CN101437163B - Multi-watermark technology based on network information theory - Google Patents

Abstract

The invention provides a method for achieving a plurality of watermarks. The basic principle is to count the process for achieving the plurality of the watermarks as a multi-user communication process containing side information and make use of a correlated source coding theorem, a multi-user communication theory and the like to perform theoretical analysis so as to obtain the side information available in the communication process. The method comprises two processes of watermark embedment and extraction and comprises the following steps: using maximum linear correlation values between a corresponding subblock of a carrier and each watermark coding signal as a selection embedding position of the side information, a detection threshold value and the embedment strength; making use of a perceptual model to perform perceptual forming on watermark signals; adjusting the watermark embedment strength according to the linear correlation values between the fixed carrier and the watermark coding signals so as to obtain a carrier containing a watermark; and performing detection through a linear correlation detector. The proposal can effectively avoid the mutual interference among the plurality of the watermarks, has better robustness, and can be applied to the copyright managements in occasions of network publishing, operation trailing and the like.

Description

The multi-watermark technology of information theory Network Based

Technical field

The invention belongs to the Communication and Information Systems field, relate to the technology such as information theory and coding and image processing, particularly digital image watermarking technology.

Background technology

Digital watermarking is considered " last line of defense " of multi-media safety as a kind of technology that rises because of copyright protection, has played important function in the transmission of copyright and preservation process.If in a Digital Media, only embedded an information, then be referred to as single watermark; If embedded two or more information, then be referred to as many watermarks.Along with concrete use increasingly extensive such as the transaction of net environment works, usage track, Web publishing, demand to multi-watermark technology is day by day urgent, what the present invention relates to mainly is many watermarks field, is characterized in many watermaking systems are considered as the multi-user communication process of an information theory Network Based.

Multi-watermark technology has been obtained certain achievement in research, and wherein the most representative method can be divided three classes: repeat embedding, piecemeal embedding and merge to embed.

Repeating to embed (Re-Watermarking) is direct, the most obvious method, it is directly transplanted by single watermarking algorithm, thereby in fact be exactly repeatedly to adopt single watermarking algorithm that a plurality of watermark informations are embedded one by one, the watermark quantity that this method embeds directly affects the quality of carrier works, and after adopting this method to embed a plurality of watermarks, when detecting i watermark, must have the i time watermarked after, the i+1 time data before watermarked, this will limit its availability in a lot of practical applications.

Piecemeal embed (Segmented Watermarking) from repeat to embed different, it is cut apart being used for watermarked space, every sub spaces embeds a different watermark information, thereby realizes the embedding of a plurality of watermark informations, and can detect simultaneously.The restricted number of cutting apart can be with this theoretical watermark quantity that embeds, when cutting apart quantity and increase, every sub spaces will reduce simultaneously, just become more difficult in that every sub spaces is watermarked this moment.And the great advantage of this method is to embed simultaneously a plurality of watermark informations, needn't carry out in order, and can detect simultaneously, therefore uses in practice more.

Be first each watermark to be merged from watermarked different a kind of scheme one by one, then the single watermark embedded mode of synthetic watermark according to routine be embedded in the carrier, namely merge and embed.This method can be broken away from preferably the carrier capacity and embed algorithm to the restriction of watermarked number, but these class methods require good application image integration technology, could obtain preferably effect, and require a plurality of watermarks to embed simultaneously, be not suitable for the situation that to predict watermark number and all watermark informations, comparatively speaking, this type of algorithm is less.But it should be noted that a transform method of these class methods---quadrature watermark method, use more.So-called quadrature watermark method refers to that the watermark that embeds is the pseudo random sequence of quadrature, when coherent detection, can not influence each other like this; This just is equivalent to the advanced line linearity stack of the pseudo random sequence of a plurality of quadratures, and then as an embed wholly, the process of this process and fusion is very similar.And when detecting watermark, because mutually orthogonal between each watermark, can the phase mutual interference, but the existence that this method can only detect watermark information usually is whether, and must quadrature or nearly orthogonal between each watermark, this is restricted in actual applications.

To sum up, existing many water mark methods mostly are the simple deformation of single watermarking algorithm, remain to be further developed at aspect of performances such as capacity, validity, robustnesss.

Containing the side information watermark is to produce on the basis of side information theory, network source coding theory and dirty paper code theory.Cox equals first watermark to be regarded as in 1999 a kind of communication that contains side information.At present, contain the side information watermaking system in the advantage of the aspects such as capacity, robustness, validity, obtain gradually people's approval.

The present invention is applied to many watermarks field with side information thought, and a kind of new many water mark methods are provided.

Summary of the invention

Existing theoretical research and experimental study show that all the use of side information can improve the performance of watermaking system really.Yet the application of side information thought in the watermark field mainly concentrates in single watermark, not yet fully used in many watermarks.

Main purpose of the present invention provides a kind of new many water mark methods, its basic principle is that the implementation procedure with many watermarks is considered as a kind of multi-user communication process that contains side information, take full advantage of the side information that can from the entities such as carrier and watermark, obtain in the embodiment side information ideologize watermark implementation procedures such as network source coding theory and multi-user communication be theoretical, and utilize these side informations to realize many watermarkings.

The multi-watermark technology that the present invention proposes comprises that a kind of information theory Network Based realizes the many water mark methods of piecemeal of method and an information theory Network Based of many watermarks.

1. information theory Network Based realizes the method for many watermarks

Existing theoretical research and experimental study show that all the use of side information can improve the performance of watermaking system really, but what adopt at present only is the simplest side information form, namely for information source X ₁With information source X ₂, at transmission information source X ₁The time, detector only is concerned about whether can effectively detect X ₁, and be indifferent to and can detect X ₂, as shown in Figure 1; Equally, at transmission information source X ₂The time, detector only is concerned about whether can effectively detect X ₂, can the pass is indifferent to detect X ₁Contain in the side information list watermaking system existing, just as supplementary, more effectively transmit watermark with auxiliary watermaking system from the side information of carrier, this is quite reasonable in single watermaking system.And in many watermaking systems, more than one of the watermark information that need to embed, if still only consider side information between carrier and the different watermarks, the side information thought in so single watermaking system can be applied directly in many watermaking systems; Yet, in fact, may also have correlation between a plurality of watermark informations, and this correlation can be utilized mutually also, and this moment be in identical status between a plurality of watermark informations, it is more reasonable to utilize correlated source coding theorem in the network information theory that it is carried out analysis meeting.Because in the correlated source coding theory, a plurality of information sources are of equal importance, and detector requires effectively to detect all information, and what Fig. 2 showed is a kind of typical correlated source traffic model.

We are on the basis of analyzing the network information theories such as correlated source coding theorem, multi-user communication, the implementation procedure of many watermarks is analogized to multi-user communication process based on side information, and the information theory Network Based that provides Fig. 3 to show realizes the embedding grammar of many watermarks.In the method, in the watermark encoder stage, from carrier and a plurality of watermark information, extract side information, each watermark information is contained coding or the preliminary treatment of side information; Embed the stage in watermark, still fully excavate the side information in carrier and each watermark, effectively to determine embedded location, embedment strength.And in the watermark detection stage, need to utilize equally some side informations in watermark encoder and the watermark embed process to determine detection threshold.

2. many water mark methods of the piecemeal of information theory Network Based

Traditional many water mark methods of typical piecemeal are directed to single watermarking algorithm, carrier is carried out piecemeal after, inadequate to the correlation utilization between a plurality of of carrier and the many watermarks, be also referred to as blind many watermarking algorithms, the performances such as its validity are not high.

We utilize the relevant information between carrier works and watermark information and a plurality of watermark to optimize watermark embedded location, watermark embed strength and watermark detection threshold value, proposed a kind of many water mark methods of piecemeal that take full advantage of the information theory Network Based of various side informations, what Fig. 4 showed is the block diagram that watermark embeds and extracts.The method replaces a watermark information with carrier works piecemeal and the large reference template such as generation and piecemeal with a reference template, carries out the watermark information preliminary treatment and obtains the watermark information template; Utilize the Watson sensor model to calculate the perception gap, and utilize the perception gap that the watermark information template is carried out the perception shaping and process, to improve to greatest extent the fidelity of carrier, reduce embedding distortion; Utilize carrier works side information to seek the optimum position that watermark embeds in the mode of maximum correlation, so that the interference between carrier and a plurality of watermark information reaches minimum, the validity when guaranteeing watermark detection; Utilize the carrier side information to determine embedment strength in the mode that fixed linear is relevant, so that between carrier partition and the corresponding watermark information fixing linear correlation values is arranged, thus further guarantee the validity of watermark detection.

Description of drawings

Fig. 1 utilizes form for the simplest side information, and this also is that side information the most frequently used in single watermaking system utilizes mode.

Fig. 2 is a kind of typical correlated source traffic model.

Fig. 3 is that information theory Network Based provided by the invention realizes the block diagram that many watermarks embed.

Fig. 4 is many water mark methods of piecemeal schematic diagram of information theory Network Based provided by the invention.

Fig. 5 is the validity test result of method when selecting carrier image at random that the present invention proposes.

Fig. 6 is the validity test result of method when selecting watermark information at random that the present invention proposes.

Embodiment

Describe each detailed problem that relates in the method provided by the present invention in detail below in conjunction with accompanying drawing.

1. information theory Network Based realizes the method for many watermarks

As shown in Figure 3, the information theory Network Based provided by the invention specific embodiments that realizes many watermarks is as follows:

(1) analyze a plurality of watermark m[i to be embedded] (1≤i≤N) and support C _oBetween correlation and the correlation between a plurality of watermark information, be that side information is to watermark information m[i with these passes] contain the coding of side information, obtain watermark encoder signal W _i, wherein N represents the watermark number that needs embed.

(2) in conjunction with the embedding strategy of fixing robustness, fixedly the embedding strategy etc. of fidelity contains the embedding strategy of side information, according to support C _oWith all watermark encoder signal W _i(the relational implementation W between 1≤i≤N) ₁Embedding, in telescopiny, comprise and utilize side information to select embedded location, embedment strength, finally obtain containing watermark signal C _W1

(3) repeat above-mentioned steps, until all watermark signals all are encoded and embed, finally obtain containing watermark signal C _W

According to foregoing description, watermark encoder and embedded device and conventionally contain identical in the side information list watermaking system among the present invention, can adopt various codings and embedded mode, and watermark extraction process also with routine to contain the watermark of side information list identical, its special character is, relates to a plurality of watermarks in the telescopiny, thereby from the angle analysis problem of multi-user communication, and with a plurality of watermark information fair plays, set up the method that realizes that many watermarks embed based on the correlated source coding theory.Compare with existing many water mark methods, its difference is: in the process of a plurality of watermark informations being encoded and embedding, encoder and embedded device take full advantage of the correlation between carrier and watermark and a plurality of watermark, and this is the embodiment of network source coding theory.

2. many water mark methods of the piecemeal of information theory Network Based

As shown in Figure 4, the many water mark methods of piecemeal provided by the invention at first utilize the corresponding piecemeal of carrier works and the maximum linear correlation between the watermark signal to select embedded location as side information, detection threshold and the embedment strength factor, secondly the carrier works gap array correspondence that will utilize the Watson model to obtain is assigned to its perception is shaped, obtain the watermark encoder signal, then regulate watermark embed strength by linear correlation values between immobilization carrier works and the watermark encoder signal, finish telescopiny, utilize at last the linear correlation detection device to detect, the output watermark information.Relate generally to following 4 kinds of modes of utilizing side information in the implementation process:

(1) utilize the corresponding piecemeal of carrier and the maximum linear correlation between the watermark information to select embedded location, detection threshold and embedment strength as side information;

(2) utilize Watson model extraction carrier side information, use the gap array that the information model that represents watermark is carried out perception and be shaped, obtain the watermark encoder signal;

(3) utilize carrier to make linear correlation values between the watermark encoder signal as side information, regulate watermark embed strength in the mode of linear correlation values between immobilization carrier and the watermark encoder signal;

(4) detection threshold of determining according to the maximum linear correlation between the corresponding piecemeal of carrier and the watermark information detects watermark information in the mode of linear correlation.

Select the implementation step of embedded location, detection threshold and embedment strength 2.1 utilize side information

(1) establish carrier image size and be M1 * N1, watermark quantity to be embedded is N, then according to formula (1) to k watermark m[k] carry out preliminary treatment and obtain watermark information template w _m[k],

$w_m\left[k\right]=\left\{\begin{array}{cc}{w}_r\left[k\right],& m\left[k\right]=1\\ -w_r\left[k\right],& m\left[k\right]=0\end{array}\right.---\left(1\right)$

W wherein _r[k] (1≤k≤N) be size for M * M and between [0,1] pseudo random sequence of Normal Distribution, w _r[k, i, j] (1≤i, k value that sequence is located at [i, j] of the expression of j≤M).

(2) according to watermark quantity, carrier is divided into size is the piece c of M * M and non-overlapping copies ₀[t]

And use c ₀[t, x, y] (1≤i, pixel value in every of the expression of j≤M).

(3) calculate the information model w that represents k watermark _mAll piecemeal c of [k] and carrier ₀[t]

Between linear correlation values, if watermark m[k]=1, then select and w _m[k] has the piece of maximum linear correlation as embedded location, and with maximum related value and the scaling factor β [k] of time difference of large correlation as watermark, simultaneously will time large correlation threshold tau during as watermark detection _Lc[k]; If m[k]=0, then select and w _m[k] has the piece of minimal linear correlation as embedded location, and with the difference of minimum correlation value and time little correlation scaling factor β [k] as watermark, simultaneously will time little correlation threshold tau during as watermark detection _Lc[k].Wherein zoom factor β [k] is used for follow-up definite embedment strength.

2.2 utilize Watson model extraction side information to carry out the implementation step of watermark encoder

(1) according to formula (2), utilize DC coefficient behind each Block DCT of carrier to the predefined frequency sensitive kilsyth basalt of Watson model t[i, j] adjust, obtain brightness and shelter function threshold t _L[k, i, j],

$t_L[k,i,j]=t[i,j]{\left(C_o\right[k,\mathrm{0,0}]/{\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="H2009100007071E00022.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathrm{0,0}})}^{{\mathrm{\&alpha;}}_T}---\left(2\right)$

α wherein _TBe a constant, value is 0.649, C usually _o[k, 0,0] is the DC coefficient of k piecemeal after discrete cosine transform in the carrier image, C _0,0Be the mean value of all piecemeal DC coefficient of carrier image, also can be set as the constant of representative image expection intensity.

(2) according to formula (3) Calculation Comparison degree masking threshold s[k, i, j],

s[k，i，j]＝max{t _L[k，i，j]，|C _o[k，i，j]| ^w[i，j]t _L[k，i，j] ^1-w[i，j]} (3)

W[i in the formula, j] be a constant between 0 and 1, and can be different because of the difference of coefficient of frequency, all w[i in the Watson model, j] all be taken as 0.7.Final thresholding s[k, i, j] estimated be the every a variation size that just can stand in the perceptible scope of piece discrete cosine transform, also be called the gap.

(3) utilize the gap that the watermark information template is carried out perception and be shaped, namely at first the watermark information template is carried out discrete cosine transform and obtain W _m[k] then utilizes formula (4) to W _m[k] carries out perception and is shaped and obtains perception shaping information W under the discrete cosine transform domain _s[k],

W _s[k]＝W _m[k]s[k] (4)

At last to W _s[k] carries out inverse discrete cosine transform and obtains spatial domain shaping template w _s[k], i.e. watermark encoder signal.

Determine the implementation step of embedment strength 2.3 utilize side information

(1) embedment strength of supposing k watermark is α [k], then watermark encoder signal w _s[k] will be embedded in the corresponding piecemeal by formula (5),

c _w[k]＝c _o[k]+α[k]w _s[k] (5)

At this moment, can contain watermark signal c according to formula (6) calculating _w[k] and watermark information template w _mLinear correlation values between [k],

z _lc(w _m[k]，c _w[k])＝(c ₀[k]·w _m[k]+w _a[k]·w _m[k])/(M×M) (6)

W wherein _α[k] determines according to formula (7).

w _a[k]＝α[k]w _s[k] (7)

In formula (6), use τ _Lc[k]+β [k] replaces z _Lc(w _m[k], c _w[k]), can obtain watermark embed strength and be

$\mathrm{\&alpha;}\left[k\right]=\frac{L\left({\mathrm{\&tau;}}_{\mathrm{lc}}\right[k]+\mathrm{\&beta;}[k\left]\right)-c_0\left[k\right]\&CenterDot;w_m\left[k\right]}{w_s\left[k\right]\&CenterDot;w_m\left[k\right]}---\left(8\right)$

(2) embedment strength that adopts (8) formula to obtain obtains containing watermarking images according to formula (5) embed watermark information.

2.4 extract the implementation step of watermark in conjunction with side information

(1) adopt with telescopiny in identical mode to carrier c to be detected _nCarry out piecemeal, and obtain each piecemeal c _n[t]

(2) with the embedded location in the telescopiny as key, may contain the piecemeal c of watermark information according to formula (9) _nDetect watermark information in [k],

Z wherein _Lc(w _r[k], c _n[k]) expression carrier block c _n[k] and watermark information w _rLinear correlation values between [k], τ _Lc[k] is the detection threshold that utilizes the linear correlation values between carrier partition and the watermark information template to determine in the telescopiny.

3. test result

We are applied in the method that proposes in the multiple situations such as different images, different watermark informations, have carried out sufficient experiment, have verified the validity of many water mark methods proposed by the invention.The below provides with the method for the present invention's proposition and the experiment comparative result of the many water mark methods of conventional blind piecemeal.In the experiment, the carrier of employing is 256 * 256 gray level image, and the watermark quantity of embedding is 128.The many water mark methods of conventional blind piecemeal are divided into the piece of 256 non-overlapping copies with gray level image, and every block size is 16 * 16, then select at random 128 piecemeals to be used for embedding 128 watermark informations from 256 piecemeals, and identical embedment strength is adopted in all watermarks.

(1) the at random validity of carrier image experiment

Consider that different images may have certain Random Effect to experiment, in order to prove absolutely the broad applicability of this method, we test carrier at random, and it is constant namely to fix 128 watermark informations, 1000 experiments are carried out in the continuous conversion of carrier image in 1000 width of cloth images.

Fig. 5 is the distribution situation of the average error rate of the watermark information that extracts of two kinds of methods, experimental result shows: in the situation that carrier image is selected at random, the average error rate of this method mainly is distributed near 0, can obtain good validity, and the average error rate of the many water mark methods of conventional blind piecemeal mainly is distributed on 0.6, and its validity is relatively poor.

(2) random watermark validity experiment

Consider that different watermarks also may affect to experiment, in order to prove absolutely the broad applicability of this method, we test random watermark, and namely the immobilization carrier image is constant, 128 watermark informations constantly change, and 1000 groups of watermark informations are carried out 1000 experiments.

Fig. 6 is the distribution situation of the average error rate of the watermark information that extracts of two kinds of methods, experimental result shows: in the situation that watermark is selected at random, the average error rate of the method that the present invention proposes is distributed near 0, can obtain good validity, and the average error rate of the many water mark methods of conventional blind piecemeal is distributed between 0.5 and 0.6, and its validity is relatively poor.

(3) robustness experiment

In order further to test the performance of method provided by the invention, we test the robustness of this method, and what table 1 showed is that various common images are processed the average error rates of attacking a plurality of watermarks of lower extraction.As seen from Table 1, process under the attack at normal image, method provided by the invention can obtain the lower error rate, namely has preferably robustness.

To sum up, many water mark methods that the present invention proposes have good validity, and normal image processing attack is had preferably robustness.

The robustness of table 1. this method under the normal image processing is attacked

Attack	The error rate
		Amplify 2 times	0
Dwindle 1/2	0.023
		Low-pass filtering (3 * 3)	0.257
Medium filtering (3 * 3)	0.047
		Shear 1/9	0.148
JPEG compresses (50%)	0.035
		JPEG compresses (70%)	0.092
Gas noise (0.0008)	0.098

Claims (2)

1. many water mark methods of the piecemeal of an information theory Network Based, it is characterized in that: utilize the corresponding piecemeal of carrier and the maximum linear correlation between the watermark information to select embedded location, detection threshold and embedment strength as side information, utilize Watson model extraction carrier side information, using the gap array that the information model that represents watermark is carried out perception is shaped, obtain the watermark encoder signal, utilize linear correlation values between carrier and the watermark encoder signal as side information, regulate watermark embed strength in the mode of linear correlation values between immobilization carrier and the watermark encoder signal; The method realizes that the concrete steps that a plurality of watermarks embed are:

(1) establish carrier image size and be M1 * N1, watermark quantity to be embedded is N, then according to formula (1) to k watermark information m[k] carry out preliminary treatment and obtain watermark information template w _m[k],

$w_m\left[k\right]=\left\{\begin{array}{cc}{w}_r\left[k\right],& m\left[k\right]=1\\ -w_r\left[k\right],& m\left[k\right]=0\end{array}\right.---\left(1\right)$

W wherein _r[k] (1≤k≤N) be size for M * M and between [0,1] pseudo random sequence of Normal Distribution, w _t[k, i, j] (1≤i, k value that sequence is located at [i, j] of the expression of j≤M);

(2) according to watermark quantity to be embedded, carrier is divided into size is the piece c of M * M and non-overlapping copies ₀[t] (1≤t≤[M1 * N1/ (M * M)]), and use c ₀[t, x, y] (1≤i, pixel value in every of the expression of j≤M);

(3) utilize the linear correlation values between carrier partition and the watermark information template to determine watermark embedded location and detection threshold, namely calculate the information model w that represents k watermark information _mAll piecemeals of [k] and carrier

Between linear correlation values, if watermark information m[k]=1, then select and w _m[k] has the piece of maximum linear correlation as embedded location, and with maximum related value and the scaling factor β [k] of time difference of large correlation as watermark, simultaneously will time large correlation threshold tau during as watermark detection _Lc[k]; If m[k]=0, then select and w _m[k] has the piece of minimal linear correlation as embedded location, and with the difference of minimum correlation value and time little correlation scaling factor β [k] as watermark, simultaneously will time little correlation threshold tau during as watermark detection _Lc[k], wherein zoom factor β [k] is used for follow-up definite embedment strength;

(4) according to Watson model extraction side information, utilize the gap that the watermark information template is carried out perception and be shaped, namely at first the watermark information template is carried out discrete cosine transform and obtain W _m[k] then utilizes formula (2) to W _m[k] carries out perception and is shaped and obtains perception shaping information W under the discrete cosine transform domain _s[k],

W _s[k]＝W _m[k]s[k] (2)

S[k wherein] expression carrier block c ₀The general perceives distance of [k] is at last to W _s[k] carries out the perception shaping template w that inverse discrete cosine transform obtains the spatial domain _s[k], i.e. watermark encoder signal;

(5) embedment strength of supposing k watermark is α [k], then watermark encoder signal w _s[k] will be embedded in the corresponding piecemeal by formula (3),

c _w[k]＝c _o[k]+α[k]w _s[k] (3)

At this moment, can contain watermark signal c according to formula (4) calculating _w[k] and watermark information template w _mLinear correlation values between [k],

z _lc(w _m[k]，c _w[k])＝(c ₀[k]·w _m[k]+w _a[k]·w _m[k])/(M×M) (4)

W wherein _a[k] determines according to formula (5);

w _a[k]＝α[k]w _s[k] (5)

In formula (4), use τ _Lc[k]+β [k] replaces z _Lc(w _m[k], c _w[k]), can obtain watermark embed strength α [k];

$\mathrm{\&alpha;}\left[k\right]=\frac{L\left({\mathrm{\&tau;}}_{\mathrm{lc}}\right[k]+\mathrm{\&beta;}[k\left]\right)-c_0\left[k\right]\&CenterDot;w_m\left[k\right]}{w_s\left[k\right]\&CenterDot;w_m\left[k\right]}---\left(6\right)$

(6) embedment strength that employing formula (6) obtains is according to formula (3) embed watermark information.

2. many water mark methods of the piecemeal of information theory Network Based according to claim 1 is characterized in that the concrete steps that realize a plurality of watermark extracting are:

(1) adopt with telescopiny in identical mode to carrier c to be detected _nCarry out piecemeal, and remember that each piecemeal is

(2) with the embedded location in the telescopiny as key, may contain the piecemeal c of watermark information according to formula (7) _nDetect watermark information in [k],

$m^{\&prime;}\left[k\right]=\left\{\begin{array}{cc}1& z_{\mathrm{lc}}\left(w_r\right[k],c_n[k\left]\right)>{\mathrm{\&tau;}}_{\mathrm{lc}}\left[k\right]\\ \mathrm{no\; watermark}& \left|z_{\mathrm{lc}}\left(w_r\right[k],c_n[k\left]\right)\right|\&le;{\mathrm{\&tau;}}_{\mathrm{lc}}\left[k\right]\\ 0& z_{\mathrm{lc}}\left(w_r\right[k],c_n[k\left]\right)<-{\mathrm{\&tau;}}_{\mathrm{lc}}\left[k\right]\end{array}\right.---\left(7\right)$

Z wherein _Lc(w _r[k], c _n[k]) expression carrier block c _n[k] be used for pretreated pseudo random sequence w is carried out in watermark _rLinear correlation values between [k], τ _Lc[k] is the detection threshold that utilizes the linear correlation values between carrier partition and the watermark information template to determine in the telescopiny.

Images