracy value;

(1c) obtain the number T of Gaussian distribution in gauss hybrid models by Dirichlet process;

(1d) Beta process is combined with Dirichlet process, obtains the value of the parameter of each Gaussian distribution in gauss hybrid models:

x _i～N(A _t(i)w _i+μ _t(i)，α _t(i) ^-1I _N)，

${\mathrm{\λ}}_t={\mathrm{\υ}}_t\underset{l=1}{\overset{t=1}{\mathrm{\Π}}}(1-{\mathrm{\υ}}_l),$

υ _t～Beta(1，η)，

$Z_t~\underset{k=1}{\overset{K}{\mathrm{\Π}}}\mathrm{Bernoulli}\left({\mathrm{\π}}_k\right),$

${\mathrm{\π}}_t~\underset{k=1}{\overset{K}{\mathrm{\Π}}}\mathrm{Beta}(a/K,b(K-1)/K),$

μ _t～N(μ，τ ₀ ^-1I _N)；

Wherein: λ _tbe each Gaussian distribution in gauss hybrid models weight and a represents the matrix that one group of base is N × J, w in hybrid cytokine analytical model _ifor the coefficient of the linear subspaces that A opened in hybrid cytokine analytical model, μ _tfor average, α _tobey Gamma for accuracy value and distribute, I _nthe unit matrix of N × N, the column vector that meets the Gaussian distribution of zero-mean, z _tto meet the column vector that Bernoulli Jacob distributes, υ _tfor λ _tfactor of influence, η is υ _tfactor of influence, υ _lfor λ _tcontrolling elements, π _tz _tfactor of influence, a is π _tthe super parameter in a left side, a=1, b is π _tthe super parameter in the right side, b=1, τ ₀for μ _tsuper parameter, τ ₀=10 ^-6, K is the factor of influence number of the hybrid cytokine analytical model of supposition, I _kit is the unit matrix of K × K;

(1e) according to the number T of Gaussian distribution in above-mentioned gauss hybrid models and all unknown parameters, obtain each Gaussian distribution, the probability density that the weighted sum of this Gaussian distribution is target:

Step 2. is evenly divided into the entire image at target place the fritter of size 32 × 32;

The priori of step 3. using the probability density of the target obtaining in step 1 as target joins restructuring procedure, and the small images obtaining in step 2 is reconstructed respectively:

(3a) each small images x is carried out respectively random observation and is obtained its random observation vector y:

y＝Φx+v

Wherein: x is the small images for the treatment of reconstruct, its dimension is N, the random observation vector that y is small images, and the gaussian random observing matrix that Φ is, the noise producing when v is observation is obeyed the Gaussian distribution of zero-mean, and its dimension is N, wherein N=1024;

(3b) obtain the posterior probability density of small images x according to Bayesian formula, estimate that the average of this probability density is the reconstruction result of small images x:

Wherein: p (x/y) is posterior probability density, the probability density that p (x °) is the target that trains, p (y/x) is conditional probability density, for the weights of each Gaussian distribution in gauss hybrid models, for the average of each Gaussian distribution in gauss hybrid models, for the covariance of each Gaussian distribution in gauss hybrid models, the inverse of the covariance of the noise producing when R is observation, wherein average be the reconstructed image of small images x.

Step 4. by the small images reconstructing in step 3 order during by piecemeal again piece together and be reduced to original complete image, the entire image that obtains reconstructing output.

Effect of the present invention can be verified by following emulation experiment.

(1) experiment condition setting

Experiment use image be natural image as Fig. 2, image size is 256 × 256, target is the dolly in scene, the size of target training image is 32 × 32.

(2) experimental result and analysis

Emulation experiment one, in the situation that sampling rate is 20%, utilize the present invention and existing weighting two norm reconstructing methods respectively to Fig. 2 reconstruct, result as shown in Figure 3, wherein: Fig. 3 (a) is the reconstruction result of existing weighting two norm reconstructing methods, and Fig. 3 (b) is reconstruction result of the present invention.

Emulation experiment two, in the situation that sampling rate is 40%, utilize the present invention and existing weighting two norm reconstructing methods respectively to Fig. 2 reconstruct, result as shown in Figure 4, wherein: Fig. 4 (a) is the reconstruction result of existing weighting two norm reconstructing methods, and Fig. 4 (b) is reconstruction result of the present invention.

(3) the simulation experiment result

Can see from Fig. 3 (a), in the situation that sampling rate is 20%, by target reconstruct clearly not out, target appearance is fuzzy cannot identification for existing weighting two norm reconstructing methods, and whether people exist target from visually can not determine this scene.

Can see from Fig. 3 (b), in the situation that sampling rate is 20%, by target reconstruct clearly out, target appearance is clear and more outstanding in scene in the present invention, and people are from visually can directly determining the position of target.

Can see from Fig. 4 (a), in the situation that sampling rate is 40%, existing weighting two norm reconstructing methods are unintelligible by object reconstruction, and target signature is not outstanding.

Can see from Fig. 4 (b), in the situation that sampling rate is 40%, the present invention by gem-pure target reconstruct out, target appearance is clear and very outstanding in scene, and people, from visually can directly determining the position of target scene, have reached the object that detects target.

Claims (2)

1. the object reconstruction method based on compressed sensing, comprises the following steps:

(1) by hybrid cytokine analytical model, target is carried out to Gaussian Mixture modeling, obtains the probability density of target:

Wherein: x ° of be target training sample, χ _tfor the average of each Gaussian distribution of comprising in gauss hybrid models, Ω _tfor the covariance of each Gaussian distribution of comprising in gauss hybrid models, λ _tfor the weight of each Gaussian distribution in gauss hybrid models, T is the number of the Gaussian distribution that comprises in gauss hybrid models, and N is dimension;

(2) entire image at target place is evenly divided into the identical fritter of size, the size of the size of fritter and the training image of target is identical and guarantee target is complete on a certain fritter;

(3) each small images is reconstructed respectively:

(3a) each small images x is carried out respectively random observation and is obtained its random observation vector y:

y＝Φx+ν

Wherein: x is the small images for the treatment of reconstruct, its dimension is N, the random observation vector that y is small images, and the gaussian random observing matrix that Φ is, the noise producing when v is observation is obeyed the Gaussian distribution of zero-mean, and its dimension is N, wherein N=1024;

(3b) from random observation vector y, recover small images x according to following Bayesian formula:

Wherein: p (x/y) is posterior probability density, the probability density that p (x °) is the target that trains, p (y/x) is conditional probability density, for the weights of each Gaussian distribution in gauss hybrid models, for the covariance of each Gaussian distribution in gauss hybrid models, the inverse of the covariance of the noise producing when R is observation, for the average of each Gaussian distribution in gauss hybrid models, this average be the reconstructed image of small images x;

(4) small images reconstructing in step (3) is pieced together and is reduced to original complete image, the entire image that obtains reconstructing output.

2. the object reconstruction method based on compressed sensing according to claim 1, wherein the described hybrid cytokine analytical model of passing through of step (1) is carried out Gaussian Mixture modeling to target, carries out as follows:

(2a) photographic subjects is at the image n of different angles width, and using these images as training image, by arest neighbors interpolation method, training image being unified into size is 32 × 32 pixels, 1000≤n≤1600;

(2b), by Beta process, obtain the order J of the covariance matrix of following Gaussian distribution:

x _i～N(Aw _i+μ,α ^-1I _N)；

Wherein: x _ifor training sample, dimension is N, and A represents the matrix that one group of base is N × J in hybrid cytokine analytical model, a being aligned temper space, w _ifor the coefficient of the linear subspaces that A opened in hybrid cytokine analytical model, its dimension is J, and μ is that average dimension is N, I _nbe the unit matrix of N × N, α is accuracy value;

(2c) obtain the number T of Gaussian distribution in gauss hybrid models by Dirichlet process;

(2d) Beta process is combined with Dirichlet process, obtains the value of the parameter of each Gaussian distribution in gauss hybrid models:

x _i～N(A _t(i)w _i+μ _t(i),α _t(i) ^-1I _N)，

${\mathrm{\λ}}_t={\mathrm{\υ}}_t\underset{l=1}{\overset{t=1}{\mathrm{\Π}}}(1-{\mathrm{\υ}}_l),$

υ _t～Beta(1,η)，

$z_t~\underset{k=1}{\overset{K}{\mathrm{\Π}}}\mathrm{Bernoulli}\left({\mathrm{\π}}_k\right),$

${\mathrm{\π}}_t~\underset{k=1}{\overset{K}{\mathrm{\Π}}}\mathrm{Beta}(a/K,b(K-1)/K),$

μ _t～N(μ,τ ₀ ^-1I _N)；

Wherein: λ _tbe each Gaussian distribution in gauss hybrid models weight and a represents the matrix that one group of base is N × J, w in hybrid cytokine analytical model _ifor the coefficient of the linear subspaces that A opened in hybrid cytokine analytical model, μ _tfor average, α _tobey Gamma for accuracy value and distribute, I _nthe unit matrix of N × N, the column vector that meets the Gaussian distribution of zero-mean, z _tto meet the column vector that Bernoulli Jacob distributes, υ _tfor λ _tfactor of influence, η is υ _tfactor of influence, υ _lfor λ _tcontrolling elements, π _tz _tfactor of influence, a is π _tthe super parameter in a left side, a=1, b is π _tthe super parameter in the right side, b=1, τ ₀for μ _tsuper parameter, τ ₀=10 ^-6, K is the factor of influence number of the hybrid cytokine analytical model of supposition, I _kit is the unit matrix of K × K;

(2e) according to the number T of Gaussian distribution in above-mentioned gauss hybrid models and all unknown parameters, obtain each Gaussian distribution, the probability density that the weighted sum of this Gaussian distribution is target: