CN101561879B - Curvelet representation-based method for image underdetermined blind source separation - Google Patents

Abstract

The invention discloses a curvelet expression-based method for image underdetermined blind source separation. The method comprises the following steps: firstly, performing underdetermined blind sourceseparation under a sparse condition to acquire pre-separated signals in the same number as source signals; secondly, using the pre-separated signals as mixed signals to change an underdetermined stat e into an even-determined state; finally, adopting the conventional FastICA method to perform even-determined blind source separation to acquire final separated signals to realize the effect of the underdetermined image blind source separation. Aiming at the underdetermined blind source separation problem, the method provides a separation method based on underdetermined and even-determined combination, makes full use of a Curvelet domain coefficient property to complete initial underdetermined blind source separation, creates the mixed signals for conversion into even-determined blind source separation to adopt the FastICA to perform even-determined separation of the pre-separated signals at the same time, thereby improving the image blind source separation accuracy and improving image separation effect. The method has significant application potential in radio communication systems, sonar and radar systems, and audio, acoustic and medical signal processing in military and nonmilitary fields.

Description

Image based on Qu Bobiao shows owes to decide blind separating method

Technical field

The present invention relates to a kind of image denoising method, particularly a kind of image based on Qu Bo (Curvelet) expression owes to decide blind separating method.The important use potentiality are all arranged in the Flame Image Process in military field or non-military field.

Background technology

Usually, image its obtain or transmission course in all can receive the pollution of other signals, for follow-up further processing, the necessary separating treatment of carrying out.The purpose of separation of images is exactly to extract each independent signal component that receives in the signal as much as possible, to improve the quality of image.At present, image denoising method mainly is divided into traditional filtering method and blind separating method, and is wherein the most representative with blind separating method.

Blind separating method is under information source S and the equal condition of unknown of signal transmission feature, only carries out the separation of these separate source signals through the mixed signal X that receives.Now; Main blind separating method mainly contains independent component analysis method (ICA), the maximum entropy method (Infomax) based on gradient decline at random, the natural gradient learning method (NGA) based on high-order statistic and adopts the quick ICA method (FastICA) of negentropy criterion, i.e. fix-point method (Fixed-point).Although these methods are obtaining effect preferably aspect the blind separation, they all are subject to a hypothesis, i.e. supposition receives the signal number and is no less than the source signal number, just fits fixed and overdetermination situation.In actual separation research, the source signal number is unknown, and the quantity of sensor is very limited, so the situation that sensor number (or receiving signal number) is less than the source signal number is ubiquitous in real life.This sensor number is less than the ill blind separation of source signal number, and we are referred to as to owe blind surely separation.For this pathological situation, existing blind separation algorithm, all powerless like FastICA and NGA etc., can't realize the separation of all signals.

Based on the sparse separation method of signal is a hot research direction now.Wavelet transformation is main rarefaction method; Though wavelet transformation can be analyzed one dimension segmentation continuous signal efficiently; But handle for two dimensional image; Be beyond expression at " along the edge " information of (along edge) of the two-dimensional wavelet transformation that is formed by the tensor product of one dimension small echo, its sparse property has certain limitation.To the limitation of wavelet transformation, the notion of Curvelet conversion is proposed by people such as Candes and Donoho.The Curvelet conversion not only has the multiple dimensioned characteristics of wavelet transformation, also has anisotropy (anisotropy) characteristics, has very strong directivity, can more sparse information representation be provided for Flame Image Process, aspect separation of images, has outstanding advantage.

Relevantly owe the research direction that blind Study on Separation was just risen in recent years under the stable condition,, get more and more people's extensive concerning though up to the present it also is in the starting developing stage.

Summary of the invention

The objective of the invention is to propose a kind of image that shows based on Qu Bobiao and owed to decide blind separating method to the technical matters that exists in the prior art, this method can improve the precision of owing the blind separation of fixed condition hypograph, reaches desirable separation of images effect.

In order to achieve the above object, the image that shows based on Qu Bobiao of the present invention is owed to decide blind separating method and adopted following technical proposals: this method is at first carried out the blind surely separation of owing under the sparse condition, obtains the pre-separation signal consistent with the source signal number; Again with the pre-separation signal as mixed signal; To owe to be converted into surely to fit and decide, and adopt traditional F astICA method to fit the blind separation under the fixed condition, obtain final separation signal; Reach and owe to decide the Image Blind separating effect, its concrete steps are following:

A, initialization setting, signal rarefaction: adopt second generation Curvelet conversion, carry out rarefaction to received signal, obtain the high frequency subimage of low frequency sub picture and a series of different directions, different frequency;

B, source signal number estimation: to choose high frequency subimage the most sparse after two received signal rarefactions arbitrarily right at every turn; Utilize the spike number in the PHASE DISTRIBUTION to carry out the signal source number estimation, so repeat n time, that numerical value that the frequency of occurrences is the highest is the number of source signal; Adopt all star chart data points to straight line cluster nearest with it gather the axle apart from sum as sparse property criterion; Distance and more little illustrates that cluster is clear more, and the sparse property of signal is good more;

C, hybrid matrix are estimated: utilize sparse property criterion to select the most sparse high frequency subimage group, in conjunction with the source signal number, adopt clustering algorithm to estimate to obtain the hybrid matrix estimated value.Sparse here property standard is the same;

D, pre-separation signal are estimated: adopt linear programming to try to achieve each frequency subimage of separation signal in the sparse territory, adopt the Curvelet inversionization to try to achieve the pre-separation signal again;

E, will go up the pre-separation signal that obtains of step, and adopt traditional F astICA method to fit the blind separation under the fixed condition, obtain final separation signal as mixed signal.

The inventive method has following conspicuous outstanding substantive distinguishing features and remarkable advantage compared with prior art, is embodied in:

1,, proposed based on the separation method of owing fixed and suitable phasing combination to owing blind surely separation problem;

2, carry out the Curvelet rarefaction to received signal and handle, owe to decide separation, obtain the pre-separation signal in sparse territory.Make full use of Curvelet domain coefficient characteristic in its implementation process and carry out source signal number estimation, hybrid matrix estimation and the estimation of pre-separation signal, accomplished the preliminary blind surely separation of owing, constructed simultaneously to the mixed signal of fitting fixed blind separation conversion;

3, adopt FastICA that the pre-separation signal is fitted the separation under the fixed condition, improved the precision that Image Blind is separated, improved the effect of separate picture.

The image that shows based on Qu Bobiao of the present invention owes to decide blind separating method can solve the blind separation problem of owing under the fixed condition, can improve effectively and owe the fixed condition hypograph blind separation accuracy, reaches desirable separation of images effect.In radio communications system, sonar and radar system, audio frequency and the acoustics in military field or non-military field and medical signals are handled, the important use potentiality are arranged all.

Description of drawings

Fig. 1 is that the image that shows based on Qu Bobiao of one embodiment of the invention owes to decide the blind separating method block diagram;

Fig. 2 is that Fig. 1 example is owed blind surely separating resulting photo figure.

Embodiment

A preferred embodiment of the present invention combines detailed description of the drawings following:

The image that shows based on Qu Bobiao of the present invention owes to decide blind separating method, and is as shown in Figure 1, at first carries out the Curvelet rarefaction to receiving image sets; Under sparse condition, estimate source signal number and hybrid matrix, and then adopt linear programming and Curvelet inverse transformation to realize that tentatively owing blind surely separates, and obtains the pre-separation signal consistent with the source signal number; Again with the pre-separation signal as mixed signal; To owe to be converted into surely to fit and decide, and adopt traditional F astICA method to fit the blind separation under the fixed condition, obtain final separation signal; Reach and owe to decide the purpose that Image Blind is separated, its concrete steps are:

1., the initialization setting, set the direction Number of Decomposition D in decomposition number of plies K and every layer of Curvelet conversion _k, to the vision-mix X that receives ₁, X ₂..., X _MCarry out multiple dimensioned, multidirectional Curvelet Sparse Decomposition respectively, promptly

$[X_{\mathrm{ilf}},X_{\mathrm{ihf}}^{\left(\mathrm{1,1}\right)},\·\·\·,X_{\mathrm{ihf}}^{(I,D_1)},{X_i}_{\mathrm{hf}}^{\left(\mathrm{2,1}\right)},\·\·\·,{X_i}_{\mathrm{hf}}^{(k,D_k)}]=T\left(X_i\right),$

Wherein, T () is the Curvelet conversion, thereby obtains a width of cloth low frequency sub as X _IlfWith a series of high frequency subimage X with different resolution _Ihf ^{(k, l)}, wherein k ∈ (1, K) with l ∈ (1, D _k) indicating that subimage is positioned at k decomposition layer l direction, i represents 1,2 ..., M;

2., source signal number estimation: choose two at every turn arbitrarily and receive signal (X _iAnd X _j), according to sparse property criterion, it is right to select high frequency subimage the most sparse after the rarefaction, utilizes the spike number in the PHASE DISTRIBUTION to carry out the signal source number estimation.So repeat n time, that numerical value that the frequency of occurrences is the highest is the number N of source signal;

3., hybrid matrix is estimated: utilize sparse property criterion to select the most sparse high frequency subimage group; In conjunction with the source signal number, adopt means clustering algorithm (K-means) to estimate to obtain hybrid matrix estimated value

4., the pre-separation signal is estimated: try to achieve according to the last step

Each sparse coefficient sets to the Curvelet territory adopts linear programming to try to achieve each the frequency subimage in the sparse territory of pre-separation signal, adopts the Curvelet inversionization to try to achieve pre-separation signal Y again ₁ ^p, Y ₂ ^p..., Y _N ^p

5., will go up the pre-separation signal Y that a step obtains ₁ ^p, Y ₂ ^p..., Y _N ^pAs mixed signal, adopt traditional F astICA method to fit the blind separation under the fixed condition, obtain final separation signal Y ₁, Y ₂..., Y _N, promptly

$[{\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="H2009100520344E00021.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1,Y_2,\&CenterDot;\&CenterDot;\&CenterDot;,Y_N]=\mathrm{FastICA}[Y_1^p,Y_2^p,\&CenterDot;\&CenterDot;\&CenterDot;,Y_N^p].$

Above-mentioned steps utilizes sparse property criterion to select the most sparse high frequency subimage group 3. in the hybrid matrix estimated value, and concrete steps are:

C1, order $Z_{k,l}={[X_{\mathrm{Ihf}}^{(k,l)},X_{\mathrm{Jhf}}^{(k,l)}]}^T,$ X wherein _Ihf ^{(k, l)}And X _Jhf ^{(k, l)}For choosing the high frequency subimage group after the Curvelet conversion, and k ∈ (1, K), l ∈ (1, D _k), i, j=1,2 ..., M;

Less coefficient component in C2, the removal signal is to eliminate The noise;

C3, data points all in the star chart is projected on the unit sphere, i.e. Z _{K, l}=Z _{K, l}/ ‖ Z _{K, l}‖;

C4, all signaling points are moved on to positive hemisphere face: if first coordinate of data point $z_{k,\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="H2009100520344E00021.png"\; state="\{\{state\}\}">l</figure-callout>}}^1<0,$ Z _{K, l}=-Z _{K, l}, otherwise, Z _{K, l}=Z _{K, l}

C5, confirm to gather axle and gather a center through clustering algorithm;

C6, calculate all data points to gather recently from self the axle distance and H _{K, l}, and weigh sparse property, H with this _{K, l}More little, sparse more, in its star chart to gather axle just clear more;

C7, to all Z _{K, l}Calculate H _{K, l}, seek its minimum value, order $(k_{\mathrm{Sel}},l_{\mathrm{Sel}})=\underset{k,l}{\mathrm{Arg}\mathrm{Min}}\left(H_{k,l}\right);$

C8, the most sparse sub-image group

and the

Can find out like Fig. 2, originally owe to decide the Image Blind separation method and can separate the independent image component that receives in the signal effectively, reach and owe to decide the purpose that Image Blind is separated.

Table 1 has provided the objective evaluation index that the present invention owes to decide the Image Blind separating resulting.

Adopt Y-PSNR (PSNR) to weigh the quality of noise reduction image in the table, and then estimated the quality that the present invention owes to decide the Image Blind separation method.

From table 1, can draw same conclusion, originally owe to decide the Image Blind separation method and can separate the independent image component that receives in the signal effectively, reach the separation accuracy requirement of owing to decide Image Blind.

In a word, no matter be from the human eye vision effect, still from the objective evaluation index, show that all the inventive method has higher separation accuracy, good separating effect.

Table 1 owes to decide objective evaluation index (PSNR value, the unit: dB) of Image Blind separating effect

	Separate picture 1	Separate picture 2	Separate picture 3
				The inventive method separation accuracy	31.6227	33.6644	34.8711

Claims (1)

1. an image that shows based on Qu Bobiao owes to decide blind separating method; This method is at first carried out the blind surely separation of owing under the sparse condition, obtains the pre-separation signal consistent with the source signal number, again with the pre-separation signal as mixed signal; To owe to be converted into surely to fit and decide; Adopt traditional F astICA method to fit the blind separation under the fixed condition, obtain final separation signal, reach and owe to decide Image Blind source separating effect; Concrete steps are following:

A, initialization setting, signal rarefaction: adopt second generation Curvelet conversion, carry out rarefaction to received signal, obtain the high frequency subimage of low frequency sub picture and a series of different directions, different frequency;

B, source signal number estimation: to choose high frequency subimage the most sparse after two received signal rarefactions arbitrarily right at every turn; Utilize the spike number in the PHASE DISTRIBUTION to carry out the signal source number estimation, so repeat n time, that numerical value that the frequency of occurrences is the highest is the number of source signal; Adopt all data points to straight line cluster nearest with it gather the axle apart from sum as sparse property criterion; Distance and more little illustrates that cluster is clear more, and the sparse property of signal is good more;

C, hybrid matrix are estimated: utilize sparse property criterion to select the most sparse high frequency subimage group, in conjunction with the source signal number, adopt clustering algorithm to estimate to obtain the hybrid matrix estimated value;

D, pre-separation signal are estimated: adopt linear programming to try to achieve each frequency subimage of separation signal in the sparse territory, adopt the Curvelet inversionization to try to achieve the pre-separation signal again;

E, will go up the pre-separation signal that obtains of step, and adopt traditional F astICA method to fit the blind separation under the fixed condition, obtain final separation signal as mixed signal;

Said step C utilizes sparse property criterion to select the most sparse high frequency subimage group in the hybrid matrix estimated value, and its concrete steps are:

C1, order

Wherein

With For choosing the high frequency subimage group after the Curvelet conversion, and k ∈ (1, K), l ∈ (1, D _k), i, j=1,2 ..., M; Wherein K is the decomposition number of plies of Curvelet conversion, D _kBe the direction Number of Decomposition in every layer;

Less coefficient component in C2, the removal signal is to eliminate The noise;

C3, all data points are projected on the unit sphere, i.e. Z _{K, l}=Z _{K, l}/ || Z _{K, l}||;

C4, all signaling points are moved on to positive hemisphere face: if first coordinate of data point

Z _{K, l}=-Z _{K, l}, otherwise, Z _{K, l}=Z _{K, l}

C5, confirm to gather axle and gather a center through clustering algorithm;

C6, calculate all data points to gather recently from self the axle distance and H _{K, l}, and weigh sparse property, H with this _{K, l}More little, sparse more, in its star chart to gather axle just clear more;

C7, to all Z _{K, l}Calculate H _{K, l}, seek its minimum value, order

C8, The most sparse sub-image group was

and

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