CN102867186B - Partial correlation analysis method of digital signal based on statistical characteristics - Google Patents

Abstract

The invention discloses a partial correlation analysis method of a digital signal based on statistical characteristics. The partial correlation analysis method comprises digital signal block division and partial correlation analysis of the signal; the partial correlation analysis of the signal includes probability of a statistical block center value in each block, distribution of unrepeated signal value quantity in the statistical block, position distribution of the statistical block center value in a signal value sequence, position distribution of the statistical block center value in an ordered signal value sequence, the position distribution of the statistical block center value firstly appearing in the ordered signal value sequence, the probability of the statistical block center value appearing in each block and the position distribution of the statistical block center value in the signal value sequence. Compared with the existing method, the method is simple in mathematical model, strong in intuitiveness, small in calculated amount, and easy in implementation; the digital signal can be reasonably subjected to partial correlation analysis from a plurality of aspects, and the method can be used for a low-resolution image and can achieve high analysis precision. The method can be widely applied to the aspects such as signal noise reduction, filtering, division, feature extraction and identification.

Description

The digital signal local correlations analytical approach of Corpus--based Method feature

Technical field

The present invention relates to Digital Signal Analysis and mode identification technology, particularly the digital signal local correlations analytical approach of the robust of Corpus--based Method feature.

Background technology

Along with computer technology and the rapid of Digital Electronic Technique are popularized and development, Digital Signal Analysis technology is widely used.The digital signal obtained by nature, such as data image signal or sound signal, one of its characteristic feature is that the value of signal in subrange is relevant.The local correlations of digital signal is widely used in the aspects such as signal de-noising, filtering, segmentation, Feature extraction and recognition, and therefore digital signal local correlations analytical technology receives publicity always.

A Major Difficulties of digital signal local correlations analytical technology how to analyze the mutual relationship in subrange between signal value, comprises relation of equality, order relation etc.The people such as M.Kirchner propose the ratio being adjacent item by the histogrammic central item of image local first differential (probability that differential value equals 0), analyze, thus identify dissimilar signal processing operations to local correlations; The people such as G.Cao give chapter and verse the probability that local first differential value equals 0 in image texture region, analyze, thus identify dissimilar signal processing operations to local correlations; The disadvantage of these two kinds of methods only to reflect the probability that the signal value of direct neighbor is equal, and can not reflect in subrange have that how many signal values are equal and which signal value is equal. propose to analyze image local correlation by the high-order Markov Chain (Markov chain) of image first differential Deng people, 686 dimensional feature vectors are extracted from image, recycling SVM (support vector machine) carries out training and classifying, thus realizes differentiating image integrity.The disadvantage of this method limits by image resolution ratio, is difficult to carry out effective analysis to the image with low resolution (less than 128 × 128), is secondly that mathematical model is complicated, application inconvenience.

Summary of the invention

Namely the problem of the mutual relationship in subrange between signal value is analyzed in order to solve Major Difficulties of the prior art, the object of the invention is based on the statistics to mutual relationship between the range signals value of local for this reason, provide a kind of and can carry out accurately digital signal local correlations, the method for reasonable analysis.

To achieve these goals, the digital signal local correlations analytical approach that the present invention is based on statistical nature comprises step:

Step 1: the mode taking every s signal value to be divided into 1 piece to digital signal is done block and divided, s be greater than 1 odd number; Signal value opsition dependent order in every block is expressed as signal value sequence wherein k is block number, k ∈ 1,2 ..., N}, N represent block sum; Represent with m , then just represent the block median of kth block; With orderly signal value sequence represent the according to value sequence arrangement of signal value in every block, then just represent the block intermediate value of kth block;

Step 2: the correlativity checking the signal value in every block; The correlativity of the signal value in described every block, adopts following methods to analyze:

A. the probability that occurs in every block of statistics block median, is expressed as wherein: represent that the probability of i time appears in block median in every block, i, j ∈ 1,2 ..., s}; | { } | represent a cardinality of a set; $\mathrm{\δ}(u,v)=\left\{\begin{array}{cc}1,& \mathrm{ifu}=v\\ 0,& \mathrm{otherwise}\end{array}\right.$ For conditional function, only when two independents variable are equal, functional value is 1, and other situation minor function values are 0; Vector h ^oBCin element can reflect digital signal local correlations;

B. the distribution of not repeating signal value quantity in statistics block, is expressed as wherein: represent that in block, repeating signal value quantity is not the probability of the block appearance of i; Vector h ^qGLin element can reflect digital signal local correlations;

C. the position distribution of statistics block intermediate value in signal value sequence, is expressed as wherein: represent that block intermediate value appears at the probability of position i in signal value sequence; Vector h ^dBMin element can reflect digital signal local correlations;

D. the position distribution of statistics block median in orderly signal value sequence, is expressed as wherein: represent that block median appears at the probability of position i in orderly signal value sequence; Vector h ^dBCin element can reflect digital signal local correlations;

E. the position distribution that first occur of statistics block median in orderly signal value sequence, is expressed as $h^{\mathrm{FBC}}=(h_1^{\mathrm{FBC}},h_2^{\mathrm{FBC}},...,h_s^{\mathrm{FBC}}),$ Wherein: $h_i^{\mathrm{FBC}}=\frac{\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\δ}(\arg \underset{j}{\min }(y_{\left(j\right)}^k=y_m^k),i)}{N}$ Represent that block median appears at the probability of position i first in orderly signal value sequence; represent the minimum j that equation is set up; Vector h ^fBCin element can reflect digital signal local correlations;

F. the probability that occurs in every block of statistics block intermediate value, is expressed as wherein: represent that the probability of i time appears in block intermediate value in every block; Vector h ^oBMin element can reflect digital signal local correlations;

G. the position distribution of statistics block median in signal value sequence, is expressed as wherein: represent that block median appears at the probability of position i in signal value sequence; Vector h ^sBMin element can reflect digital signal local correlations;

Described A, B, C, D, E, F and G method can independence or combinationally use, i.e. vectorial h ^oBC, h ^qGL, h ^dBM, h ^dBC, h ^fBC, h ^oBMand h ^sBMthe combination in any of middle all elements, can reflect digital signal local correlations from multiple angles.

The present invention has several obvious advantage both at home and abroad compared with the up-to-date method delivered at present:

1) mathematical model is simple, and intuitive is strong, and calculated amount is little, is easy to realize;

2) reasonably can analyze digital signal local correlations from multiple angles;

3) can be used in low-resolution image, higher analysis precision can be reached.

The present invention can be widely used in the aspects such as signal de-noising, filtering, segmentation, Feature extraction and recognition.

Accompanying drawing explanation

Fig. 1 technical solution of the present invention process flow diagram

Fig. 2 digital picture block divides schematic diagram

Fig. 3 is respectively by vectorial h ^oBC, h ^dBCor h ^fBCthe analysis result obtained

Fig. 4 is respectively by vectorial h ^mFF, the analysis result that obtains of scalar f, and with the performance comparison of additive method

Fig. 5 image local tampering detection schematic diagram

Fig. 6 to the analysis result of low resolution jpeg compressed image, and with the performance comparison of additive method

Embodiment

Each detailed problem involved in technical solution of the present invention is described in detail below in conjunction with accompanying drawing.Be to be noted that described embodiment is only intended to be convenient to the understanding of the present invention, and any restriction effect is not play to it.

Thought main points of the present invention are:

1) digital signal obtained by nature, such as data image signal or sound signal, one of its characteristic feature is that the value of signal in subrange is relevant.

2) in certain subrange, the median of digital signal or intermediate value can be considered signal value representative in this subrange, and the probability that therefore median and intermediate value occur in subrange or position distribution can the local correlations of reflected signal.

3) in subrange, the distributed number of repeating signal value can the local correlations of reflected signal.

Whole technical scheme process flow diagram of the present invention as shown in Figure 1.Below with digital image evidence collecting (Digital ImageForensics) for application scenarios, be explained ins and outs involved in invention, last experimental results also carries out Performance comparision with the fresh approach delivered in same domain both at home and abroad.This digital image evidence collecting scene refers to by Feature extraction and recognition, judges whether image overall or local live through certain image processing operations.

1. digital signal block divides

The mode taking every s signal value to be divided into 1 piece to digital signal is done block and is divided, s be greater than 1 odd number.For two-dimensional digital signal, such as digital picture, known piece of division methods has (as shown in Figure 2, wherein dark pixels represents the 1st block marked off, and in block, numerical value represents the sequence of positions of signal value in every block):

1) carry out in the horizontal direction;

2) vertically carry out;

3) carry out along level and vertical both direction simultaneously.

Can have lap between the block divided or not have lap, principle of decision-making is: for high-definition picture (> 128 × 128), for improving operation efficiency, usually adopts non overlapping blocks to divide; For low-resolution image (≤128 × 128), for ensureing the quantity of block, overlapping block is usually adopted to divide.In the embodiment of the present invention, get above-mentioned 3rd kind of block division methods, block size is 3 × 3, now s=9.

Block obtains N number of piece after dividing altogether.Signal value opsition dependent order in every block can be expressed as signal value sequence wherein be designated as position number down, k is block number, k ∈ 1,2 ..., N}; Represent with m then just represent the block median of kth block; Signal value in every block according to value sequence arrangement can be expressed as orderly signal value sequence wherein be designated as down signal value according to value sequence arrangement sequence number, then just represent the block intermediate value of kth block.According to value sequence arrangement mode has ascending order or descending two kinds, can optionally use by one.In the embodiment of the present invention, get signal value and arrange by ascending order, namely $y_{\left(1\right)}^k\≤y_{\left(2\right)}^k\≤...\≤y_{\left(9\right)}^k.$

2. signal local correlations is analyzed

The correlativity of the signal value in every block, adopts following methods to analyze:

A. the probability that occurs in every block of statistics block median, is expressed as wherein: represent that the probability of i time appears in block median in every block, i, j ∈ 1,2 ..., 9}; | { } | represent a cardinality of a set; $\mathrm{\δ}(u,v)=\left\{\begin{array}{cc}1,& \mathrm{ifu}=v\\ 0,& \mathrm{otherwise}\end{array}\right.$ For conditional function, only when two independents variable are equal, functional value is 1, and other situation minor function values are 0; Vector h ^oBCin element can reflect digital signal local correlations;

B. the distribution of not repeating signal value quantity in statistics block, is expressed as wherein: represent that in block, repeating signal value quantity is not the probability of the block appearance of i; Vector h ^qGLin element can reflect digital signal local correlations;

C. the position distribution of statistics block intermediate value in signal value sequence, is expressed as wherein: represent that block intermediate value appears at the probability of position i in signal value sequence; Vector h ^dBMin element can reflect digital signal local correlations;

D. the position distribution of statistics block median in orderly signal value sequence, is expressed as wherein: represent that block median appears at the probability of position i in orderly signal value sequence; Vector h ^dBCin element can reflect digital signal local correlations;

E. the position distribution that first occur of statistics block median in orderly signal value sequence, is expressed as $h^{\mathrm{FBC}}=(h_1^{\mathrm{FBC}},h_2^{\mathrm{FBC}},...,h_s^{\mathrm{FBC}}),$ Wherein: $h_i^{\mathrm{FBC}}=\frac{\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\δ}(\arg \underset{j}{\min }(y_{\left(j\right)}^k=y_m^k),i)}{N}$ Represent that block median appears at the probability of position i first in orderly signal value sequence; represent the minimum j that equation is set up; Vector h ^fBCin element can reflect digital signal local correlations;

F. the probability that occurs in every block of statistics block intermediate value, is expressed as wherein: represent that the probability of i time appears in block intermediate value in every block; Vector h ^oBMin element can reflect digital signal local correlations;

G. the position distribution of statistics block median in signal value sequence, is expressed as wherein: represent that block median appears at the probability of position i in signal value sequence; Vector h ^sBMin element can reflect digital signal local correlations;

Described A, B, C, D, E, F and G method can independence or combinationally use, i.e. vectorial h ^oBC, h ^qGL, h ^dBM, h ^dBC, h ^fBC, h ^oBMand h ^sBMthe combination in any of middle all elements, can reflect digital signal local correlations from multiple angles.

In the embodiment of the present invention, get following 3 kinds of array modes exemplarily:

1) the vectorial h of independent use ^oBC, h ^dBCor h ^fBc;

2) vectorial h is selected ^oBC, h ^qGL, h ^dBM, h ^dBCand h ^fBCcarry out combination and obtain a vectorial h ^mFF:

h ^MFF＝(h ^DBM，h ^OBC，h ^QGL，h ^DBC，h ^FBC)；

3) select the Partial Elements in different vector to combine, obtain a scalar f:

$f=\frac{h_5^{\mathrm{DBM}}{h}_2^{\mathrm{OBC}}{h}_6^{\mathrm{QGL}}(h_3^{\mathrm{DBC}}+h_7^{\mathrm{DBC}}-h_2^{\mathrm{DBC}}-h_8^{\mathrm{DBC}})h_3^{\mathrm{FBC}}}{h_1^{\mathrm{OBC}}{h}_9^{\mathrm{QGL}}(h_2^{\mathrm{DBC}}+h_8^{\mathrm{DBC}}-h_1^{\mathrm{DBC}}-h_9^{\mathrm{DBC}})h_2^{\mathrm{FBC}}{h}_9^{\mathrm{FBC}}}.$

In example of the present invention, by the analysis result that above 3 kinds of array modes obtain, be respectively used to digital image evidence collecting, namely whether the detected image overall situation or local live through certain image processing operations.The inventive method carries out Performance comparision by with the fresh approach delivered in same domain both at home and abroad, and these fresh approach comprise:

1) people such as ρ method: M.Kirchner propose based on the histogrammic image local correlation analytical approach of first differential (the parameter B=64 provided in document got by the document that sees reference [1]);

2) the image local correlation analytical approach (document that sees reference [2], gets the parameter B=7 provided in document, τ=100) equaling the probability of 0 based on first differential value that proposes of the people such as DMT method: G.Cao;

3) 2 rank SPAM methods: deng the image local correlation analytical approach based on image first differential higher-order Markov chain (the parameter T=3 provided in document got by the document that sees reference [3]) that people proposes;

Together with being entrained in the image of 2500 width non-filtered process through the image of 3 × 3 medium filtering process by 2500 width, the size of all images is 512 × 512.Therefrom get the image compute vector h respectively of 40% at random ^oBC, h ^dBCor h ^fBC, then utilize SVM to carry out training respectively to obtain 3 sorters.Difference extracted vector h from the image of residue 60% ^oBC, h ^dBCor h ^fBC, then classify with corresponding sorter respectively, result, as shown in the ROC curve in Fig. 3, shows that often kind of method can both obtain accurate testing result.In Fig. 3, False Positive Rate represents false drop rate, and True Positive Rate represents verification and measurement ratio, corresponding ROC area under a curve (AUC) of the numeric representation on the right side of legend, and its value, more close to 1, represents that detection perform is better.

Together with the image of medium filtering image and other types (image of digital camera shooting, digital scanner scan the image, Gassian low-pass filter image, enlarged image, the image that reduces that obtain) equal proportion is entrained in, have 10704 width images, image size is not less than 512 × 384.The therefrom image compute vector h of Stochastic choice 40% ^mFFand utilize SVM to train, then the image compute vector h to residue 60% ^mFFand classify, result as shown in Figure 4, shows vectorial h ^mFFcan accurately detect medium filtering image, and successful is better than ρ method and DMT method.Experimental result shows that scalar f also accurately can detect medium filtering image (SVM need not be utilized to carry out training and classifying) simultaneously, and successful is better than ρ method and DMT method.

By figure Selection Center 64 × 64 part from above-mentioned 10704 width images, obtaining 10704 width sizes is the image of 64 × 64.The therefrom image compute vector h of Stochastic choice 40% ^mFFand utilize SVM to carry out training to obtain sorter.Getting two width sizes is the original image of 512 × 512, as shown in Figure 5,3 × 3 mean filter process are carried out to original image 1 and obtains treated image 1,3 × 3 medium filtering process are carried out and the label copied wherein to original image 2, label is pasted in treated image 1, obtain a width and forge image.Not superimposed images block forgery image uniform being divided into 64 × 64 is also every block compute vector h ^mFF, classified by described sorter, experimental result shows h ^mFFaccurately can detect that the local of image is distorted (in Fig. 5 analysis result, white portion represents tampered region).

Together with being entrained in the image of 10000 width non-filtered process through the image of 3 × 3 medium filtering process by 10000 width, and perform JPEG compression (quality factor is 90) to every width image, all image sizes are 128 × 128.The therefrom image compute vector h of Stochastic choice 40% ^mFFwith 2 rank SPAM features, and utilize SVM to carry out training respectively to obtain 2 sorters, then the image compute vector h to residue 60% ^mFFwith 2 rank SPAM features, then classify with corresponding sorter respectively, result as shown in Figure 6, shows vectorial h ^mFFcan penetrate JPEG compression process and detect medium filtering image, and effect is better than 2 rank SPAM methods (ρ method and DMT method all can not be applied to the image after JPEG compression).Further reduction image resolution ratio is also tested, and result shows vectorial h under low resolution ^mFFdetection perform relatively stable, and performance advantage increases along with the reduction of image resolution ratio.

The above; be only the embodiment in the present invention; but protection scope of the present invention is not limited thereto; any people being familiar with this technology is in the technical scope disclosed by the present invention; the conversion or replacement expected can be understood; all should be encompassed in and of the present inventionly comprise within scope, therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.

Attached list of references:

[1]M.Kirchner and J.Fridrich，“On detection of median filtering in digital images，”in Proc.SPIE，ElectronicImaging，Media Forensics and Security II，vol.7541，pp.1-12，2010.

[2]G.Cao，Y.Zhao，R.R.Ni，L.F.Yu，and H.W.Tian，“Forensic detection of median filtering in digital images，”in Proc.2010IEEE Int.Conf.Multimedia and EXPO，pp.89-94，2010.

[3] P.Bas，and J.Fridrich，“Steganalysis by subtractive pixel adjacency matrix，”IEEE Trans.Inf.Forensics and Security，vol.5，no.2，pp.215-224，2010.

Claims (1)

1. the digital signal local correlations analytical approach of Corpus--based Method feature, is characterized in that, comprise step:

Step 1: the mode taking every s signal value to be divided into 1 piece to digital signal is done block and divided, s be greater than 1 odd number; Signal value opsition dependent order in every block is expressed as signal value sequence wherein k is block number, k ∈ 1,2 ..., N}, N represent block sum; Represent with m then just represent the block median of kth block; With orderly signal value sequence represent the according to value sequence arrangement of signal value in every block, then just represent the block intermediate value of kth block;

Step 2: the correlativity checking the signal value in every block; The correlativity of the signal value in described every block, adopts following methods to analyze:

A. the probability that occurs in every block of statistics block median, is expressed as wherein: represent that the probability of i time appears in block median in every block, i, j ∈ 1,2 ..., s}; | { } | represent a cardinality of a set; $\mathrm{\δ}(u,v)=\left\{\begin{array}{cc}1,& \mathrm{ifu}=v\\ 0,& \mathrm{otherwise}\end{array}\right.$ For conditional function, only when two independents variable are equal, functional value is 1, and other situation minor function values are 0; Vector h ^oBCin element can reflect digital signal local correlations;

B. the distribution of not repeating signal value quantity in statistics block, is expressed as wherein: represent that in block, repeating signal value quantity is not the probability of the block appearance of i; Vector h ^qGLin element can reflect digital signal local correlations;

C. the position distribution of statistics block intermediate value in signal value sequence, is expressed as wherein: represent that block intermediate value appears at the probability of position i in signal value sequence; Vector h ^dBMin element can reflect digital signal local correlations;

D. the position distribution of statistics block median in orderly signal value sequence, is expressed as wherein: represent that block median appears at the probability of position i in orderly signal value sequence; Vector h ^dBCin element can reflect digital signal local correlations;

E. the position distribution that first occur of statistics block median in orderly signal value sequence, is expressed as $h^{\mathrm{FBC}}=(h_1^{\mathrm{FBC}},h_2^{\mathrm{FBC}},...,h_s^{\mathrm{FBC}}),$ Wherein: $h_i^{\mathrm{FBC}}=\frac{\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\δ}(\arg \underset{j}{\min }(y_{\left(j\right)}^k=y_m^k),i)}{N}$ Represent that block median appears at the probability of position i first in orderly signal value sequence; represent the minimum j that equation is set up; Vector h ^fBCin element can reflect digital signal local correlations;

F. the probability that occurs in every block of statistics block intermediate value, is expressed as wherein: represent that the probability of i time appears in block intermediate value in every block; Vector h ^oBMin element can reflect digital signal local correlations;

G. the position distribution of statistics block median in signal value sequence, is expressed as wherein: represent that block median appears at the probability of position i in signal value sequence; Vector h ^sBMin element can reflect digital signal local correlations;

Described A, B, C, D, E, F and G method can independence or combinationally use, i.e. vectorial h ^oBC, h ^qGL, h ^dBM, h ^dBC, h ^fBC, h ^oBMand h ^sBMthe combination in any of middle all elements, can reflect digital signal local correlations from multiple angles.